Measurements of D-hadron azimuthal correlations with ALICE at the LHC

Transcription

1 UNIVERSITÀ DEGLI STUDI DI BARI ALDO MORO Dipartimento di Fisica M. Merlin DOTTORATO DI RICERCA IN FISICA Ciclo XXVI Settore scientifico-disciplinare Fis/04 Measurements of D-hadron azimuthal correlations with ALICE at the LHC Dottorando: Fabio Colamaria Coordinatore: Ch.mo Prof. Gaetano Scamarcio Supervisore: Dott. Giuseppe E. Bruno ESAME FINALE 2014

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3 Contents Introduction 5 1 Charm production in hadronic collisions Charm production in pp collisions The strong interaction and the QCD Heavy flavour production as a test of perturbative QCD Charm production at the LHC Benchmark for heavy ion collisions analysis Charm production in Pb-Pb collisions The Quark Gluon Plasma: a theoretical prospect Charm production cross section in nucleus-nucleus collisions Deviations from binary scaling Main observables for probing QGP Selection of experimental results Open charm production cross section in pp collisions Nuclear modification factor and elliptic flow of charm quarks Two-particle correlations Study of charm production: from hard process to hadronization Characterization of parton energy loss via jet quenching The ALICE experiment at the LHC The Large Hadron Collider Luminosity definition and luminous region LHC experiments and physics programme Overview of ALICE Experiment ALICE barrel detectors Inner Tracking System Time Projection Chamber Time Of Flight ALICE Performance PID capabilities in central barrel Vertex reconstruction Track reconstruction

4 3 Measurements of charm with ALICE Introduction D meson reconstruction from hadronic decays in pp collisions D meson reconstruction and selection Corrections and systematic uncertainties Cross sections and ratios Measurement of the D 0 p T -differential cross section in pp collisions at s = 7 TeV with the channel K π + π π D 0 candidates selection and invariant mass distributions Corrections Systematic uncertainties evaluation Cross section and comparison with D 0 K π + results Other charm analyses in pp collisions Measurement of charm and beauty hadron production from e+x decays Measurement of charm and beauty hadron production from µ+x decays J/Ψ reconstruction from dileptonic decays Results in Pb-Pb collisions R AA measurements v 2 measurements D meson preliminary results in p-pb collisions D-hadron azimuthal correlation analysis Introduction Analysis strategy Evaluation of D 0 -hadron correlations D 0 meson selection and signal extraction Charged track selection Correlation evaluation Subtraction of the background correlations Correction of the correlation distributions Event Mixing correction Tracking efficiency correction D 0 meson efficiency correction Subtraction of feed-down contribution Removal of secondary tracks contribution Evaluation of the systematic uncertainties D 0 meson yield extraction Background subtraction Associated track efficiency D 0 meson efficiency Residual contamination from secondary tracks

5 4.5.6 Rejection of D + decay pions Overall systematic uncertainty Monte Carlo closure test Fit to the correlation distributions Results from pp analysis D 0 -hadron azimuthal correlation distributions and p T trends Average of D 0 and D + results Results for higher associated track p T thresholds Comparison with Monte Carlo Outlook and perspectives for p-pb and Pb-Pb analyses Conclusions 189 Appendix A 191 Bibliography 195 3

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7 Introduction This thesis describes the production of charm quarks in hadronic collisions. In particular, charm production has been studied in proton-proton collisions by reconstructing the D 0 meson in the K π + π π + decay channel. The focus of the thesis is the description of the azimuthal correlations between D 0 mesons and unidentified charged particles, in proton-proton collisions at s = 7 TeV. The analysis was performed on the data collected with ALICE, one of the main experiments at the Large Hadron Collider. Perspectives for the studies in p-pb and Pb-Pb collisions are also discussed. Due to their heavy mass, the production of charm quarks in hard parton scattering processes can be described with perturbative QCD. The factorization theorem allows us to study the production of open charm mesons at the LHC to test pqcd calculations in an unexplored energy domain. By analyzing pp collisions at s = 7 TeV, delivered by the LHC during 2010 and 2011, it is possible to probe the parton distribution functions for Bjorken x values as low as x , at central rapidity. Thanks to its excellent tracking, vertexing and particle identification performance, ALICE allows us to measure the production cross section of charmed mesons down to very low p T values, a unique feature at the LHC. Measurements of charm in pp collisions are also useful as benchmarks for analogue measurements in Pb-Pb collisions. In ultra-relativistic heavy ion collisions, indeed, under certain conditions the nuclear matter experiences a phase transition to a Quark Gluon Plasma (QGP) state. In this phase, confinement of quarks into hadrons no longer occurs and a strongly interacting medium is formed. The conditions for the QGP phase transition are predicted by lattice QCD calculations. Former heavy ion experiments, at SPS and RHIC, were able to study the properties of the QGP in a different energy domain. At the LHC the system should reach much higher temperatures and energy densities, thus persisting much longer in the QGP phase. LHC experiments, hence, are expected to provide a more complete description of the QGP features. The ALICE experiment, in particular, is mainly devoted to investigate the QGP properties through a series of measurements. The study of heavy flavour hadrons, in this context, is of striking importance. Since they are produced in the early stages of the collision, heavy quarks experience the full evolution of the fireball. In particular, they are subject to several modifications during the QGP phase, such as a progressive energy loss while traversing the hot nuclear medium. Their hadronization products, hence, carry along the footprints of 5

8 Introduction the QGP effects. In both pp and Pb-Pb collision systems, two-particle azimuthal correlations, where at least one is a charmed hadron, are an important tool to study in better details the charm production. In pp collisions, these measurements allow us to investigate the fragmentation and hadronization of charm quarks, as well as their production mechanisms. The various pqcd hard processes for cc production, indeed, result in different ϕ distributions between the two heavy quarks. This feature can be exploited to disentangle the contribution to charm production from the different processes, by analyzing the azimuthal correlations of the quark hadronization products, as D mesons. In particular, the study of DD correlation distributions provides direct information about the cc pair, but it is much tougher to be performed. The D-hadron measurement, instead, is more loosely related to the cc distributions, since it includes also correlations with light flavour hadrons. Anyway, it allows us to gain information on the quark pair by analyzing the features of the correlation peaks at ϕ = 0 and ϕ = π. In Pb-Pb, charm azimuthal correlation studies allow us to measure the parton energy loss in the fireball from a different point of view, with respect to the usual measurements of modification of the transverse momentum spectra of charged hadrons. Modifications of the ϕ correlation pattern between charmed hadrons and charged particles, especially on the away side ( ϕ π), are sensitive to the energy loss of charm quarks in the QGP medium and allow us, in addition, to quantify how this energy loss affects the jet production. Performing the same study in p-pb collisions can help to disentangle the cold nuclear matter effects, present in both p-pb and Pb-Pb collision systems, from the modifications due to the presence of the QGP, produced only in Pb-Pb collisions. The structure of the thesis is described in the following. The first chapter provides an overview of charm production in hadronic collisions. The first section enlists the basic aspects of the QCD theory, which describes the interaction of hadrons and their constituents, and enounces the conditions to perform perturbative calculations of the cross sections. The most important schemes for pqcd calculations of heavy flavour hadron production are also presented, together with their predictions for charm production at LHC energies. In the following section a description of the QGP phase is provided. It is described how the QGP phase transition can be achieved in ultra-relativistic heavy ion collisions and which are the observables sensitive to the medium properties that can be studied in the heavy flavour sector. A selection of experimental results related to charm measurements in the various collision systems is also presented. The last section describes the role of charmed hadron azimuthal correlations, both in pp and in Pb-Pb collisions, in understanding the QCD processes which are still not well known, as quark fragmentation and hadronization, or the different heavy quark production mechanisms and their relative contributions. The second chapter is devoted to the description of the ALICE experiment. After a general overview of the apparatus, the focus is given to the detectors used for the D 0 -hadron correlation analysis, namely the Inner Tracking System, for tracking and vertexing, the Time Projection Chamber, the main tracking system, and the 6

9 Introduction Time-Of-Flight detector, for particle identification. The algorithms used for particle identification, track and vertex reconstruction are then discussed, along with their performance in pp collisions. A description of the offline analysis framework used to execute the correlation analysis is presented in Appendix A. In the third chapter the main ALICE results on the production of charmed hadrons are discussed. In the first section, the analyses performed with ALICE in the heavy flavour sector are summarized. Then, the pp and Pb-Pb analyses are described and the results are shown. Particular relevance is given to the D meson reconstruction from hadronic decays. This analysis is a fundamental prerequisite for the D 0 -hadron correlation analysis. Indeed, it provides the instruments to reconstruct the D 0 mesons, which are correlated with the other charged particles found in the event. In particular, a comprehensive report on the D 0 meson reconstruction from the Kπππ hadronic decay channel in pp collisions is provided. This analysis was performed during the first part of the PhD course and its strategy and results will be described in details. The fourth and final chapter describes the D 0 -hadron correlation analysis, the framework and the tools which were developed to perform this study, and its results. The analysis starts with the selection of D 0 mesons and charged tracks and with the D 0 signal extraction. The angular correlations are then evaluated in three p T intervals and for different p T thresholds of the associated charged tracks. After the subtraction of the background contribution, several corrections are applied to the correlation distributions. Effects due to the detector inhomogeneities and limited acceptance, the limited efficiency for track and D 0 meson reconstruction, the contribution from feed-down D 0 correlations (i.e. correlations where the D 0 meson comes from a beauty hadron decay) and the contamination from secondary particles are taken into account. Different sources of systematic uncertainties are identified and their relative contribution is estimated. The final results are fully corrected azimuthal correlation distributions. Results are shown for D 0 meson only and for the average of D 0 and D + mesons. By applying a fit function to the correlation distributions, some values quantifying their properties are extracted and the dependence of these quantities on the D meson p T is evaluated. These observables can be used to obtain a quantitative description of the fragmentation and hadronization of charm quarks into jets. These quantities will be important for a future comparison to results in p-pb and Pb-Pb collision systems, possibly allowing us to spot effects of the nuclear medium on the correlation pattern. To this end, the perspectives of the correlation analysis in p-pb and Pb-Pb collisions are presented. The current status of these analyses is reported and their feasibility with the currently available statistics is discussed. 7

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11 Chapter 1 Charm production in hadronic collisions 1.1 Charm production in pp collisions The strong interaction and the QCD The strong nuclear interaction is one of the four fundamental interactions of nature, together with gravity, electromagnetism and weak nuclear interaction. It was introduced to describe the behaviour of protons and neutrons inside the nuclei and then extended to explain the interactions among all the hadrons (from Greek hadrós, strong). The identification of the quarks as the basic constituents of the hadrons led to the development of a gauge field theory, the Quantum Chromo- Dynamics (QCD), which formally expresses the strong interaction and its features. QCD was developed in partial analogy to another gauge field theory, the Quantum Electro-Dynamics (QED), which formalizes the electromagnetic interaction. The two theories, however, differ in many respects: while QED has only one chargeless force mediator, the photon, in QCD eight mediators are present, called gluons. Furthermore, the gluons themselves are carriers of the strong charge (defined as the colour), hence they can also interact between each other. This feature is related to the gauge group: instead of the abelian 1 group U(1) of the QED, the QCD is based on the non-abelian group SU(3), with eight generators. The QCD Lagrangian is obtained by imposing invariance under local transformations and is defined as follows: L QCD = 1 4 F a µνf µν a + q ψ i qγ µ (D µ ) ij ψ j q q m q ψ i qψ iq, (1.1) having defined: F a µν = µ G a ν + ν G a µ g s f abc G b µg c ν (1.2) 1 A group is abelian (or commutative) if the result of the application of the group operation to two elements does not depend on their order. 9

12 CHAPTER 1. Charm production in hadronic collisions and: (D µ ) ij = δ ij µ + ig s λ a ij 2 G aµ. (1.3) In the equations above, G a ν (a = 1,..., 8) represents the gluon field, ψ i q the quark field (with flavour q and colour i), g s the coupling constant of the interaction, m q the mass of the quark, the matrices λ a are the eight SU(3) generators and f abc their structure constants. The last term in the F µν definition describes the interaction between the gluons. It is proportional to the structure constants and its form depends on the fact that the gauge group is non-abelian. This property translates in the structure of the Lagrangian (Eq. 1.1), which contains a kinetic term for gluons, the interaction among 3 or 4 gluons, a kinetic term for quarks and the quark-gluon interaction. The dimensionless coupling constant of the strong interaction can be redefined as α s = g 2 s/4π and, as for the QED, its value depends on the square of the momentum exchanged in the interaction Q: α s = α s (Q 2 ). The presence of the self-interaction term for the gluons, however, leads to a very different behaviour of the coupling constant, which increases for low values of Q 2 and asymptotically tends to zero for large Q 2. The dependence of α s from the exchanged momentum has been studied in several experiments, as shown in Fig. 1.1, and can be calculated as follows [1, 2]: α s (Q 2 ) = 12π (33 2n f ) log(q 2 /Λ 2 ). (1.4) In Eq. 1.4, n f is the number of the active quark flavours and Λ is a parameter, not predicted by the theory, expected of the order of the hadronic masses. This parameter acts as a boundary value between a regime in which quarks and gluons are quasi-free, interacting very weakly (for Q 2 Λ 2 ) and a regime where the effective coupling is strong and quarks are firmly bound into hadrons (for Q 2 Λ 2 ). This point can be made clearer by adopting a simple model to describe the interaction potential between a q and a q bound into a meson. This potential can be approximately defined as a combination of a short-range term with a Coulombian form and a long-range component similar to an elastic potential: V qq (r) = 4 α s + λr. (1.5) 3 r Inserted into the Schrödinger equation, this potential predicts with good accuracy the spectrum of heavy quarkonium mesons, namely the charmonium and bottomonium families. By looking at the strength of the bounding potential as a function of the separation r between the quark pair, two completely different behaviours are predicted for very small and large values of r: asymptotic freedom: it establishes at very low values of r, where the Coulombian term of the potential dominates and the linear term is negligible. Due to the decreasing value of α s for increasing Q 2, the interaction potential is very weak at small distances (corresponding to high values of Q 2 ) and vanishes for zero separation, making the two quarks almost free; 10

13 CHAPTER 1. Charm production in hadronic collisions Figure 1.1: Value of the QCD coupling constant as a function of the exchanged momentum Q, from experimental data and theoretical predictions [3]. confinement: it arises when r reaches high values. In this region the linear term of the potential dominates, growing further and further when the separation between the two quarks increases, thus not allowing to isolate one quark from the other. This feature can be explained in terms of the string model: because of the gluons self-coupling, the lines of force of strong interaction are stretched in a sort of a tube in the region between the two quarks, through which a flux of colour charge flows from each quark to the other. When the energy stored in the tube exceeds 2m q, it becomes energetically favorable for the tube to break down, spending the released energy to produce a new qq pair. No free quarks have indeed ever been observed in nature, but all of them are bound in hadronic states. Nevertheless, it has been suggested that in particular conditions, as those occurring in heavy ion collisions, the mechanism of the confinement can be superseded. This case will be discussed in detail in Section Heavy flavour production as a test of perturbative QCD Extracting the cross section of a given hadronic process from the Lagrangian of the QCD is not an easy task, since a complete theoretical knowledge of the various 11

14 CHAPTER 1. Charm production in hadronic collisions QCD processes (e.g., the quark fragmentation 2 ) is still not available. Furthermore, calculations are made difficult by the infinite number of topologically inequivalent interactions contributing to a single QCD process. Anyway, over short distances, i.e. in the regime of asymptotic freedom, the strong coupling is small enough that this infinite number of terms can be approximated with sufficient accuracy by a finite number of elementary processes, which can be described by Feynman diagrams. This approach is the basis of perturbative QCD (pqcd). More specifically, in pqcd calculations the hard scattering amplitude for a given interaction is expanded in powers of α s. In this tree-expansion, the elementary processes appear at different α s orders, based on of the number of vertices of the corresponding Feynman diagrams: for each QCD vertex in a diagram of the process, an α s factor appears in its numerical evaluation. The condition α s 1 grants the convergence of the power expansion: the higher the order of α s, the smaller the contribution of the diagram to the overall amplitude. It is thus possible to quantitatively evaluate with the desired approximation the amplitude and, from it, the cross section of the process, by stopping the expansion at a certain order of α s. In terms of exchanged momentum, the perturbative expansion of the transition amplitudes is possible only if Q 2 Λ 2, as it results from Eq The production of heavy flavour quarks (charm and beauty) is one of the most suitable processes to be studied with a perturbative approach. Due to their large mass values, charm and beauty quark pairs are produced in hard scattering processes with large momentum transfer (Q 2 4m 2 Q Λ2 ). In this Q 2 region the value of the strong coupling constant is lower than 1 (0.25 α s (Q 2 ) 0.6 for the threshold of charm production), allowing one to predict the cross section for charm and beauty production using pqcd calculations. The p T -differential cross section for the inclusive production of a single heavy flavour hadron (H Q ) can be calculated by means of the factorization theorem. This theorem splits the calculation into a convolution of the hard scattering cross section, which can be evaluated with a perturbative approach, with long-distance terms, i.e. the parton distribution functions and the fragmentation functions, which are independent of the hard scattering but cannot be evaluated with pqcd. This allows one to calculate the cross section as follows: dσ pp H QX dp T = i,j=q,q,g dx 1 dx 2 f i (x 1, µ 2 F )f j (x 2, µ 2 F ) d σij QQ (α s, µ 2 F, µ 2 d p R, m Q, p T )D H Q Q (z, µ2 F ), T (1.6) are, respectively, the where m Q is the mass of the heavy flavour quark, µ 2 F and µ2 R factorization and renormalization scales of QCD, x 1 and x 2 are the Bjorken x of the two partons interacting in the elementary process 3, p T is the transverse momentum 2 The fragmentation is a QCD process for which high p T partons split and hadronize into colorless hadrons with lower p T. 3 The Bjorken x of a parton is defined as the fraction of the nucleon momentum which is carried by the parton, assuming that all the transverse momenta of the partons can be neglected (i.e. in the infinite momentum frame). 12

15 CHAPTER 1. Charm production in hadronic collisions of the heavy flavour hadron and p T that of the partons. The three terms comprised in Eq. 1.6 are described in the following: d σ ij QQ is the cross section of the elementary process involving the two partons in the initial state. This cross section can be calculated using perturbative QCD. At leading-order, the only contributions to the partonic cross section come from quark pair annihilation (qq QQ) and gluon fusion (gg QQ), while at next-to-leading-order more diagrams contribute, namely flavour excitation (qq qq) and gluon splitting (g QQ). These processes will be described in detail in Section 1.1.3; f i (x 1, µ 2 F ) and f j(x 2, µ 2 F ) are the parton distribution functions (PDFs), which describe the probability for a parton i (or j) of the interacting nucleons to carry a fraction x 1 (or x 2 ) of the nucleon momentum. The PDFs can be determined by measuring them for given values of Q 2 (typically in deep inelastic scattering of electrons on protons) and then using a particular class of equations (DGLAP) to extrapolate them to different Q 2 values [4 6]. Examples of PDF extrapolated from measurements of deep inelastic scattering are shown in Fig. 1.2; D H Q Q (z, µ2 F ) is the fragmentation function of the quark Q, denoting the probability for that quark to generate an hadron H carrying a fraction z of the quark momentum. The fragmentation functions can be evaluated by using theoretical models, as the Lund string model [7,8] or the cluster hadronization model [9], and fitting them to data, obtained mainly analyzing e + e, e + p and pp collisions. In the left panel of Fig. 1.3 measurements of the z distribution for charmed hadrons extracted from e + e and e + p data are shown. The average of the fragmentation functions evaluated from several experiments is shown as a function of the center-of-mass energy and compared to theoretical calculations in the right panel of Fig A schematic view of heavy flavour hadron production in a pp collision is shown in Fig Charm production at the LHC At the Large hadron Collider (LHC), which is described in Section 2.1, pp collisions at center-of-mass energies of s = 0.9, 2.36, 2.76, 7 and 8 TeV have already been collected and studied by the experiments, while pp collisions at s = 14 TeV will be delivered in the next years. The highest energy of the collected data is already a factor 4 higher with respect to the maximum center-of-mass energy of pp collisions previously achieved at the Tevatron collider. The study of heavy flavour production assumes great relevance at LHC energies, where cross sections for their production are expected to be much larger than at Tevatron, allowing us to study charm and beauty properties with much better 13

16 CHAPTER 1. Charm production in hadronic collisions Figure 1.2: Parton distribution functions extracted from ZEUS and H1 experiments at HERA. The PDFs at Q 2 = 10 (GeV/c) 2 are shown for valence and sea quarks separately [10 12]. Figure 1.3: Left: comparison of the z variable distributions from CLEO, OPAL, ALEPH and H1 experiments, normalized to unit area in the range 0.4 < z < 1. Right: mean value of the fragmentation function for charm quark as a function of s from various experiments, compared to curves obtained from next-to-leading logarithms (NLL) and fixed-order (FO) theoretical calculations with a non-perturbative fragmentation obtained using the data at the Z 0 energy [13]. 14

17 CHAPTER 1. Charm production in hadronic collisions Figure 1.4: Scheme of the production of a heavy flavour hadron from the scattering of two protons. precision. Predictions for heavy flavour production at the LHC are available from several theoretical models, based on perturbative QCD; new measurements at LHC energy allow us to test their accuracy and to discriminate among the different theoretical approaches. A particular focus on the charm sector will be given in this section, since the study of charm meson production is the subject of this thesis. Accessible range for the Bjorken x variable Heavy flavour production at LHC energies is sensitive to the parton distribution functions at extremely low values of the Bjorken x. The following calculation describes the production of a heavy flavour quark pair via the gluon fusion process gg QQ in a collision of two generic ions, with atomic and mass numbers (Z 1, A 1 ) and (Z 2, A 2 ). The Bjorken x range of the gluons involved in the QQ production depends on the center-of-mass energy per nucleon pair s NN, on the invariant mass of the heavy quark pair M QQ and on its rapidity y QQ. These quantities can be written as a function of x as follows [14]: M 2 QQ = x 1x 2 s NN = x 1 Z 1 A 1 x 2 Z 2 A 2 s pp (1.7) and: y QQ = 1 [ ] E + 2 ln pz = 1 [ E p Z 2 ln x1 Z1A ] 2, (1.8) x 2 Z 2 A 1 where x 1 and x 2 are the fractions of momentum carried by the gluons and s pp is the center-of-mass energy for pp collisions. Starting from these relations, it is possible to extract the Bjorken x values of the gluons as a function of M QQ and y QQ : x 1 = A 1 Z 1 MQQ spp exp(y QQ ), x 2 = A 2 Z 2 MQQ spp exp( y QQ ). (1.9) 15

18 CHAPTER 1. Charm production in hadronic collisions For collisions of ions of the same specie (A 1 = A 2, Z 1 = Z 2 ), the relations above simplify to: x 1 = M QQ snn exp(y QQ ), x 2 = M QQ snn exp( y QQ ). (1.10) At central rapidity (y 0) the two values coincide and are equal to the ratio of the quark pair invariant mass over the center-of-mass energy. The ranges of the Bjorken x variable probed by studying charm and beauty at the most recent colliders, for production of the QQ pair at the threshold energy (M cc = 2m c 2.4 GeV/c 2, M bb = 2m b 9 GeV/c 2 ) at central rapidity are given in Tab At the LHC design energy ( s pp = 14 TeV) it will be possible to reach x values about a factor 7 lower than at Tevatron (in pp collisions) and about 2 orders of magnitude lower than at RHIC (in heavy ion collisions). Furthermore, at forward rapidity it will be possible to probe even lower ranges of x, reaching values of x 10 6 for y 4. Table 1.1: Bjorken x values corresponding to charm and beauty production at threshold energy and at rapidity y = 0, at Tevatron, RHIC and LHC colliders. Machine RHIC LHC LHC Tevatron LHC LHC System Au-Au Pb-Pb Pb-Pb pp pp pp snn 200 GeV 2.76 TeV 5.5 TeV 1.96 TeV 7 TeV 14 TeV cc x 10 2 x x x x x bb x x x x x A schematic drawing of the ranges of the Bjorken x variables accessible with ALICE is shown in Fig Figure 1.5: ALICE coverage for the Bjorken x variable of the two interacting partons, for Pb-Pb collisions (left) and pp collisions (right) at the design energies. 16

19 CHAPTER 1. Charm production in hadronic collisions Role of next-to-leading-order processes in heavy flavour quark production Heavy quark production in hadron-hadron collisions can occur through several QCD processes involving quarks and gluons. These processes can be classified in three categories: 1. pair production: it is the O(α 2 s) leading-order contribution to heavy quark production and includes quark annihilation (qq QQ) and gluon fusion (gg QQ) processes. It leads to a final state of the hard subprocess with 2 heavy quarks, which are emitted back-to-back; 2. flavour excitation: it is a next-to-leading-order process, of O(α 3 s), in which a heavy quark of the sea of one initial-state hadron is put on mass shell by the scattering with a parton of the other hadron, having thus as diagram qq qq or gq gq, with only one heavy flavour quark participating in the hard subprocess; 3. gluon splitting: it is another O(α 3 s) process, in which a gluon splits in a QQ pair in the initial state or final state shower (g QQ), with no heavy flavour quarks in the final state of the hard subprocess. The diagrams of the processes enlisted above are shown in Fig Figure 1.6: Diagrams of the different processes for heavy flavour quark production: a) and b) LO processes, respectively gluon fusion and quark annihilation; c) Pair production with gluon emission from one final state parton; d) Flavour excitation (NLO); e) Gluon splitting (NLO); f) Events classified as gluon splitting but entering into flavour excitation category. The relative contribution of the three different types of hard processes to heavy quark production is expected to vary with the center-of-mass energy of the collision, as shown in Fig. 1.7 [15]. From pqcd calculations, assuming the absence of nonperturbative contributions to the hard scattering, a clear trend is predicted for the three processes: pair production dominates at low energies, as those of fixed-target experiments, flavour excitation is the largest contribution at intermediate energies 17

20 CHAPTER 1. Charm production in hadronic collisions and, at very high energies, gluon splitting becomes the dominant process, with pair production contribution being very small. For charm quarks, with lower mass, the energies at which the different regimes establish are lower than for beauty: at LHC energies pair production is by far the lowest relative contribution to charm quark production. Hence, analyzing charm quarks at LHC allows us to study the next-toleading-order processes responsible for their production. Figure 1.7: Contributions of pair production, gluon splitting and flavour excitation to the total charm production cross section in pp collisions, as a function of the center-of-mass energy [15]. Furthermore, as it will be described in Section 1.4, studying the angular correlations of heavy flavour hadrons could help to separate the NLO processes contributing to heavy quark production from the LO ones. In fact, while it is not possible to separate the various hard processes on the basis of the production cross section measurements, the different angular correlation between the two quarks leads to different angular correlation between their hadronic final states, which are experimentally accessible, even if challenging to address. pqcd predictions for heavy flavour quark production at the LHC A first estimate of the cross section for charm and beauty quark production in pp collisions at LHC energies was calculated with the NLO perturbative approach implemented by Mangano, Nason and Ridolfi (HVQMNR) [16]. The calculations were performed with two sets of PDFs, MRST HO [17] and CTEQ 5M1 [18], including the small-x measurements by HERA. Results from these calculations are summarized in Tab All the values are affected by an overall uncertainty of a factor around 2-3, mainly coming from the theoretical uncertainties on the m c, m b, µ F and µ R parameters. Despite the large spreads in the cross section values, the ratio of the cross section at 5.5 TeV over that at 14 TeV is fairly stable at the value of 0.52 for charm and 0.41 for beauty when varying these parameters. It was found [19] that also the ratios of the p T -differential cross sections for charm and beauty production are 18

21 CHAPTER 1. Charm production in hadronic collisions Table 1.2: NLO pqcd calculations from HVQMNR program for total cc and bb production cross section in pp collisions at different energies, using MRST HO and CTEQ 5M1 as PDFs. [16]. σpp cc [mb] σpp bb [mb] s 5.5 TeV 8.8 TeV 14 TeV 5.5 TeV 8.8 TeV 14 TeV MRST HO CTEQ 5M Average quite stable against the variation of the parameters, hence pqcd calculations can be used to scale the results obtained from data analyses to different collision energies. This allows us to compare data results for Pb-Pb collisions at s NN = 5.5 TeV to references obtained from p-pb collisions at s NN = 8.8 TeV and from pp collisions at s = 14 TeV 4. The predictions from HVQMNR model for the p T -differential and y-differential inclusive charm production cross sections in pp collisions at 5.5, 8.8 and 14 TeV are shown in Fig Figure 1.8: p T -differential (left) and y-differential (right) cross sections for inclusive charm quark production evaluated from NLO pqcd calculations using the HVQMNR model, for pp collisions at 5.5, 8.8 and 14 TeV [14]. NLO calculations for heavy quark production use the mass of the heavy quark as an infrared cut-off on collinear singularities and involve a power expansion of the cross section in α s at a renormalization scale µ R near the mass of the quark. 4 When this study was performed, the LHC was expected to develop pp collisions at s = 14 TeV and Pb-Pb collisions at s NN = 5.5 TeV. Hence, an energy scaling between these two energies was required to produce a pp reference for the Pb-Pb results. In the first runs of the LHC, however, lower energies were used, but a scaling of the results at these energies remains possible. 19

22 CHAPTER 1. Charm production in hadronic collisions This method, however, fails when the p T of the quark is larger than its mass, since in this situation large logarithmic terms of the ratio p T /m appear in the power expansion, preventing it from converging. These logarithmic terms appear in the forms αs(α 2 s log p T /m) k (leading-logarithm terms, or LL), αs(α 3 s log p T /m) k (next-toleading-logarithm terms, or NLL), and with higher α s powers. Several techniques have been proposed to overcome this problem, which avoids a correct evaluation of p T -differential cross sections at high p T values. The FONLL approach [20, 21] (standing for fixed-order plus next-to-leading logarithms) combines fixed next-to-leading-order (NLO) calculations with an all-order resummation of the next-to-leading logarithmic terms (NLL), recovering the convergence of the series expansion of the cross section. In this way, it is possible to evaluate predictions for single inclusive distributions of heavy flavour quarks (or hadrons), typically p T -, y- or η-dependent, integrating out the degrees of freedom of the other particles in the event. This approach, thus, is unable to make predictions for heavy flavour quark and antiquark correlations. In order to calculate distributions for a single heavy flavour hadron, i.e. a D meson, the FONLL approach convolutes a perturbative hard scattering cross section dσq F ONLL with a non-perturbative fragmentation function DQ H NP Q, improved with respect to the HVQMNR model as well, and a decay function g weak H Q D : dσ F ONLL D = dσ F ONLL Q D NP Q H Q g weak H Q D. (1.11) The central value of FONLL predictions is evaluated by setting the scales at the quark transverse mass: µ F = µ R = m T p 2 T + m2. The theoretical uncertainties are estimated as the quadratic sum of three components: (i) the scale uncertainty, evaluated by varying independently µ R and µ F over the range 0.5 µ R,F /m T 2 with the constraint 0.5 µ R /µ F 2 and taking the envelope of the resulting predictions; (ii) the quark mass uncertainty, estimated by using three values for the masses (m c = 1.5, 1.3, 1.7 GeV/c 2 for charm, and m b = 4.75, 4.5, 5 GeV/c 2 for beauty) and taking the envelope of the different results; (iii) the uncertainty on the PDF, for which the specific value suggested by the PDF set was taken as uncertainty. The default PDF set used for FONLL calculations is the CTEQ6.6 [22]. FONLL calculations coincide with the NLO calculations in the HVQMNR program in the low and intermediate p T region. The left panel of Fig. 1.9 shows the FONLL predictions for the p T -differential cross section for prompt D 0 meson production (i.e. D 0 produced from the hadronization of charm quarks, directly or through decays of excited states, like the D + ) in pp collisions at s = 7 TeV in the rapidity range y < 1. Predictions for the contribution of the D 0 coming from B meson decays (feed-down D 0 ) are shown as well. Another approach to evaluate the heavy flavour production cross section at high p T is the GM-VFNS (general-mass variable-flavour-number scheme) [23]. In this scheme, the large logarithmic terms of the type log(p 2 T /m2 ) in the p T m region are absorbed in the heavy quark PDFs of the colliding hadrons and in the fragmentation function for the transition Q H Q. The remaining dependence from the quark 20

23 CHAPTER 1. Charm production in hadronic collisions mass, like the m 2 /p 2 T terms, is kept into the hard scattering cross section. In order to calculate the production cross section for charmed hadrons, i.e the D mesons, the charm quark mass is set at m c = 1.5 GeV/c 2, the renormalization, initial state and final state factorization scales are matched to the quark transverse mass (µ R = µ F = µ F = m T p 2 T + m2 ), the fragmentation functions are extracted from measurements by OPAL [24], employing the CTEQ6.1M [25] parton distribution functions as default PDF set. To estimate the theoretical uncertainties, as in the FONLL approach, the values of µ R /m T, µ F /m T and µ F /m T are independently varied between 0.5 and 2, taking as uncertainty the envelope of the different results. The right panel of Fig. 1.9 shows GM-VFNS predictions for the p T -differential cross section for D 0 meson inclusive production in pp collisions at s = 7 TeV, in the rapidity range y < 0.5, compared to ALICE measurements [26]. From the comparison of the FONLL and GM-VFNS predictions, some discrepancies appear both in the absolute value and in the p T -dependence of the cross sections. The source of these deviations cannot be assigned to a unique source, due to the conceptual differences between the two schemes in several respects. As it will be shown in Chapter 3, measurements of charm production at LHC allow us to test the goodness of these predictions and to discriminate among the available models. Figure 1.9: Left: FONLL predictions for the inclusive D 0 meson production cross section in pp collisions at s = 7 TeV, in the rapidity range y < 1. The green and the yellow bands show the cross section for prompt and feed-down D 0, respectively. Right: GM-VFNS central predictions for the inclusive D 0 meson production cross section in pp collisions at s = 7 TeV, for y < 0.5, compared to ALICE measurements. Figure taken from [27]. Despite being the state-of-the-art of pqcd calculations, neither FONLL nor GM- VFNS schemes can be used when the transverse momenta of the charm quark and antiquark are not equal. Thus, these schemes are not suitable for the study of correlations of heavy flavour quark pairs and other similar observables. To allow this kind of measurements an alternative technique to the standard collinear-factorization approach has been developed: the k T factorization approach [28 30]. In this scheme, which is formally a LO calculation, the low-x effects that arise in the perturbative 21

24 CHAPTER 1. Charm production in hadronic collisions calculation are included in the unintegrated gluon distribution functions (UGDFs), which constitute the basic element of this formalism. Since most of the production of charm quarks at LHC energies comes from gluon fusion, LHC experimental data are crucial to select the best model for the UGDFs. Among several possibilities, the Kimber-Martin-Ryskin (KMR) set seems to grant the best agreement with cross sections and first correlation results measured at the LHC for charm production [31]. To evaluate the theoretical uncertainties on the predictions, the charm quark mass is varied in the range m c (1.2, 1.8) GeV/c 2 and the renormalization and factorization scales are varied in the range µ 2 F,R (0.5m2 T, 2m2 T ), with m T being the transverse mass of the quark, taking as uncertainty the uppermost and lowermost deviations from the central predictions, obtained with the default values. Fig shows the k T -factorization approach predictions for the inclusive cc production cross section in the rapidity range y < 0.5, in pp collisions at s = 7 TeV, obtained using the MSTW08 PDF functions [32,33]. The predictions are compared to calculations from FONLL and fixed-order NLO (NLO PM in the figure) schemes. Figure 1.10: Predictions from k T -factorization approach for the inclusive cc production cross section in the rapidity range y < 0.5, in pp collisions at s = 7 TeV. The solid line shows the central prediction, while the gray band represents the total theoretical uncertainty. Comparison with central predictions from FONLL (long dashes) and fixedorder NLO (short dashes, denoted as NLO PM in the figure) schemes is also shown Benchmark for heavy ion collisions analysis Studying heavy flavour production and characterizing heavy quark properties in pp collisions at LHC is the basis for analogue analyses in heavy ion collisions. In such interactions a peculiar state of matter, predicted by lattice QCD calculations, can be produced, the Quark Gluon Plasma (QGP). Its properties can be studied 22

25 CHAPTER 1. Charm production in hadronic collisions through several observables directly accessible through measurements on the particles produced in the collisions. This topic will be described in further details in Section To quantify and characterize the effects of the presence of a QGP on heavy flavour hadrons, in fact, it is necessary to compare heavy ion measurements to pp collision results at similar energy, where no QGP state is produced. Analysis of p-pb collisions has also an important role, since it allows us to disentangle the effects of QGP from, e.g., the initial state effects of the collision, which modify the properties of the interacting partons before the hard scattering due to the presence of many other nucleons in addition to the interacting ones. 1.2 Charm production in Pb-Pb collisions This section will briefly describe the QCD phase diagram, the predicted phase transition of ordinary nuclear matter to the Quark Gluon Plasma, and how this state can be produced in heavy ion collisions. Finally, it is discussed how heavy flavour measurements can be exploited to investigate the properties of the QGP. The following is not a comprehensive summary of QGP properties and of its signatures, since only those directly related to heavy flavour quarks will be discussed in detail. More exhaustive reviews can be found in [34,35] for the QCD phase diagram, in [36] for the QCD lattice calculations and in [37, 38] for the QGP characterization The Quark Gluon Plasma: a theoretical prospect The QCD phase diagram Strongly interacting matter does not only exist in the hadronic state, where quarks are bound into hadrons. The features of strongly interacting matter can indeed dramatically differ, with respect to the behaviour described in Section From QCD calculations on the lattice and thermodynamical considerations, it is expected that different states can be formed if the values of the temperature T and of the baryo-chemical potential µ B are modified. The baryo-chemical potential can be defined as the minimum energy necessary to increase by one the total baryonic number (N B = baryons antibaryons) of the system: µ B = E/ N B. Fig shows the QCD phase diagram as a function of T and µ B along with the main transitions among the different states. For low values of temperature and µ B m p 938 MeV, the standard conditions of nuclear matter are found, with the quarks being confined in nucleons. Increasing the temperature of the system and/or its baryo-chemical potential, an hadron gas state is obtained: here the nucleons interact with each other producing pions, excited states of the nucleons (like the resonances) and other hadrons. From this state, moving rightwards in the diagram by further increasing µ B, a transition toward a colour superconductor state is predicted to occur. At ultra-high densities, a CFL (colour-flavor-locked) 23

26 CHAPTER 1. Charm production in hadronic collisions state is expected, where the quarks of all the three colours and of all the three light flavours (u, d, s) form zero-momentum spinless Cooper pairs [39]. This kind of transition is expected to occur during the process of formation of neutron stars, where the gravitational field of the collapsing star produces a huge increase of the baryonic density at very low temperatures. If, starting from the hadronic gas state, the temperature is increased while keeping low µ B, a different transition occurs and a Quark Gluon Plasma state is reached. In this state, quarks and gluons reach so high temperature and density values that, although still interacting among one another, they are no longer bound into hadrons, but they become deconfined in a sort of plasma, in analogy to what happens to electrons and ions brought to very high temperatures 5. The degrees of freedom of the system become the flavour, spin, colour and charge states of quarks and gluons. A transition from QGP state into hadronic state should have occurred during the early stages of Universe, due to its expansion and to the consequent decrease of the temperature. Although not directly observable, this transition could have left footprints, i.e. in the relative abundances of light elements in the Universe [42, 43]. The same transition can be produced in heavy ion collisions at very high center-of-mass energies, as it will be discussed next. Figure 1.11: Phase diagram of QCD matter. 5 The existence of a state in which quarks and gluons are deconfined was theorized already in 1975 by Cabibbo and Parisi [40], and by Collins and Perry [41], after the discovery of asymptotic freedom. 24

27 CHAPTER 1. Charm production in hadronic collisions The QGP phase transition Phase transitions between different states are generally characterized by breaking or restoring symmetries in the Lagrangian of the system. In the case of QCD, if the quark masses are identical, the Lagrangian of Eq. 1.1 exhibits a flavour symmetry, described by the symmetry group SU(N), with N being the number of quark flavours. This implies that the strong interaction does not depend on the flavour of the quarks. A consequence of this property is the invariance under isospin transformations, commonly observed in hadronic processes. If the quarks are also massless, the Lagrangian shows an additional symmetry, called chiral symmetry, associated to the SU(3) L SU(3) R group (considering the only the lightest quarks, i.e. u, d and s). This symmetry implies the invariance of QCD under helicity transformations, in addition to flavour invariance. As a consequence of chiral symmetry, the chiral condensate ψψ, defined as: ψψ = ψ L ψ R + ψ R ψ L, where ψ L,R = 1 2 (1 γ 5)ψ (1.12) should be zero. However, its value in the vacuum is not zero, but about (235 MeV) 3, as also confirmed by the existence of the pion [44, 45], being interpreted as the Goldstone boson of this symmetry. The chiral symmetry, hence, is broken in the ordinary state of matter. This breaking adds a contribution to the quark masses, called constituent mass, which sums to the mass value generated by the coupling of the quarks with the Higgs boson (bare mass). In addition, in the ordinary state of matter, even the flavour symmetry described by SU(3) group is found to be broken, since the bare masses of the quarks have not the same value. At least for the three lightest flavours u, d and s, anyway, the quark bare masses are quite similar and close to zero: m u = 2.3 ± 0.5 MeV, m d = MeV, m s = 95 ± 5 MeV [46]. For this reason, the three states of the pion have very similar and small masses, if compared to the typical hadron mass scale ( 1 GeV/c 2 ). Lattice QCD calculations, described in the next section, predict that when increasing the temperature of the system to values close to the critical temperature predicted for the QGP transition, the chiral symmetry is restored. In this conditions, the value of the chiral condensate ψψ should vanish, as the quark constituent masses. Hence, in the QGP phase the chiral symmetry is restored. Another distinctive feature of the phase transition to QGP state is the modification of the qq bounding potential of Eq. 1.5, which leads to deconfinement of quarks and gluons. This aspect can be explained in terms of the Debye screening, an effect already observed for electromagnetism and occurring when charged particles are placed inside a charged medium. In this situation, due to the presence of the medium, the strength of the mutual interaction between two charges is reduced by a factor exp r λ D, where λ D is the Debye length, representing the separation over which the interaction between two charges becomes screened by the medium. For strongly interacting matter, if the temperature of the system is increased over the critical value for the QGP transition, a large number of qq pairs is created inside 25

28 CHAPTER 1. Charm production in hadronic collisions the hot medium. These pairs screen the colour charge between the original quark pairs, as shown in Fig. 1.12, and reduce the strength of the interaction, which can be expressed as follows: V qq (r) = 4 α s 3 r r exp λ D. (1.13) Figure 1.12: Schematic view of the Debye screening of colour charge in a hot and dense medium (right), with respect to the vacuum (left). The long-range component of the potential which caused the confinement disappears, while the Coulombian component is strongly reduced. The quark cannot feel anymore the presence of the other quark at distances greater than few λ D. Hence, hadronic bound states are no longer formed and the whole medium acts like a strongly interacting medium composed of deconfined quarks and gluons. Lattice QCD calculations The phase transition between hadronic matter and QGP is characterized by the presence of long-range interactions and collective phenomena. For these processes, the strong coupling constant α s is too large to allow perturbative calculations. The best non-perturbative approach to study the properties of the phase transition and quantify the critical values of T and µ B is given by lattice QCD (lqcd). In this approach, space and time are discretized in a lattice composed of a finite number of points, where the QCD Lagrangian can be numerically solved. The largest source of uncertainty arises from the finite spacing between consecutive points, although the current computing technologies allow this spacing to be kept small enough to grant very accurate predictions. Using lattice QCD to study QGP phase transition produces results which depend on the number of flavours and on the values of the quark masses considered in the model. In addition, calculations are relatively easy only for µ B = 0, which is anyway a reasonable assumption for the QGP transition occurring in heavy ion collisions at very high energies. Considering massless quarks, the calculations predict a phase transition at a critical temperature of T = 173 ± 15 MeV, with µ B = 0 [35]. The corresponding critical energy density is ɛ = 0.7±0.3 (GeV/fm) 3, and above the critical temperature ɛ grows proportionally to T 4. This is the behaviour expected for an ideal ultrarelativistic gas. The proportionality factor, though, is lower by about a 20% with 26

29 CHAPTER 1. Charm production in hadronic collisions respect to the expected value for a gas of massless u, d, s quarks and gluons, as shown in the left panel of Fig [47]. The assumption of massive quarks slightly modifies the expected value of the critical temperature, which is however in the range MeV. In addition, for massive quarks the order of the transition changes, becoming a smooth cross-over without any critical point 6. These results are shown in the right panel of Fig. 1.13, which describes the order of the QGP phase transition as a function of the quark masses, for two or three quark flavours included in the calculations [47, 48]. Figure 1.13: Left: lqcd predictions for the energy density as a function of the temperature of the hadronic matter for µ B = 0. Calculations are performed for three massless quarks (3 flavour), two massless quarks (2 flavour) and 2 massless quark + 1 quark with the mass of strange quark (2+1 flavours). In the massless cases an abrupt transition is obtained, while with a massive strange quark the transition becomes a cross-over. The arrows show the T reach for SPS, RHIC and LHC experiments, while the limit on the right vertical axis points to the expected value of ɛ/t 4 for an ideal gas of massless u, d, s quarks and gluons. Right: lqcd results for the order of the QGP phase transition as a function of the u, d and s quark masses, for µ B = 0 and assuming m u = m d. In the QGP state, the system should be described by the equation of state ɛ = 3p, where p is the pressure of the system. The energy density, as anticipated above, should have a T 4 dependence, given by the Stefan-Boltzmann law: ɛ = g π2 (k B T ) 4, (1.14) ( c) 3 30 with g the number of degrees of freedom of the system. The large jump in the energy density over a small temperature interval (of about 40 MeV) visible for the 6 A phase transition belongs to first order if it shows discontinuities on the first derivative of the free energy; if discontinuities appear in higher order (n) derivatives, the transition belongs to the n-th order. A transition having a continuous behaviour of the free energy first derivative is called a cross-over. 27

30 CHAPTER 1. Charm production in hadronic collisions massless cases in the left panel of Fig is therefore due to the dramatic increase of the degrees of freedom of the system. These increase from 3 of the hadronic gas phase (the three states of the pion) to 37 of the QGP phase, for two massless quarks, obtained from: g = N g N pol + 7/8 N ff N col N spin. (1.15) In the previous relation, N g = 8 is the number of gluons, with N pol = 2 polarization states, while N ff = 4 is the number of flavours for quarks (u and d) and antiquarks (u and d), with N spin = 2 spin states and N col = 3 colour states. The 7/8 factor arises from the different statistics for gluons (Bose-Einstein) and quarks (Fermi-Dirac). Evolution of a heavy ion collision If the energy density of the medium created in the early stages of ultra-relativistic heavy ion collisions is higher than the critical value, it is possible to produce Quark Gluon Plasma. The first explorative studies of heavy ion collisions were attempted at the AGS at Brookhaven, in Au-Au collisions at 11.5 A GeV/c. Later on, at the SPS, the conditions for the formation of a QGP should have been reached in Pb-Pb collisions at s NN = 17 GeV [49]. At RHIC the properties of the QGP could be studied in deeper detail in Au-Au collisions at s NN = 200 GeV. The first analyses for the QGP characterization at the LHC are currently ongoing in Pb-Pb collisions at s NN = 2.76 TeV collected from 2010 onwards. To allow the study of QGP properties, some thermodynamical observables have to be exploited, since direct measurements on the partons are not possible. The thermodynamical approach is based on the hypothesis that a local thermal equilibrium is reached. For that, a minimum time, estimated to be about τ eq = 1 fm/c, is needed. Moreover, the spatial extension of the medium has to be large enough to grant a sufficient number of scatterings for the partons, otherwise it would not be possible for the system to get to the equilibrium. It is possible to estimate the energy density of the system produced in a given collision using a simple hydrodynamical model developed by Bjorken [50]. This model is valid under the assumption that the constituents of the medium are produced in a very short time after the collision and that the net baryon density is zero. These assumptions imply collisions taking place at ultra-relativistic energies. The latter hypothesis is justified by considering that, in this case, the baryons of the initial state are carried away by the fragments of the colliding nuclei (full transparency condition). This model considers the particles produced in the central rapidity region, in the so called Dirac plateau, where the energy density is maximum. The energy density of the medium immediately after the collision can then be evaluated as: ( ) dnh w h ɛ = dy πra 2 τ, (1.16) 0 y=0 where (dn h /dy) y=0 is the number of hadrons produced at mid-rapidity, with average energy in the transverse direction w h, R A is the transverse size of the system and τ 0 is 28

31 CHAPTER 1. Charm production in hadronic collisions the formation time of the hot nuclear medium. If a formation time of τ 0 = 1 fm/c is assumed, it is possible to evaluate the energy density for central heavy ion collisions at the SPS (ranging from 1 to 3.5 GeV/fm 3 ), RHIC (around 5 GeV/fm 3 ) and LHC (about a factor three higher than at RHIC), much higher than the critical value required for QGP formation. Even after the thermalization time, energy densities are expected to stay above the threshold, allowing the formation of an equilibrated deconfined medium, which can be studied through a thermodynamical approach. The expected properties of the hot nuclear medium produced in heavy ion collisions in different s domains are summarized in Tab. 1.3 [51]. Table 1.3: Comparison between the expected properties of the hot nuclear medium produced in the early stages of ultra-relativistic heavy ion collisions at SPS, RHIC and LHC. Parameter SPS RHIC LHC snn [GeV] dn gluons /dy dn ch /dy Initial Temperature [MeV] > 600 Energy density at τ 0 = 1 [GeV/fm 3 ] Freeze-out volume [fm 3 ] few 10 3 few 10 4 few 10 5 Life-time [fm/c] < > 10 Fig describes the main stages of the evolution of a heavy ion collision with energy density high enough to allow the QGP formation. Immediately after the collision, the nucleons not involved in the reaction (spectator nucleons) continue to travel along the beam axis, while the nucleons that suffered interactions with other nucleons (participant nucleons) release a large amount of energy. A large number of quark-antiquark pairs and gluons is created using the available energy. The nuclear medium, also called fireball during this phase, has a very high temperature, zero net baryonic density and its extension along the beam direction is negligible with respect to its dimensions perpendicularly to the beams, due to the Lorentz contraction of the colliding nuclei. While the medium expands and cools down, quarks and gluons undergo a series of scatterings, which bring the system to thermal equilibrium after a time of the order of 1 fm/c. From this moment on, the temperature of the expanding fireball decreases until the critical temperature T c is reached, when the phase transition to hadronic gas occurs. At the transition, when the quarks begin to hadronize, they continue to scatter with the other particles present in the medium. At the chemical freeze-out T ch, found to be very close to T c, no more inelastic collisions occur and the abundances of the particle species do not modify anymore. Only elastic collisions occur after this moment, which can modify the momentum distributions of the hadrons. At the kinetic freeze-out T fo, measured to occur at about 120 MeV at RHIC and just below 100 MeV at LHC from the p T distributions of hadrons, the hadrons emerge from the medium without any further interaction. 29

32 CHAPTER 1. Charm production in hadronic collisions Figure 1.14: Evolution of a heavy ion collision in which QGP phase is reached. Horizontal axis represents the spatial axis, vertical axis shows the time, starting from the instant of the collision. Charm and beauty as probes of the QGP Heavy flavour quarks are excellent probes to characterize the QGP produced in ultra-relativistic heavy ion collisions. Since the minimum value of the virtuality of a heavy quark pair is large (Q min = 2m Q ), the production of cc and bb pairs occurs in a very short time scale, of about t cc = 2m 1 c 0.1 fm/c for charm and even less for beauty. This time interval is much lower than the time for the formation of the QGP, hence the heavy quark pairs experience the full evolution of the QGP phase and are subject to all the effects induced by the medium. Therefore, by studying the emerging heavy flavour hadrons it is possible to retrieve information about all these effects, in particular about the parton energy loss in the medium, where a colour charge and a quark mass dependence is predicted from theoretical models [52 55]. In addition, as already discussed in Section 1.1.2, because of their large mass (m c,b Λ QCD ) it is possible to use perturbative QCD calculations to compute the expected production cross section in pp collisions and to rescale measurements at different energies and from different systems, to perform comparisons of production cross sections or other derived observables. pqcd calculations predict a cross section for charm production about 20 times larger than for beauty at LHC energies; in addition, it is much easier to reconstruct charmed hadrons from exclusive decay channels (e.g. the D 0 K π +, exploited for the correlation analysis described in this thesis) than beauty hadrons. In the following, thus, particular attention will be given to charm production, rather than to beauty production. 30

33 CHAPTER 1. Charm production in hadronic collisions Charm production cross section in nucleus-nucleus collisions In nucleus-nucleus collisions several effects are expected to modify the production and the propagation of heavy quarks with respect to pp collisions, due to the presence of other nucleons before the collision and of the QGP after it. Supposing to neglect all these effects, a nucleus-nucleus collision can be considered as a superposition of a certain number of independent pp collisions. This allows us to calculate the cross section for hard processes by a scaling from the pp collision cross section. The scaling is based on the Glauber model [56, 57] and assumes that the cross section of the hard processes scales linearly with the number of inelastic nucleon-nucleon collisions which take place in the nuclei scattering (binary scaling). Let us calculate the inelastic cross section in collisions of two nuclei having respectively A and B nucleons. Introducing the impact parameter of the collision as the distance between the centers of the two colliding nuclei in the plane perpendicular to the beam axis, it is possible to use this quantity to define the centrality of the collision and to evaluate the inelastic cross section in a given centrality range. For example, to obtain the inelastic cross section for the 5% or 10% most central events in case of Pb-Pb collisions, it is necessary to take only those collisions with impact parameter b inside the cut values b l and b h : b l b < b h, with b l = 0 and b h = 3.5 fm for the 5% case or b h = 5 fm for the 10% case [14]: σ inel AB (b l, b h ) = bh b l db dσinel AB db = 2π bh b l b db {1 [1 σ pp T AB ] AB }. (1.17) In the equation above σ pp is the nucleon-nucleon inelastic cross section and T AB is the nuclear overlap function, defined as: T AB = d 2 st A ( s )T B ( s b ), (1.18) starting from the nuclear thickness functions T A and T B, which in turn can be evaluated for nuclei using a Wood-Saxon nuclear density profile [58]. The definition of the vectors s and b can be deduced considering Fig If in Eq the inelastic cross section for nucleon-nucleon collisions σ pp is substituted by the cross section for a given hard process, like the charm quark production, the cross section for that hard process in nucleus-nucleus collisions inside a given centrality range is obtained: σ hard AB (b l, b h ) = bh b l db dσhard AB db = 2π bh b l b db {1 [1 σ hard pp T AB ] AB }, (1.19) where, as already noticed, the centrality range is defined by the cut values b l and b h. In case of minimum-bias collisions (no centrality selection, thus b l = 0 and b h = ), the equation above simply becomes: σ hard AB = A B σ hard pp. (1.20) 31

34 CHAPTER 1. Charm production in hadronic collisions Figure 1.15: Geometry of a nucleus-nucleus collision, with transverse (a) and longitudinal (b) views Deviations from binary scaling The calculations made above hold only if there are no effects which modify the binary scaling. However, both theoretical models and experimental measurements have suggested several effects which can cause deviation from binary scaling, influencing thus the value of the cross sections for hard processes. These features can be classified in two categories: initial state effects: these are produced by the presence of other nucleons in the colliding nuclei and depend on the mass number and on the energy of the nuclei; they do not include, instead, any influence caused by the medium produced after the collision; final state effects: these are caused by the presence of the medium generated in the collision and modify the kinematical variables of the hard quarks produced in the collision. They mainly depend on the properties of the medium and can be a source of information to study its features. Among the initial state effects, the most relevant are the nuclear shadowing and the broadening of the k T distribution of the partons, which are described in the following. Nuclear shadowing From several experiments it was observed that the structure functions of the nucleons are severely modified when they are bound into nuclei [59]. For Q 2 in the range 5 < Q 2 < 20 (GeV/c) 2, a depletion in the parton distribution functions was measured over the x < 0.1 and 0.3 < x < 0.7 ranges of Bjorken x variable, while an enhancement was found for 0.1 < x < 0.3 and for x > 0.7. For x < 0.1, region of particular interest for the LHC, this effect is referred to as nuclear shadowing. This different behaviour of the PDFs is caused by different effects involving sea and valence partons. Thus, it is difficult to build a single model able to describe all these 32

35 CHAPTER 1. Charm production in hadronic collisions features and it is simpler to parameterize the modifications of the parton distribution functions using measurements from deep inelastic scattering experiments. A widely used parametrization for the nuclear PDFs is the EKS98 [60] (later updated to EPS08 [61] and EPS09 [62]), which reproduces well data results and also provides an extrapolation for x < , a region not accessible to any experiment before the LHC era. The nuclear modified PDFs can be quantitatively described by evaluating the ratio of the distribution function for a given parton i (valence quark, sea quark, gluon) in a nucleus with mass number A over the PDF in a proton: R A i = f A i (x, Q 2 ) f p i (x, Q2 ). (1.21) The left panel of Fig shows the EKS98, EPS08 and EPS09 calculations for the gluon modification R in a lead nucleus (A = 208) for Q 2 = 1.69 (GeV/c) 2, compared to calculations obtained using other PDF parameterizations [63]. The different x regions presenting a depletion and an enhancement of the distribution functions are clearly visible. In the right panel of the same figure, the gluon modification R in a lead nucleus, evaluated using EKS98 parametrization, is shown against x for increasing Q 2 values [14]. Figure 1.16: Left: gluon modification R from EKS98 parametrisation in lead nuclei for Q 2 = 1.69 (GeV/c) 2, in the range 10 4 < x < 1. Comparison with other parameterizations is shown [63]. Right: gluon modification R in lead nuclei as a function of Bjorken x for different Q 2 values, evaluated using the EKS98 parametrization for the gluon distribution functions. As discussed in Section 1.1.3, measuring heavy flavour hadrons at the LHC opens the possibility to explore a very low x region, down to about x 10 4 at central rapidity and x for rapidity y 4, regions where the main contribution to heavy quark production comes from gluon fusion. Hence, the production cross section for heavy flavours is significantly affected by nuclear shadowing effects which, as 33

36 CHAPTER 1. Charm production in hadronic collisions visible from Fig. 1.16, heavily suppress the gluon distribution functions at very low x values. Calculations performed using the HVQMNR program [16] and using EKS98 parametrisation for the nuclear PDFs predict a decrease of the charm (beauty) cross section of about 35% (20%) in Pb-Pb collisions at 5.5 TeV and of about 15% (10%) in p-pb collisions at 8.8 TeV [14]. The best approach to disentangle the nuclear shadowing effects (and, in general, initial state effects) from the medium effects is to analyze proton-nucleus collisions. This system, indeed, should not provide enough energy density after the collision to allow QGP formation, but the colliding partons feel in any case the presence of the other nucleons in the colliding nuclei and are hence affected by the initial state effects. For this reason, p-pb collisions at s NN = 5.02 TeV have already been delivered at LHC in the first months of 2013 and further studies are planned for the upcoming years. Broadening of parton k T distribution In order to correctly reproduce measurements for charm production in pp collisions, it is necessary to introduce in pqcd calculations an intrinsic transverse momentum k T for the interacting partons. The value of k T is extracted using a Gaussian distribution with kt 2 1 (GeV/c)2 [64]. In proton-nucleus and nucleusnucleus collisions the average value of kt 2 for the interacting partons is expected to increase and its distribution to broaden. This increase is caused by multiple scattering of the partons of each nucleus with the partons in the other nucleus and it constitutes an additional initial state effect. A feature of this kind has already been observed in measurements of the Drell-Yan cross section and in the study of charmonium and bottomonium production. From theoretical estimations, in protonnucleus collisions the average intrinsic transverse momentum of partons should rise to kt (GeV/c)2, while in nucleus-nucleus collisions it should increase to kt (GeV/c)2. The observable effect of the broadening of the k T distribution for c quarks is a modification of the shape in the p T distribution of charm hadrons at low p T, while the overall cross section for their production is not modified. In addition, this effect should also reduce the back-to-back azimuthal correlation of the cc pair produced from the hard scattering, which reflects in the correlation distribution of charmed hadrons. At the LHC, however, the magnitude of this effect is expected to be negligible with respect to the other effects induced by the medium. The most important final state effects which affect heavy flavour quarks are briefly described below. Thermal production of cc pairs The high values of temperature reached in the early stages of heavy ion collisions might allow the creation of cc pairs via thermal production, in addition to the usual 34

37 CHAPTER 1. Charm production in hadronic collisions production through hard parton scatterings. At LHC energies, the temperature of the QGP should be of about GeV, i.e. not much lower than the c quark mass. Thus, a secondary contribution from thermal production should be present in the total charm yield. Anyway, it should present different kinematical distributions with respect to hard scattering production. In particular, thermal cc pairs ought to have a lower invariant mass value than primary pairs and, hence, their final hadronic states should lie in the lower region of the p T spectrum of charm hadrons. In Tab. 1.4 the yield of cc pairs from thermal production is calculated for Pb-Pb collisions at the LHC nominal center-of-mass energy ( s NN = 5.5 TeV) in two different scenarios for the initial conditions of the hot nuclear medium: a parton gas with a rather long kinetic equilibration time and a minijet gas with a short equilibration time. Calculations are performed for two values of the charm quark mass and for massless/massive quarks and/or gluons [65]. Table 1.4: Total yield of thermal cc pairs expected in Pb-Pb collision at s NN = 5.5 TeV. Two scenarios are considered for the initial conditions of the nuclear medium (parton gas and minijet gas). Calculations are performed considering both a massless and massive pure gluon gas (g) and a massless or massive quark-gluon system (g + q). System m c = 1.2 GeV/c 2 m c = 1.5 GeV/c 2 properties parton gas minijet gas parton gas minijet gas m = 0 g m 0 g m = 0 g + q m 0 g + q Charmonium suppression and regeneration The suppression of charmonium states was considered a golden signature for the creation of a hot deconfined medium in ultra-relativistic heavy ion collisions since the first studies on QGP [66]; these expectations were already confirmed by SPS measurements about the J/Ψ state. The source of this suppression is the Debye screening of the colour charge, which establishes due to the presence of a large number of deconfined or free qq pairs in the system, as described in Section The Debye screening weakens the binding potential of the cc pairs produced in the medium, unbinding at last the pairs if the screening radius becomes lower than the binding radius of the quark-antiquark system. The highest charmonium excitations should dissolve for temperatures even lower than the critical temperature for the QGP transition. Increasing the temperature of the system should cause the melting of tighter bound charmonium states and, for extreme values of T, should unbind also the most bound bottomonium states. Figure 1.17 shows the S-wave spectral function for charmonium (left panel) and bottomonium (right panel) for different values of the temperature, in units of T c [67]. The spectral functions, and the 35

38 CHAPTER 1. Charm production in hadronic collisions dissociation temperatures of the quarkonium states, can be evaluated using potential models based on full QCD lattice calculations of the free energy of the static QQ pair. They confirm a sequential suppression of the quarkonium states at increasing temperatures of the system, with only the J/Ψ and the Υ(1S) surviving for T = T c, and the J/Ψ dissolving as well just above T c. At LHC energies, even a fraction of the Υ(1S) state may break up, since its dissociation temperature is expected to be T Υ (1S) 2T c, easily reached in Pb-Pb collisions at s NN = 5.5 TeV. Figure 1.17: S-wave spectral functions for charmonium (left panel) and bottomonium (right panel) for different temperatures of the system, taken from [67]. However, at least part of the charmonium suppression should be recovered by a regeneration of cc bound states, due to the recombination of the c and c quarks from the hot nuclear medium. This process gains importance as the cross section for cc production increases. Hence, it had no influence at SPS and should be weak at RHIC, but it should play a prominent role at the LHC, as the first results from its experiments have suggested. The recombination process for bottomonium should instead be negligible even at the LHC energies. Parton energy loss in the medium The formation of QGP should cause an energy loss for high momentum partons traversing the medium [68]. The energy loss is due to multiple scattering with the other partons in the medium (collisional contribution) and to medium-induced gluon radiation (radiative contribution). Depending on the in-medium path length and on the energy of the travelling parton, one of the two contributions can dominate the other. The amount of the energy lost by collisions increases linearly with the inmedium path length and has only a logarithmical dependence on the initial parton energy. For partons travelling few fm, as it is the case in heavy ion collisions, at low energies collisional and radiative mechanism have similar contributions to the energy loss, while at higher parton energies the collisional contribution is expected to be very small and can be neglected with respect to radiative energy loss. A theoretical model of the in-medium radiative energy loss of the partons was proposed by Baier, Dokshitzer, Müller, Peigné and Schiff (BDMPS model) [52, 53]. 36

39 CHAPTER 1. Charm production in hadronic collisions In this model, while traversing the medium the partons produced in the hard scattering undergo a series of collisions in a Brownian-like motion, with mean free path decreasing with increasing medium density. During this multiple scattering process, gluons in the parton wave function gain transverse momentum with respect to the parton direction and can be eventually radiated in a gluonstrahlung process, in analogy with QED bremsstrahlung for electrically charged particles which are decelerated inside a medium. The characteristic energy of the radiated gluons ω c depends on the path length inside the medium L and on the properties of the medium, described by its transport coefficient q: ω c = q L 2 /2. (1.22) The transport coefficient q is defined as the average squared transverse momentum kt 2 transferred to the emitted gluon over the mean free path of the traversing particle: q = kt 2 /λ, [69]. An estimate for the hadronic matter gives q 0.05 GeV 2 /fm, while for the QGP formed at LHC energies the expected value could rise up to 100 GeV 2 /fm [52]. For a static medium, the energy distribution of the radiated gluons can be expressed in the form: ω di dω 2α sc R ωc (1.23) π 2ω for energies ω ω c, with C R being the Casimir factor, equal to 4/3 for qg coupling and to 3 for gg coupling. The average energy loss of the parton can be obtained by integrating the previous equation up to ω c : E = ωc 0 ω di dω dω α s C R q L 2. (1.24) E is thus proportional to the strong coupling constant α s, to the Casimir factor C R, to L 2 and does not depend on the initial energy E of the parton. The independence from the energy is a peculiar feature of the BDMPS model, since other theoretical approaches give, instead, a logarithmic dependence on E [70 72]. In any case, an intrinsic dependence on the initial energy is always present, since radiated energy cannot overcome the initial parton energy: E E. The average radiated energy is proportional to L 2 at variance with QED case, where this dependence is linear: E brem L. The difference arises from the non-abelian nature of QCD: the radiated gluons can also release energy by emitting other gluons. This introduces another L proportionality factor, leading to the overall L 2 factor for the primary parton. Finally, the Casimir factor dependence, which accounts for the different qg and gg couplings, brings to an higher amount of energy lost by gluons rather than by quarks. The left panel of Fig shows the expected energy loss for a c quark traversing the QGP medium produced in Pb-Pb collisions at s NN = 2.76 TeV, separating collisional and radiative contributions [73]. The right panel of the same figure describes the energy dependence of the collisional and radiative relative energy loss for light 37

40 CHAPTER 1. Charm production in hadronic collisions and heavy flavour quarks travelling in the medium produced in Au-Au collisions at RHIC, evaluated from two theoretical models [74]. Figure 1.18: Left: theoretical predictions for collisional, radiative and total energy loss for a charm quark traversing the nuclear medium created in Pb-Pb collisions at s NN = 2.76 TeV, as a function of the quark energy [73]. Right: theoretical predictions for collisional and radiative relative energy loss for light and heavy flavour quarks traversing the QGP medium created in Au-Au collisions at RHIC, as a function of the parton energy [74] Dead cone effect The average energy loss by gluon radiation is expected to depend on the mass and colour charge of the traversing parton, with a hierarchy: E heavyq < E lightq < E gluon [54]. The mass dependence arises from the so called dead cone effect. Heavy quarks travelling in the vacuum with moderate energy (m/e 1) have a velocity significantly lower than light velocity c: β = 1 (m/e) 2 1. In this situation, the gluon radiation inside a front cone with opening angle Θ = m/e is expected to be suppressed due to destructive interference processes [55]. The higher the mass of the parton, the larger the angular opening of the dead cone, and consequently the smaller the energy loss by gluonstrahlung. This effect is expected to hold also for partons travelling in the medium, with a suppression of the gluon radiation from heavy quarks with respect to light quarks predicted to be: ω di / dω ω di Heavy dω = Light [ ] [ 2 ( 1 + Θ2 0 m = 1 + Θ 2 E ) 2 ω 3 q ] 2 F H/L (m/e, q, ω), (1.25) where the characteristic gluon emission angle, Θ ( q/ω 3 ) 1/4, was inserted. The dead cone suppression factor F H/L, thus, is lower (i.e. less energy loss) for partons with heavy masses, as charm and beauty quarks (the effect being sizeable for beauty only) but it increases for increasing energies of the parton, where the effect of the mass starts to become negligible. In addition, it is higher for large 38

41 CHAPTER 1. Charm production in hadronic collisions values of ω, indicating a strong suppression of the hardest part of the emitted gluon spectrum. As a consequence, one should observe at intermediate transverse momentum a larger suppression of light flavour hadrons than for D and B mesons 7, in comparison to what is observed in absence of energy loss [75] Main observables for probing QGP Several observables have been proposed to study the QGP properties. Most of them have already been exploited in experiments at SPS, RHIC and LHC, allowing us to gain fundamental information. In this section only the observables used in the heavy flavour domain will be described. Nuclear modification factor R AA One of the most distinctive features of QGP is the parton energy loss due to multiple scatterings with other partons and gluon radiation, as described above. It is not possible to directly measure the energy loss, but this can be inferred by comparing the p T -differential yield for hadron production in heavy ions collisions (AA), where QGP is formed, with that in proton-proton collisions, where no energy loss effects are present. A high p T parton which has lost energy in the medium will gave rise to a leading particle of the resulting jet with a reduced momentum. In some cases, when the parton has travelled a long distance in the medium and only small amount of energy is still available for the fragmentation process, it is possible that no high-p T particles could emerge from the medium, without the production of a jet. For this reason, a suppression of the yields in AA collisions is expected with respect to pp collisions, at given (high) momentum. The nuclear modification factor (R AA ) observable can be hence defined as follows: R AA (p T ) = dn AA /dp T N coll dn pp /dp T, (1.26) where dn AA /dp T and dn pp /dp T are the measured p T -differential yields in AA collisions and pp collisions, respectively, and N coll is the estimated number of binary collisions taking place in the AA interaction. This value depends on the centrality of the collision and can be evaluated from the Glauber model [56]. If binary scaling is respected, no nuclear medium effects are influencing the AA collision and R AA = 1. A different value of R AA indicates the presence of initial state or final state effects. In particular, the suppression of the hadron production at high p T in heavy ion collisions due to the parton energy loss reduces the value of the nuclear modification factor: R AA < 1. 7 The different suppression between light quark hadrons and D mesons is mainly due to the different Casimir factor, since at the LHC light flavour hadrons are mainly produced from gluons (gg coupling), while D mesons originate by quarks (qg coupling); for B mesons, instead, the mass dependence and the dead cone effect play a much more relevant role. 39

42 CHAPTER 1. Charm production in hadronic collisions By studying the magnitude and the p T dependence of R AA for heavy flavour hadrons (which give insight into the heavy flavour quark energy loss) it is possible to check if the parton type (gluon versus quark) and mass (b versus c) hierarchies for the radiative energy loss, predicted by the models, are respected. To isolate the effects of QGP on hadron production, however, it is necessary to separate the final state effects from the initial state effects (as nuclear shadowing, k T broadening) which also influence the R AA value. This can be achieved by studying the modification of hadronic spectra in proton-nucleus (pa) collisions, where only cold nuclear matter effects are present, measured by the R pa observable, with a similar definition as R AA. Elliptic flow coefficient v 2 After the creation of the fireball in a heavy ion collision, the particles inside the medium start a chaotic motion characterized by multiple scatterings, as previously described. If the system is strongly interacting, however, on top of this motion also collective behaviours can take place: the system collective motion is defined as flow. The standard approach to describe the flow relies on hydrodynamical models. These are based on the assumption that the fireball reaches thermal equilibrium and thermodynamical variables as pressure and temperature can be defined for the system. In these models, flow is induced by particular conditions present in the fireball in the first moments of its evolution. For this reason, these collective motions can provide precise indications about the properties of the system in the early stages of the collision. More details about the flow can be found in [76]. It is possible to define two main flow classes: (i) radial flow, which is caused by the fireball expansion and is isotropic; it can be studied by measuring the p T distributions of the particles emerging from the collision; (ii) anisotropic flow, which is generated if the system shows asymmetries in the pressure gradients and which can be measured by studying the azimuthal distribution of the produced particles. To separate the various components of the anisotropic flow, a Fourier expansion of the azimuthal distribution of the particles in the transverse plane 8 can be considered: ( E dn d 3 p = 1 d 2 N π p T dp T dy ) v n cos[n(φ Ψ RP )], (1.27) where E is the particle energy, p its momentum, φ the azimuthal angle, y the rapidity and Ψ RP indicates the reaction plane angle. Each of the v n coefficients in the previous equation quantifies a certain component of the anisotropic flow and has a physical interpretation. The most important coefficient is the elliptic flow coefficient v 2, 8 By defining the z axis as the direction of one of the beams and the x axis as the direction of the impact parameter vector, the plane defined by these axes is called reaction plane; the transverse plane is defined by the x and y axes and is orthogonal to the reaction plane, as shown in Fig [76]. 40 n=1

43 CHAPTER 1. Charm production in hadronic collisions which brings indication on the asymmetries for the emission of particles inside or outside the reaction plane. When a peripheral collision (with large impact parameter) occurs between two heavy ions, the interaction region assumes an almond shape, as shown in Fig. 1.19, presenting a larger extension orthogonally to the reaction plane and a thinner extension along it. If the system is strongly interacting, the pressure gradient will be stronger in the reaction plane, producing an enhancement of the momentum components of the partons lying in that plane. As the fireball expands, the pressure gradients cancel out the initial spatial asymmetry, having as net effect the presence of more particles flying in the direction of the reaction plane than orthogonally to it. The magnitude of this effect is described by the value of the v 2 coefficient of the Fourier expansion which, in turn, can be determined by measuring the particle azimuthal distribution. Figure 1.19: Sketch of a non central heavy ion collision (left). The nuclear medium shows the typical almond shape, which is converted, for a strongly interacting system, into a momentum anisotropy (right) as the fireball evolution proceeds. The measurement of the value of v 2 for heavy flavour hadrons provides insight into the collective behaviour of heavy quarks. In particular, in the low p T region this observable can provide information on the degree of thermalization of the heavy quarks, while at high p T it can give clues about the path length dependence of heavy quark in-medium energy loss. 1.3 Selection of experimental results In this section a selection of results on charm production will be presented. The production cross section in pp and pa collisions versus the center-of-mass energy will be shown, while for heavy ion collisions the measurements of the nuclear modification factor R AA and of the elliptic flow coefficient v 2 will be reported. Only an overview of the latest results from the four main LHC experiments will be shown here; a comprehensive description of charm measurements from ALICE will be presented in Chapter 3. 41

44 CHAPTER 1. Charm production in hadronic collisions Open charm production cross section in pp collisions Due to the large mass of the charm quark, the first measurements on charm production were possible only after the 70s, at the beginning of the collider era. Quantitative results were obtained from experiments located at SPS (NA25, NA32, NA35), at Fermilab (E743, E653) and at the ISR, where the integrated cross section for cc pair production was measured in pp and pa collisions, for different values of the center-of-mass energy. Figure 1.20 shows these results as a function of s, compared to pqcd calculations at NLO [64] (pa results are rescaled by the number of binary collisions). With the exception of some results from ISR and some older measurements, most of the data points lie just above the theoretical predictions and confirm the increasing trend of the cross section against s. Figure 1.20: Integrated charm production cross section from pp measurements at SPS (NA25, NA32, NA35), Fermilab (E743, E653) and ISR, as a function of the center-of-mass energy. Data results are compared to pqcd calculations at NLO with m c = 1.2 GeV and µ = 2m c. The calculations are performed using MRS D- (solid), MRST HO (dashed) and MRST LO (dot-dashed) sets for parton distribution functions [64]. More precise and detailed measurements were obtained by CDF and D0 experiments, at the Tevatron collider, where data from pp collisions at energies up to s = 1.96 TeV were collected. In particular, pt -differential cross sections for the production of prompt D 0, D +, D + and D + s mesons were measured by CDF [77]. Figure 1.21 shows these measurements compared to FONLL theoretical predictions [20] (not available for the D + s meson). The measured p T -differential cross sections are higher than pqcd predictions by about 100% at low p T and 50% at high p T, though being compatible within the uncertainties. A major step forward was done also in the charm baryonic sector, where some states like the Ξ c were 42

45 CHAPTER 1. Charm production in hadronic collisions observed for the first time, and in the charmonium studies, where the inclusive production of cc states was extensively studied and new states were observed as well (details in [78]). Figure 1.21: p T -differential cross sections for prompt D 0, D +, D + and D + s production in y 1, measured by CDF in pp collisions at s = 1.96 TeV [77]. Inner bars represent statistical uncertainties, outer bars the quadratic sum of statistical and systematic uncertainties. Data results for D 0, D + and D + are compared to FONLL theoretical predictions, whose uncertainties are indicated by the yellow band. Additional charm production cross section measurements were performed at RHIC, where STAR and PHENIX experiments analyzed the data collected in pp, p-au and Au-Au collisions at s NN = 200 GeV. As an example of pp measurements, Fig shows the invariant differential cross section for electrons produced in heavy flavour hadron decays, measured by STAR (left panel, [79]) and PHENIX (right panel, [80]). For STAR measurements, contributions for charm and beauty decays are separated. Data are compared to FONLL theoretical predictions for charm and beauty contributions to heavy flavour decay electron cross section. The bottom panels show the data over theory ratios; data results and predictions are compatible within the uncertainties in all the cases, with PHENIX data point lying on the upper edge of FONLL predictions and STAR results closer to unity. With the LHC experiments the capabilities for charm studies have significantly increased. At a center-of-mass energy of s = 7 TeV, the cc production cross section is more than a factor 2 larger than at Tevatron energy and the higher luminosity allows us to collect good statistics to perform more differential and refined analyses. Fig shows the total cross section for cc pair production in pp collisions measured from LHC experiments (at s = 7 TeV and, for ALICE, also at s = 2.76 TeV), compared to measurements from previous experiments at lower center-of-mass energies [81]. LHC results confirm the increasing trend versus s, already observed in Fig and predicted by theoretical pqcd NLO calculations obtained using the HVQMNR program [16]. Being located downstream with respect to the beam intersection point, LHCb experiment can perform precise measurements on charm production at forward ra- 43

46 CHAPTER 1. Charm production in hadronic collisions Figure 1.22: Left: invariant cross section of electrons from bottom (red points) and charm (blue points) meson decays measured by STAR in pp collisions at s = 200 GeV [79]. Data results are compared to FONLL predictions for charm and beauty electrons, shown with their theoretical uncertainties. Right: invariant cross section of heavy flavour decay electrons measured by PHENIX in pp collisions at s = 200 GeV [80]. Data results are compared to the central value of FONLL predictions for charm, beauty and total contributions to heavy flavour decay electrons. For both experiments, bottom panels show the ratio of data measurements over the central value of theoretical predictions. Figure 1.23: Energy dependence of the total nucleon-nucleon charm production cross section, measured by LHC, RHIC, SPS and Fermilab experiments. In case of pa collisions the cross sections are rescaled by the number of binary nucleon-nucleon collisions, calculated in a Glauber model. The NLO MNR calculation and its uncertainty are superimposed to the data points and are represented by solid and dashed lines, respectively. 44

47 CHAPTER 1. Charm production in hadronic collisions pidity, providing complementary information with respect to the other LHC experiments. As an example, Fig shows the p T -differential cross section for prompt D 0 production at forward rapidity, measured in five y intervals, in pp collisions at s = 7 TeV [82]. D 0 mesons are reconstructed through their hadronic decay channel D 0 K π +. Data are compared to a Monte Carlo simulation produced using the PYTHIA event generator [83] and to FONLL [20] and GM-VFNS [23] theoretical predictions (indicated respectively as BAK et al. and MC et al. in the figure). Both PYTHIA simulation and theoretical predictions well reproduce the data in all the p T and y ranges. Figure 1.24: p T -differential cross section of prompt D 0 production in five y intervals, measured by LHCb in pp collisions at s = 7 TeV. Error bars show statistical and uncorrelated systematic uncertainties added in quadrature. An additional correlated uncertainty of 12% is not shown in the figure. Data are compared to PYTHIA simulations with LHCb tuning and to FONLL and GM-VFNS theoretical predictions (respectively BAK et al. and MC et al. in the figure). The gray shaded areas represent theoretical uncertainties of FONLL predictions Nuclear modification factor and elliptic flow of charm quarks The STAR and PHENIX experiments at RHIC could make some explorative studies of heavy flavour production in heavy ion collisions. These experiments analyzed Au-Au collisions at s NN = 200 GeV delivered by RHIC. The absence of 45

48 CHAPTER 1. Charm production in hadronic collisions detectors for secondary vertex reconstruction reduced the accuracy of measurements on heavy flavour hadrons. Anyway, both the observables defined in the previous section, namely the nuclear modification factor R AA and elliptic flow coefficient v 2, could be studied for D 0 mesons and heavy flavour decay electrons. As an example, the left panel of Fig shows STAR preliminary measurements for the D 0 meson R AA in the 0-10% centrality class as a function of p T, compared to predictions from POWLANG transport model using HTL and lattice-qcd transport coefficients (see [84] and references therein). Data show an enhancement of R AA with respect to unity at low p T, possibly coming from quark coalescence or related to the collective radial flow, and an increasing suppression from p T > 2 GeV/c, as predicted from the model and as expected from parton in-medium energy loss if QGP is formed. In the right panel of the same figure STAR (blue circles, [85]) and PHENIX (green triangles, [86]) measurements for R AA of heavy flavour decay electrons in the 0-10% centrality class as a function of p T are shown. Predictions from POWLANG transport model are also superimposed to the data points. Although STAR data are systematically higher than PHENIX ones, especially in the intermediate p T region, a significant suppression of heavy flavour production in Au-Au central collisions is observed for p T > 3 GeV/c in both cases. The suppression factor is similar to that measured for D 0 mesons. Figure 1.25: Left: preliminary results for D 0 meson R AA measured by STAR in the 0-10% centrality class. Data results are compared to POWLANG transport model predictions with HTL and lattice-qcd transport coefficients. Right: R AA of heavy flavour decay electrons as measured by STAR (blue circles) and PHENIX (green triangles) experiments in the 0-10% centrality class, compared to POWLANG transport model predictions. STAR and PHENIX data and theoretical predictions are all obtained at central rapidity, but for different y ranges. In both panels, error bars and boxes represent statistical and systematic uncertainties, respectively. STAR and PHENIX have also measured the elliptic flow coefficient of electrons from heavy flavour decays, finding positive values of v 2. From these results it can be inferred that heavy flavour quarks could reach some degree of thermalization during the QGP phase of the fireball and participate in the collective motions of the 46

49 CHAPTER 1. Charm production in hadronic collisions constituent partons 9. STAR measurements for v 2 of heavy flavour decay electrons in the 0-60% centrality class, extracted using different techniques, are shown in the left panel of Fig [85]. All the measurements are compatible within uncertainties and show values of v 2 greater than 0. These results are confirmed by PHENIX measurements [86], shown in the right panel of the same figure for minimum-bias collisions, where v 2 saturates for p T 2 GeV/c and then decreases, becoming compatible with zero for p T > 3 GeV/c. Figure 1.26: Left: measurements of v 2 for heavy flavour decay electrons, performed with different techniques by STAR in the 0-60% centraliy class. Right: PHENIX measurements of heavy flavour decay electron v 2 in minimum-bias events. In both panels, error bars and brackets indicate statistical and systematic errors, respectively. At the LHC, besides ALICE, which is dedicated to the study of Pb-Pb, also ATLAS and CMS study heavy ion collisions. While most of the analyses are still under development, preliminary results for J/Ψ R AA measurements from CMS are already available, as well as measurements of the suppression of single muons from open heavy flavour hadrons, performed by ATLAS [87]. Figure 1.27 shows CMS measurements for non-prompt J/Ψ R AA as a function of the event centrality in two different p T ranges, 3 < J/Ψ p T < 6.5 GeV/c (left panel) and 6.5 < J/Ψ p T < 30 GeV/c (right panel). A clear suppression is visible, with increasing strength when going to more central collisions. Since the J/Ψ are produced by B meson decays occurring long after exiting the fireball, the strength of the suppression is only due to the energy loss of the beauty quarks. CMS results are compared to the values of R AA of prompt D mesons, extracted by ALICE from D 0, D + and D + measurements. The p T ranges of the ALICE results included in the comparisons are chosen in order to have similar average p T as that of the B mesons giving birth to the non-prompt J/Ψ. This allows a direct comparison of the R AA values for hadrons coming from b and c quarks. In both panels, a stronger 9 On the bases on the v 2 results alone, however, it is not possible to provide a final answer on the heavy quark thermalization. The observed v 2 > 0 value for heavy flavour hadrons could arise from the v 2 value the of the light quarks, in case of production via coalescence, or the heavy quark could be bend in the in-plane direction through parton scattering, but without reaching a full thermalization. 47

50 CHAPTER 1. Charm production in hadronic collisions suppression of D mesons with respect to non-prompt J/Ψ is visible for most of the centrality classes. This constitutes the first hint of the mass hierarchy predicted for the parton energy loss in a QGP medium. Figure 1.27: CMS measurements of non-prompt J/Ψ R AA as a function of the collision centrality, for 3 < J/Ψ p T < 6.5 GeV/c (left panel) and 6.5 < J/Ψ p T < 30 GeV/c (right panel). CMS results are compared to ALICE measurements for D meson R AA. The D meson p T ranges grant a similar average p T as that of B mesons decaying into the nonprompt J/Ψ measured by CMS. Error bars and boxes at the points show the statistical and systematic uncertainties; for ALICE results, empty boxes represent the correlated systematic uncertainties, filled boxes the correlated systematic uncertainties. 1.4 Two-particle correlations Study of charm production: from hard process to hadronization The analysis of angular correlations between heavy flavour hadrons or their decay products can provide further insight into the heavy quark production. In detail, it could allow us to separate the various LO and NLO processes, described in 1.1.3, responsible for heavy quark production at LHC energies. Each of these processes, indeed, leads to a different distribution of the angle between the c and c quarks. This allows one to characterize and weight the contribution of each process from the analysis of the observed angular correlation distributions of the hadrons produced in the fragmentation of the c and c quarks. Using a Monte Carlo simulation based on a tune of PYTHIA event generator [83] that reproduces NLO pqcd predictions, the expected kinematical distribution of c and c quarks produced from pair production (the LO process), gluon splitting and flavour excitation (NLO processes) can be estimated. Figure 1.28 shows the results 48

51 CHAPTER 1. Charm production in hadronic collisions of this study for the production cross section of cc pairs in Pb-Pb collisions at s NN = 5.5 TeV against several kinematical variables, i.e. the invariant mass of the quark pair M cc (left panel), its transverse momentum p T (cc) and the difference of the quark azimuthal angles ϕ(cc) = ϕ(c) ϕ(c) (right panel) [19]. For each variable, together with the total cross section (solid histogram), the single contributions from pair production (dashed line), flavour excitation (dotted line) and gluon splitting (dot-dashed line) are shown. Significant differences among the distributions from the three processes are observed in all the cases. In particular, the azimuthal correlations of the quark pairs have completely different shapes: while most of the quark pairs from the LO process are produced with opposite momenta, corresponding to back-toback azimuthal correlations, for the NLO processes the quark distribution is much flatter, without any preferential value for ϕ. The NLO contributions are also expected to dominate the charm production cross section and to generate harder p T distributions with respect to pair production. The total cc production cross section from PYTHIA simulations is also compared to NLO pqcd calculations performed using the HVQMNR program [16] (triangles). The agreement between the two models is good for the M cc and p T (cc) distributions, while severe discrepancies emerge in the description of the ϕ dependence for the cross section. Figure 1.28: Comparison between charm production cross sections as a function of some cc kinematical variables from PYTHIA simulations (solid histogram) and from pqcd calculations at NLO using the HVQMNR program (triangles). Cross sections are shown as a function of the invariant mass of the cc pair M cc, its transverse momentum p T (cc) and the difference of the quark azimuthal angles ϕ(cc), in left, middle and right panel, respectively. For PYTHIA simulations, the total cross section is split into the contributions from individual processes: pair production (dashed line), flavour excitation (dotted line) and gluon splitting (dot-dashed line). Since quarks are bound into hadrons in ordinary matter, it is not possible to directly access to their kinematical distributions, but it is necessary to build observables involving their hadronic final states. Since D mesons are the lightest charmed states and are the easiest to be detected, the best possibilities are obtained by studying DD or D-hadron angular correlations. In the DD case, the correlation distributions should not differ too much from the quark distributions, preserving the possibility to study the hard scattering. The D-hadron measurement, though being 49

52 CHAPTER 1. Charm production in hadronic collisions experimentally easier to perform, is more loosely related to the cc distributions, but it allows anyway to gain some information on the quark pair by studying the shape and the height of the peaks at ϕ = 0 and ϕ = π. At the same time, in both cases the measurement of the angular distributions allows us to gain additional information about the fragmentation and hadronization stages of heavy quarks, which are currently not well known from a theoretical point of view. Measuring the D meson angular correlations with a generic charged hadrons, and even more with another charmed meson, is not an easy task, due to the low cross section for charm production and to the small branching ratios in the hadronic decay channels that allow D mesons to be experimentally reconstructed. This limits the yields of D mesons per event and hence the available statistics, especially for DD analyses. In addition, excellent capabilities for the D meson reconstruction (high efficiencies) and selection (good background D rejection) are required for the detectors, in order to reduce the influence of the background from misidentified D mesons. The first results on charm correlations in pp collisions were obtained by the STAR experiment at RHIC, from events at s = 200 GeV. Due to the absence of a vertexing detector, the S/B ratio for D 0 meson signal peaks was very small, preventing any measurement of charm-charm correlations by STAR. Anyway, it was possible to obtain azimuthal correlation distributions between D 0 mesons and nonphotonic electrons, which are mainly produced by semileptonic decays of heavy flavour mesons. The left panel of Fig shows the background-subtracted invariant mass distribution of D 0 K π + candidates reconstructed in events with at least one nonphotonic electron triggered. A clear peak is visible in correspondence to the D 0 mass. In the right panel of the same figure the azimuthal correlation distribution between nonphotonic electrons (positrons) and D 0 (D 0 ) is shown [88]. The distribution, despite the very large uncertainties, suggests that near and awayside peaks have similar yields. Data results are fitted with the correlation functions obtained from PYTHIA and MC@NLO simulations for charm and beauty contributions, having the relative contribution of the latter as a free parameter. This kind of analysis should allow us to separate charm and beauty contribution to D meson production, since selecting the charge combinations e D 0 and e + D 0 grants almost pure samples of B decays and charm quark pairs in the near side and away side peaks, respectively [89]. More detailed studies on charm-charm correlations were performed at Tevatron, where the luminosity and the center-of-mass energy were sufficient to allow the analysis of DD correlations with enough precision. In Fig the cross section for the production of D 0, D (left panel) and D +, D (right panel) meson pairs is shown as a function of the azimuthal angle difference ϕ, in pp collisions at s = 1.96 TeV [90]. The D mesons are reconstructed at central rapidity, in the high p T region. Using a D meson grants cleaner data samples. Results from PYTHIA simulations [83] with tune A [91] are superimposed to the data, both for the total cross section and for the single contributions from the three main production 50

53 CHAPTER 1. Charm production in hadronic collisions Figure 1.29: Left: background-subtracted invariant mass distribution of D 0 mesons, reconstructed from the Kπ decay channel, in events with at least one nonphotonic electron. A Gaussian fit is evaluated for the data near the peak region. Right: azimuthal correlation distribution between nonphotonic electron (positron) triggers and D 0 (D 0 ). Error bars represent statistical errors, green boxes systematic uncertainties. Fits using the correlation functions from PYTHIA (solid line) and MC@NLO (dashed line) simulations are superimposed to data. 51

54 CHAPTER 1. Charm production in hadronic collisions processes. Data show a similar contribution from collinear ( ϕ 0) and back-toback ( ϕ π) production to the correlation distribution in both cases. Although showing an overall agreement, PYTHIA simulations appear to underestimate the collinear production of D mesons, showing a shift toward production at opposite azimuthal angles. Figure 1.30: Cross section for production of D 0, D (left panel) and D +, D (right panel) meson pairs against the azimuthal angular difference, measured from CDF experiment in pp collisions at 1.96 TeV. Data results are compared to PYTHIA simulations for total cross section (black line) and for pair production (red), flavour excitation (green) and gluon splitting (blue) contributions only. Further analyses on D meson angular correlations are currently ongoing at the LHC. At present, LHCb has very recently published results for angular correlations of charmed hadrons, both in the open and in the hidden sector, evaluated in pp collisions at s = 7 TeV [31]. As an example, the ϕ and y distributions of DD meson pairs, expected to be uncorrelated since they come from independent hard processes, are compared to the distribution of DD (and D 0 Λ c ) pairs, where a significant contribution comes from mesons produced from quarks involved in the same hard scattering process. For the DD distributions, shown in Fig. 1.31, the ϕ shape is reasonably flat and the y distribution shows a triangular shape. These trends are consistent with uncorrelated production with a flat shape for the single D meson y distribution. In contrast, for the DD distributions (Fig. 1.32) an enhancement is visible for small ϕ and y values, compatible with production of charm pairs through gluon splitting mechanism. In Section the theoretical approaches for the perturbative calculation of charm production cross section have been described. Most of them, like FONLL and GM-VFNS, cannot predict the angular correlation distribution of charm quarks or of their hadronization products. The scheme with the best capabilities for the evaluation of cc or DD correlations is the k T -factorization approach [28 30]. For illustration, the predictions for azimuthal correlations of D 0 and D 0 in pp collisions at s = 7 TeV are shown in Fig. 1.33, compared to measurements from the LHCb experiment [31]. In the left panel the theoretical predictions are shown for different unintegrated gluon distributions (UGDFs) and fixed QCD factorization and renor- 52

55 CHAPTER 1. Charm production in hadronic collisions Figure 1.31: Distributions of azimuthal angle difference (left panel) and rapidity difference (right panel) for D 0 D 0 (red) and D 0 D + (blue) pairs, measured by LHCb in pp collisions at 7 TeV. The expected y distribution for uncorrelated pairs is shown with a dashed line. Figure 1.32: Distributions of azimuthal angle difference (left panel) and rapidity difference (right panel) for D 0 D 0 (red), D 0 D (blue), D 0 D s (violet) and D 0 Λ c (cyan) pairs, measured by LHCb in pp collisions at 7 TeV. The expected y distribution for uncorrelated pairs is shown with a dashed line. 53

56 CHAPTER 1. Charm production in hadronic collisions malization scales, while on the right panel the predictions obtained using KMR UGDF (better reproducing inclusive charm production data) are shown for different values of the two scales. Despite a slight shift of the predictions toward the away side region of the ϕ distribution, a good overall agreement is reached, confirming the validity of this theoretical model. Figure 1.33: k T -factorization model predictions for the distribution of the relative azimuthal angle between D 0 and D 0 produced at forward rapidity in pp collisions at s = 7 TeV. In the left panel calculations are shown for three different UGDFs at fixed values of the QCD scales; in the right panel the KMR UGDF is used and the QCD scales are varied between m c /2 and 2m c values. Measurements from LHCb (red data points) are superimposed to theoretical predictions. Figure taken from [30] Characterization of parton energy loss via jet quenching The study of two-particle correlations in heavy ion collisions can provide additional information about the parton energy loss in a QGP medium by investigating the jet quenching effect. In pp collisions the hadronization of two energetic partons produced via hard scattering usually results in a back-to-back jet production, except for cases in which high-momenta gluons are radiated from the partons, producing a third jet and breaking the back-to back azimuthal correlation. When the energetic partons are produced in a QGP medium, instead, they lose energy while travelling the medium and, if their path length in the medium is long enough, they do not have sufficient energy to manifest as a jet. The jet suppression effect results in a suppression of the away side peak (for ϕ π) in the azimuthal correlation distribution of the particles produced in the event, if the track with the highest p T is chosen as trigger particle. With this trigger choice, indeed, in most of the cases the trigger particle will be the leading particle of a jet, coming from a parton produced in a hard scattering. The correlations of the trigger with the other particles composing its jet, hence, give rise to a near side peak 54

57 CHAPTER 1. Charm production in hadronic collisions at ϕ 0. If the other parton produced in the hard scattering loses enough energy while traversing the medium, no other jets will be reconstructed in the event. This occurs, for example, when the hard scattering occurs near the surface of the medium produced in the collision, as shown in the left panel of Fig On average, the absence of the other jets in heavy ion collisions results in the suppression of the typical away side peak in the correlation distribution. The away side peak suppression was observed for the first time by STAR [92, 93] and PHENIX [94] experiments at RHIC, by comparing the ϕ correlation of charged particles with respect to a high-p T trigger particle in Au-Au, d-au and pp collisions, all at s NN = 200 GeV. The right panel of Fig shows the two-particle azimuthal distribution normalized to the number of trigger particles, measured by STAR in d-au collisions (a) and Au-Au collisions (b), compared to results from pp collisions [92]. In the Au-Au case, while the shape of the near side peak is very similar to the pp one, a dramatic suppression is visible for the away side, where the peak is completely missing, leaving a flat distribution of azimuthal correlations in the ϕ π region. The analysis of pa correlations is mandatory to disentangle the final state effects, due to the presence of the hot nuclear medium after the collisions, from the initial state effects, like the nuclear shadowing or the k T broadening [95]. These effects result in an enhancement of the baseline value of the azimuthal correlation distribution, as can be seen in Fig In this interpretation, therefore, the away side suppression is due to the medium produced in heavy ion collisions, since this feature is not observed in the d-au system. Figure 1.34: Left: sketch describing the jet production in heavy ion collision, for an hard scattering occurring near the surface of the fireball. The parton produced in the outward direction fragments in a jet, while the other one is quenched by the medium. Right: azimuthal correlations between a high-p T trigger particle and other charged particles produced in d-au events (upper panel, for minimum-bias and 0-10% centrality class events) and Au-Au central events (bottom panel), compared to pp correlation distribution (solid line). Measurements performed by STAR in s NN = 200 GeV collisions. 55

58 CHAPTER 1. Charm production in hadronic collisions At the LHC, the much larger cross section for jet production opens a new kinematic regime for jet quenching studies in heavy ion collisions, increasing at the same time the accuracy of the measurements performed at RHIC. Some results for light quark jet suppression have already been published. In Fig measurements of the I AA observable are shown, performed by ALICE in Pb-Pb collisions for different centralities at s NN = 2.76 TeV [96]. I AA is defined as the ratio of the particle yield in the near side (or away side) peak of the azimuthal correlation distribution in heavy ion collisions over the yield in pp collisions. A value of I AA = 1 denotes no effects of the nuclear medium on the jet production in heavy ion collisions, while an I AA > (<) 1 evidences an enhancement (suppression) of the number of particles present in the jets in those collisions. In particular, on the near side, I AA describes the features of the fragmenting jet escaping the medium, while on the away side it quantifies the probability that the other parton from the hard scattering survives the passage through the fireball. According to ALICE measurements, no particular medium effects are present in peripheral collisions, for both near-side and away-side peaks (red points). Dramatic effects are instead visible for the most central collisions. Here a slight enhancement ( 20-30%) of the yield occurs in the near side peaks, never observed before in experiments at lower energies [93]. Several effects could produce this enhancement, i.e. a softening of the fragmentation functions in the medium, a change of the quark/gluon jet ratio with respect to pp collisions or some bias in the parton p T spectrum after the energy loss due to the trigger particle selection. In general, all the three effects are expected to contribute. By studying I AA in the away side, instead, a decrease of the yield is evident, due to the parton in-medium energy loss. The suppression is weaker by about 50% with respect to measurements made at RHIC, differently from R AA measurements, which showed a smaller charged particle R AA measured by ALICE with respect to that obtained by RHIC [97]. The increase of the charm and beauty production cross section at LHC energies should allow, for the first time, to study jet suppression effects also for heavy flavour quarks. Combining these information with nuclear modification factor measurements, a clearer picture will be available for the behaviour of heavy quarks in a QGP medium. A study by Nahrgang, Aichelin, Gossieau and Werner has suggested that the azimuthal correlation distribution between heavy flavour mesons may give useful indications to discriminate the relative contributions of collisional and radiative parton energy loss, induced by the QGP medium in heavy ion collisions [98]. In this model, which uses a hybrid EPOS + MC@sHQ transport approach, the heavy quarks are generated according to the p T distributions from FONLL calculations [20], then propagated through the medium using the Boltzmann equation and finally hadronized, via coalescence at low p T and via fragmentation at high p T. As previously noticed, the next-to-leading order pqcd processes result in a broadening of the back-to-back correlation distribution of heavy quarks. However, due to the theoretical uncertainties on the initial azimuthal ϕ distributions, the cc pairs were 56

59 CHAPTER 1. Charm production in hadronic collisions Figure 1.35: ALICE measurements for I AA observable for near side (left panel) and away side (right panel) peaks, for central (0-5% open black symbols) and peripheral (60-90%, filled red symbols) Pb-Pb collisions. The different symbols correspond to different background subtraction schemes, using a flat pedestal (squares), using v 2 subtraction (diamonds) and subtracting the large η region (circles). generated strictly back-to-back. For bb pairs, instead, the heavier quark mass allowed to differentiate the ϕ distribution of the quark pairs coming from the various processes. In addition, a global and temperature-independent K-factor was introduced as scaling factor for the pqcd cross sections for heavy quark production, in order to match the LHC data for the high p T D meson R AA. The azimuthal correlation distribution of DD pairs coming from cc quarks initially produced together is shown in the left panel of Fig. 1.36, calculated from the model for Pb-Pb collisions at s NN = 2.76 TeV, in the 0-7.5% centrality class. In the right panel of the same figure, the distribution is shown only for the pairs where both mesons have p T > 3 GeV/c. Results for scenarios with collisional energy loss only, radiative energy loss only and with both energy loss mechanisms are shown, together with the respective values of the K-factor. The correlation distribution with no p T -cut, dominated by low p T pairs, is rather flat for the collisional+radiative scenario, while a broad peak at ϕ 0 is observed for the purely collisional scenario. This feature can be explained by the partonic wind effect: the radial flow of the medium pushes a low p T cc pair, initially produced back-to-back, toward smaller angular separations [99]. When the p T -cut is introduced and only intermediate and high p T mesons are considered, in the purely radiative scenario the characteristic away side peak at ϕ π appears in the ϕ distribution, with almost no correlations found outside it, while in the purely collisional case most of the initial correlation pattern disappears after the interaction of the quarks with the medium. Due to the differences in the distributions, the study of azimuthal corre- 57

60 CHAPTER 1. Charm production in hadronic collisions lations between heavy flavour hadrons could help in disentangling the two energy loss mechanisms, differently from the commonly used R AA and v 2 observables. In practice, however, this is an extremely challenging goal, since a large background coming from independently produced DD pairs would be also present in the correlation distributions, making difficult to distinguish the contribution coming from DD pairs produced in the same hard scattering. Figure 1.36: Azimuthal correlations of DD pairs, in purely collisional (orange solid line), collisional+radiative (balck dotted line) and purely radiative scenarios (blue dashed line), for Pb-Pb collisions at s NN = 2.76 TeV, from the model described in [98]. Results are shown without (left panel) and with (right panel) a p T -cut on both D mesons. 58

61 Chapter 2 The ALICE experiment at the LHC 2.1 The Large Hadron Collider The Large Hadron Collider is the state-of-the-art in particle accelerators, being the most powerful collider being ever built. It consists of a 26.7 km double ring of superconducting magnets, located in a tunnel dig m underground, previously hosting the electron-positron LEP collider, at the Swiss-French border, near Geneva. The LHC has already delivered proton-proton collisions at a maximum centerof-mass energy of s = 8 TeV and heavy ion (Pb-Pb) collisions at s NN = 2.76 TeV 1. The LHC can also deliver proton-ion (p-pb) collisions. The first p-pb data taking, at a center-of-mass energy of s NN = 5.02 TeV, occurred in the first months of Collisions take place in various intersection regions between the two rings, in correspondence to the main experiments installed along the LHC tunnel. Moreover, LHC grants the highest design luminosity of all current accelerators, set at cm 2 s 1 for proton beams and at cm 2 s 1 for lead beams [100]. Some of the basic features of the LHC machine are reported in Tab Since the two beams are made of particles with the same charge, they have to circulate in opposite directions and in different rings. Each ring has separate magnetic fields and vacuum chambers, except for the intersection regions. The outstanding performance of LHC are achieved by using superconducting magnets that are at the edge of actual technology. These magnets are able to sustain a magnetic field of around 8.4 T, with a cooling system which keeps them at a temperature below 2 K. Due to spacing limitations, they are realized in a 2-to-1 design, which let them accommodate inside the LHC tunnels. The proton beams accelerated by the LHC come from a series of pre-accelerators, 1 The LHC design energies are s = 14 TeV for pp collisions, 7 times higher than Tevatron energy, and s NN = 5.5 TeV for Pb-Pb collisions, a factor 30 higher than RHIC energy. They will be gradually reached in the next data taking runs. 59

62 CHAPTER 2. The ALICE experiment at LHC Table 2.1: List of LHC basic parameters. Quantity Number Circumference m Dipole operating temperature 1.9 K Number of magnets 9593 Number of main dipoles 1232 Number of main quadrupoles 392 Number of RF cavities 8 per beam Nominal energy, protons 7 TeV Nominal energy, ions (per nucleon) 2.76 TeV Peak magnetic dipole field 8.33 T Min. distance between bunches 7 m Design luminosity cm 2 s 1 (pp) No. of bunches per proton beam 2808 No. of protons per bunch (at start) Number of turns per second Number of collisions per second 600 million which bring them to the minimum energy sustainable by the collider. The basic structure of the chain of CERN accelerators is shown in Fig In particular, protons extracted from a hydrogen tank are injected in the Linear Accelerator 2 (Linac2), which accelerates them to an energy of 50 MeV. They pass then to the Proton Synchrotron Booster (PSB) and subsequently to the Proton Synchrotron (PS) accelerator, which pushes them to 50 GeV, before getting to the Super Proton Synchrotron accelerator (SPS), which brings them to the threshold energy of 450 GeV. From the SPS they are finally injected in the LHC. For the Pb beams, lead atoms are extracted from a piece of lead, heated to about 500 C to vaporize a small quantity of atoms. Some of their electrons are removed by a strong electric field, allowing the ions to be accelerated in a linear device, where they become fully ionized. The ions are then injected and accumulated in a Low Energy Ion Ring (LEIR) and then in the PS. From there on they follow the same chain as protons Luminosity definition and luminous region Luminosity (L) is one the main parameters defining the capabilities of a particle accelerator. It is linked to the cross section of any process σ int and to the rate at which it occurs R: R = L σ int. (2.1) L is completely defined by the characteristics of the beams at the interaction regions. In a collider, the beams travel in opposite directions, are composed of bunches of 60

63 CHAPTER 2. The ALICE experiment at LHC Scheme of the LHC accelerator, its experiments and its chain of pre- Figure 2.1: accelerators. particles and they collide in specific interaction points (IP). In this case it is possible to define the luminosity as described below. Let us consider the case of beams with bunches travelling in opposite z directions. At a good approximation, the distribution of the particles in two colliding bunches can be described with a Gaussian distribution G in each direction: N i (x, y, z) = N i G(x, x i, σ x,i ) G(y, y i, σ y,i ) G(z, z i, σ z,i ), (2.2) where the index i = 1, 2 identifies the bunches, N i the total number of particles in the bunch and G(x, x i, σ x,i ) the Gaussian distribution, with mean x i and standard deviation σ x,i, for the x spatial coordinate (same for y, z). Denoting N b as the number of bunches in the beams and f as the collider revolution frequency, the 61

64 CHAPTER 2. The ALICE experiment at LHC luminosity can be defined by: L = f N b dx dy dz N 1 (x, y, z) N 2 (x, y, z). (2.3) Let us assume for the sake of simplicity that the number of particles in the bunches is constant (N) and that the dispersions of the particles in the bunches in the transverse directions are the same and do not vary with time (σ x = σ y σ xy ). Since the two bunches are travelling along the z axis and they completely cross each other, the integration over this axis gives 1. The definition of L can consequently be rewritten as follows: ) N 2 L = f N b exp ( d2, (2.4) 4πσx,y 2 4σx,y 2 where d 2 is the square of the separation between the two bunches centres in the beam transverse direction. The interaction region can be defined as the convolution of the two particle distributions of the colliding bunches and, for perfectly overlapping (d = 0) collimated beams, it results in a diamond shape with extension: σ lumireg q = σ q / 2, with q = x, y, z. (2.5) The dispersion of the beams at the interaction point is defined by the transverse emittance ɛ q (a beam quality parameter) and the amplitude function β (which depends on the LHC magnets configuration): ɛq β σ q = π. (2.6) The luminosity value for each LHC experiment can by adjusted to fit its requisites by varying the β parameter. The adjustment can be performed by tuning the magnet configuration at each interaction point along the rings. Another possibility is to increase the displacement between the two colliding beams (the quantity d previously introduced); this occurs, for example, during pp data taking at the ALICE interaction point, where LHC delivers a lower luminosity than for the other experiments. From the luminosity defined above (or peak luminosity), another figure of merit can be defined, the integrated luminosity L int : L int = T 0 L(t )dt. (2.7) The integrated luminosity accounts for the decay of the luminosity with time, due to several causes, e.g. the decrease of the beam intensities with time, the growth of the transverse emittance, the increase of the bunch length. 62

65 CHAPTER 2. The ALICE experiment at LHC This quantity is directly related to the number of events N ev in which a given process, with cross section σ p, occurs: L int σ p = N ev. (2.8) The integrated luminosity allows, thus, to quickly estimate how many times any process can be observed over the statistics collected by an experiment LHC experiments and physics programme Collisions delivered by the LHC are analyzed by various experiments, located in its tunnel at the intersection points of the two beams. The main experiments hosted at the LHC are four. A Toroidal Large Acceptance Solenoid (ATLAS) [101] and the Compact Muon Solenoid (CMS) [102] are general purpose experiments designed to address a wide range of physics at the LHC, from the study of the Higgs boson to the search for supersymmetry (SUSY) and extra dimensions. Despite being dedicated to pp studies, they also study heavy ion collisions. A Large Ion Collider Experiment (ALICE) [103] has as main goal the study of the Quark Gluon Plasma properties. It was hence designed to work in an environment with extremely high density of tracks; it has a rich pp programme too. LHCb [104], the fourth main experiment, with an acceptance only in the forward rapidity region, is specialized in studying the physics of beauty quarks and in spotting CP-violation signatures in the heavy flavour sector. LHC delivered the first proton beams in September 10 th Due to a malfunctioning of an electrical connection between two superconducting magnets [105], however, the accelerator had to be stopped after only 9 days of running. LHC was restarted after more than one year, in November For safety reasons it was decided to circulate beams at lower energies, raising it gradually in the following years. The first pp collisions after the restart were thus taken at s = 900 GeV, to ensure the right functioning of the machine and its systems, while in 2010 the center-of-mass energy for pp collisions was brought to 7 TeV. During this run, the accelerator delivered a peak luminosity of L = cm 2 s 1, with 368 bunches spaced by 150 ns. This granted an integrated luminosity of about 1 pb 1 collected by ALICE. In the last months of 2010 Pb-Pb collisions at s NN = 2.76 TeV were delivered too. During this first Pb-Pb run all the main experiments collected an integrated luminosity of 10 µb 1, with a peak luminosity of L = cm 2 s 1. In 2011, while leaving the energy of the beams unchanged, the luminosity in pp runs was increased to L = cm 2 s 1 and the number of bunches was raised to 1380, with a spacing of 50 ns. This led to an integrated luminosity collected by ALICE of about 5 pb 1. In April 2011 another pp run was performed at s = 2.76 TeV, the same energy of the Pb-Pb collisions; data from this run are used as reference to directly compare the results in heavy ion and proton collisions. Finally, in the last months of the year, the Pb-Pb run took place, again at s NN =

66 CHAPTER 2. The ALICE experiment at LHC TeV, with the ALICE experiment collecting an integrated luminosity of about 0.1 nb 1. In 2012 the LHC programme was dedicated to pp collisions. The center-of-mass energy was slightly increased to s = 8 TeV and the peak luminosity brought to L = cm 2 s 1. This lead to a factor 2 for the integrated luminosity increase of ALICE with respect to the 2011 value (about 10 pb 1 collected). In the first two months of 2013 the LHC delivered p-pb collisions, with s NN = 5.02 TeV. This run is of great interest for the ALICE research programme, since it gives the possibility to study the initial state modifications on the physics observables already studied in Pb-Pb collisions, as described in the previous chapter. During this data taking ALICE gathered an integrated luminosity of almost 32 nb 1. The trend of integrated luminosity collected by the main LHC experiments during 2012 pp and 2013 p-pb data taking is shown in Fig In all the pp runs, the ALICE experiment requested a reduction of the peak luminosity delivered by LHC at its interaction point. The ALICE physics programme, indeed, is mainly focused on the study of minimum-bias collisions, even though certain rare triggers are exploited in various analyses. Having a lower luminosity, thus, allows a complete recover of the Time Projection Chamber and prevents pile-up issues in the Silicon Drift Detector (SDD). For this reason, the integrated luminosity collected for pp collisions is much lower than for the other three main experiments, as visible in the figure. After the 2013 p-pb data taking, the LHC machine entered the first long shutdown (LS1) phase, scheduled to last until the end of During this period, maintenance work and modernization of the infrastructures is taking place, while the accelerator will be prepared to operate at higher energies after the restart. A tentative schedule for the future operations after the LS1 plans to bring the center-of-mass energy to almost the maximum value (6.5 TeV energy for proton beams), increasing the peak luminosity, and to have 2-3 years of pp and heavy ion runs. Then a second long shutdown (LS2) will follow in , during which major upgrades will be brought to all the detectors and to the LHC itself. The operations would resume in 2019 with beams circulating at the design energy, to allow collisions with s = 14 TeV for pp and s NN = 5.5 TeV for Pb-Pb at the design peak luminosity, with beams composed by 2808 bunches with 25 ns spacing for the pp runs. In this configuration, the LHC should continue to provide pp, p-pb and Pb-Pb collisions for the following years. 2.2 Overview of ALICE Experiment Among the four main LHC experiments, ALICE is the one dedicated to the study of the heavy ion collisions delivered by the collider. Its primary goal is to investigate the properties of the Quark Gluon Plasma (QGP), produced in these collisions, where extremely high values of energy density and temperature are reached. The whole experiment has been designed to study QGP signatures through a set of ob- 64

67 CHAPTER 2. The ALICE experiment at LHC Figure 2.2: Integrated luminosity delivered to ALICE (red), ATLAS (black), CMS (green) and LHCb (blue) experiments in 2012 pp (left plot) and 2013 p-pb (right plot) runs [106]. servables already covered by previous experiments at different accelerators (AGS, SPS, RHIC) in nucleus-nucleus collisions, but at much higher energies. Besides this challenging heavy ion programme, ALICE can grant also solid performance in the analysis of proton-proton and proton-nucleus collisions and presents a rich programme for these systems too. Moreover, the analysis of these collisions is mandatory to produce references for the comparison of the nucleus-nucleus observables, in order to spot and quantify the modifications caused by the QGP effects. One of the hardest challenges for the study of heavy ion collisions is the highmultiplicity environment the detectors have to cope with. In particular, the first estimates for charged track multiplicity in Pb-Pb collisions at LHC energies expected a range of dn ch /dη between 1500 and They were made when ALICE was being designed, and were based on the extrapolation of AGS and SPS results only, which are at much lower energies. For this reason, ALICE was optimized to work in an environment of dn ch /dη = 8000, enhancing the potentiality of the tracking systems and the granularity of the detectors while partially sacrificing the capability to work at very high collision rates. Only after RHIC measurements the upper limit for the average dn ch /dη value was lowered to Based on the first ALICE measurements, which resulted in dn ch /dη = 1584 ± 4 (stat.) ± 76 (syst.) at s NN = 2.76 TeV, the multiplicity estimate for the maximum energy of s NN = 5.5 TeV is now about 1/4 of the design value (dn ch /dη 1800). The ALICE experiment is capable of reconstructing tracks over a wide p T range (about 3 orders of magnitude), with a very low p T reach (down to 0.1 GeV/c for pions). To grant this result, the track reconstruction is performed with the help of various detectors, each with a great number of reconstructed points (up to about 200 for a track which passes through the whole detector at central rapidity), with 65

68 CHAPTER 2. The ALICE experiment at LHC the possibility of a three-dimensional tracking. Moreover, the material budget of the whole experiment is kept very low through the usage of light materials in tiny layers, especially for the inner detectors. A remarkably low value of 13% X 0 is obtained from the primary vertex to the outer edge of the Time Projection Chamber. This helps to reduce the effects of Coulomb multiple scattering, which spoil the lowp T measurements. The tracking capabilities are also enhanced by the mild value chosen for the magnetic field of the central solenoid (B = 0.5 T). This value is a compromise between the requirement of having a bending power high enough to allow p T measurement up to GeV/c and the necessity of granting that the low-p T particles could reach the outer parts of the detector. ALICE grants also excellent particle identification (PID) performance, exploiting in its detectors all the known techniques: specific energy loss (de/dx) measurements, transition radiation, Cherenkov radiation, time-of-flight measurements, calorimetry, muon filtering and reconstruction of decay topologies. A sketch of the ALICE experiment is shown in Fig The overall dimensions of ALICE are m 3, with a total weight of about t. It is composed of 18 different detectors, mainly grouped in two regions: a central barrel, capable of measuring hadrons, electrons and photons produced at central rapidity values, and a forward muon spectrometer, being able to reconstruct muons in the forward rapidity range. A set of smaller detectors is located at forward and backward rapidity for triggering and event characterization. 66

69 CHAPTER 2. The ALICE experiment at LHC Figure 2.3: Layout of the ALICE experiment. 67

70 CHAPTER 2. The ALICE experiment at LHC The central barrel covers a pseudorapidity range of 0.9 < η < 0.9, corresponding to a polar angle coverage of 45 < θ < 135. It is embedded into a magnetic field of 0.5 T, generated by the large solenoidal magnet already used in the L3 experiment. The beam pipe in which beams circulate and collisions take place is made of beryllium, with a 3 cm radius and a 800 µm thickness, corresponding to 0.3% X 0. Going outwards from the beam pipe the following detectors are located: The Inner Tracking System (ITS), a silicon detector system for tracking and vertexing, composed of two pixel (SPD), two drift (SDD) and two strip (SSD) detector layers; The Time Projection Chamber (TPC), a huge cylindrical chamber filled with gas, which acts as the main ALICE tracking detector; The Transition Radiation Detector (TRD), excellent for high energy electron identification (γ > 1000) exploiting transition radiation emission; The Time Of Flight (TOF), dedicated to particle identification, capable of π/k separation up to 2.2 GeV/c and of K/p separation up to 4 GeV/c; The High Momentum Particle IDentification (HMPID), which is a Ring Imaging Cherenkov detector used for identification of π, K, p in the 1 < p T < 5 GeV/c range, with a coverage of 15% of the barrel ( η < 0.6, 57.6 azimuthal coverage); Two electromagnetic calorimeters, PHOS and EMCal; PHOS has an higher granularity than EMCal, but covers a smaller acceptance region; ACORDE, a scintillator array placed outside the magnet for cosmic ray measurements and triggering; The forward muon spectrometer covers the pseudorapidity region 4 < η < 2.5 and is optimized to track heavy flavour decay muons. It allows the measurement of charmonium and bottomonium (J/Ψ, Ψ and Υ, Υ, Υ ) production in the forward rapidity region. It is composed of a front absorber, to reduce the background, a dipole magnet which enables momentum measurement, and a series of tracking and trigger stations, for muons reconstruction, respectively made of Cathode Pad Chambers (CPC) and Resistive Plate Chambers (RPC). Several other systems complete the set of the ALICE detectors. The T0 and V0 systems are used for triggering purposes. The T0 is composed of two arrays of Cherenkov radiators located on the opposite sides of the interaction point, at different distances. It provides fast timing signals which are used for ALICE first level trigger, delivers a reference for the collision time used by the TOF and provides a wake-up call for the TRD detector. It covers pseudorapidity ranges of 3.3 < η < 2.9 (forward array) and 4.5 < η < 5 (backward array) and has a time resolution better than 50 ps. The V0 system comprises two disks of segmented 68

71 CHAPTER 2. The ALICE experiment at LHC plastic scintillator tiles read out by optical fibres, asymmetrically located on the two sides of the interaction point. It covers the 3.7 < η < 1.7 (VZEROC disk) and 2.8 < η < 5.1 (VZEROA disk) pseudorapidity ranges. It has a time resolution of about 0.6 ns. The main functionalities of the V0 are to supply the online first level centrality trigger for ALICE by setting a threshold on the deposited energy, to participate in the minimum-bias trigger in all the collision systems and to provide background rejection by contributing to exclude beam-gas events. It is also employed to determinate the centrality of Pb-Pb events. In addition, the Forward Multiplicity Detector (FMD) and Photon Multiplicity Detector (PMD) are used for multiplicity studies and luminosity measurements; the Zero Degree Calorimeters (ZCD), located at approximately 90 m from the interaction region, are used to evaluate the centrality of nucleus-nucleus collisions by measuring the energy released by the nucleons not participating to the collision. They also help in rejecting the background in Pb-Pb collisions. Tab. 2.2 summarizes the main characteristics and parameters of the ALICE detectors. ALICE coordinate frame is defined by taking the z axis parallel to the beam direction, pointing in the opposite direction of the muon spectrometer; the x axis is perpendicular to the beam direction, aligned with the local horizon and pointing towards the centre of the accelerator; the y axis is perpendicular to the x axis and to the beam direction, pointing upwards. Anyway, due to the cylindrical symmetry of the central barrel, a cylindrical coordinate frame is also widely used for the analyses involving barrel detectors. During the first years of data taking all the detectors were fully installed and functioning, with the exceptions of PHOS calorimeter (only 3/5 complete) and TRD (13/18 complete). Maintenance of malfunctioning components and installation of missing modules will occur in the LS1 period. 2.3 ALICE barrel detectors This section will present a detailed description of the three barrel detectors employed in the analysis of this thesis, namely ITS, TPC and TOF. The ITS was used for tracking and vertexing purposes, the TPC for reconstructing the charged tracks and, with the help of TOF, for pion and kaon identification Inner Tracking System The Inner Tracking System is the innermost detector of ALICE. It is composed of six silicon detector layers, at a distance varying from 3.9 cm to 43 cm from the beam axis. Each pair of layers constitute a different subsystem; the first two (closest to the beam pipe) are the Silicon Pixel Detector (SPD), having the best spatial resolution, the central two compose the Silicon Drift Detector (SSD), while the outer two are the Silicon Strip Detector (SSD). The ITS provides a full coverage 69

72 CHAPTER 2. The ALICE experiment at LHC Table 2.2: Main parameters of the ALICE detectors: acceptance, position, dimension and number of readout channels [103]. Detector Acceptance (η, φ) r position (m) Dimension (m 2 ) Channels ITS layer 1,2 (SPD) η < 2, η < , M ITS layer 3,4 (SDD) η < 0.9, η < , ITS layer 5,6 (SSD) η < 0.97, η < , M TPC η < 0.9 at r=2.8m 0.848, Readout 32.5 m η < 1.5 at r=1.4m Vol. 90 m 3 TRD η < , M TOF η < HMPID η < 0.6, 1.2 < φ < PHOS η < 0.12, 220 < φ < EMCal η < 0.7, 80 < φ < ACORDE η < 1.3, 60 < φ < Muon Spectrometer r position (m) Tracking station 1 4 < η < Tracking station Tracking station Tracking station Tracking station Trigger station 1 4 < η < M } Trigger station ZDC:ZN η < 8.8 ± ZDC:ZP 6.5 < η < 7.5 ± < φ < 9.7 ZDC:ZEM 4.8 < η < < φ < 16 and 164 < φ < 196 PMD 2.3 < η < FMD disc < η < 5.03 inner: 3.2 FMD disc < η < 3.68 inner: outer: FMD disc < η < 1.7 inner: outer: V0A 2.8 < η < V0C 3.7 < η < T0A 4.61 < η < T0C 3.28 < η <

73 CHAPTER 2. The ALICE experiment at LHC in the azimuthal angle, with a pseudorapidity acceptance of η < 0.9 for tracks coming from a primary vertex inside the interaction region. The main goals of the ITS detector are listed in the following: perform a standalone reconstruction of charged particles with very low p T, which curl before getting to the TPC; contribute to the combined tracking of higher p T increasing at the same time the p T resolution; particles with the TPC, reconstruct primary and secondary vertices with a spatial resolution good enough to separate the decay vertices of charm and beauty hadrons; contribute to PID by measuring the specific energy deposit (de/dx) in the 1/β 2 region of Bethe-Bloch curve (in SDD and SSD subsystems), with capabilities for standalone PID for low p T tracks. The ITS layout has been optimized in order to maximize the performance on tracking efficiency and impact parameter resolution (of vital importance for heavy flavour decay reconstruction). The inner radius (first SPD layer) was constrained by the dimension of the beam pipe, while the value for the outer radius (second SSD layer) was tuned to allow the best matching between ITS and TPC tracks. Another remarkable feature of the ITS is the exceptionally low material budget of the layers, the worst of which accounts for only 1.26% of a radiation length X 0. Even considering the support structures, the electrical interfaces and the cooling system, the overall material budget reaches only 7.66% of X 0 for perpendicular tracks, which limits the influence of the Coulomb multiple scattering. Fig. 2.4 shows the structure of the ITS detector, while Tab. 2.3 summarizes the main parameters of the six layers composing the detector [107, 108]. Table 2.3: List of basic parameters of each ITS layer: detector type, dimensions, number of modules, their active area, intrinsic spatial resolution, material budget [107]. Layer Type r [cm] ±z [cm] Number Active Area Material of per module Resolution budget modules rφ z [mm 2 ] rφ z [µm 2 ] X/X 0 [%] 1 pixel pixel drift drift strip strip

74 CHAPTER 2. The ALICE experiment at LHC Figure 2.4: Layout of the Inner Tracking System. Silicon Pixel Detector The two innermost layers of the ITS are equipped with pixel detectors (SPD), which have a crucial role in primary vertex reconstruction and secondary vertex tagging. Being very close to the beam pipe, this subsystem has to deal with high track density (up to 50 tracks/cm 2 ); hence, it is realized with high-granularity pixels of very small dimensions, with excellent resolution and two-track separation power. Each pixel is made of a diode junction with reverse bias and has a dimension of 50 µm (rφ) 425 µm (z), which grants an intrinsic spatial resolution of 12 (rφ) 100 (z) µm 2. Pixels are arranged in arrays of 32 (z) 256 (rφ) = 8192 pixels each, with a sensitive area of mm 2. To connect the pixels to the readout channels, each array is bump-bonded to a readout chip, which is segmented in 8192 pads (one for each pixel); this allows us to read separately each single pixel with a striking limitation of cabling and interfaces. The output of each pixel is a digital signal, without any information on the energy release of the crossing particle. The SPD thus does not contribute to the particle identification via specific energy loss determination. Five sets of pixel arrays are accommodated into a ladder, a silicon layer 200 µm thick with 12.8 mm (rφ) 69.6 mm (z) dimensions, while two ladders compose a half-stave, the basic detector element. The two SPD layers are composed of 60 total staves (each is made of two half-staves and covers the full SPD length), for a total of about pixels. The staves are slightly tilted and displaced, according to a turbo geometry, in order to ensure a coverage of the azimuthal angle without holes. 72

75 CHAPTER 2. The ALICE experiment at LHC The front view of the SPD detector is shown in Fig In addition to tracking and vertexing capabilities, the SPD can provide a first level (L0) trigger signal and it is commonly used in the definition of the selection of minimum-bias events, in all collision systems. It can also be used to define rare triggers, e.g. the one selecting high multiplicity events in pp collision. When at least one of the pixels of a chip array is fired, the chip generates a FAST-OR signal, which is able to reach the Central Trigger Preprocessor (CTP) with an overall time latency from the time of the interaction of about 800 ns [109]. Moreover, having a pseudorapidity coverage of η < 1.98, the inner SPD layer is able to provide a continuous coverage in pseudorapidity of about 8 units when combined with the FMD. This feature is exploited for measurements of charged particle multiplicity. Figure 2.5: Front view of the of SPD. It is possible to observe the disposition of the 60 staves composing the two detector layers. Silicon Drift Detector The two central layers of the ITS are composed of drift detectors (SDD). The SDD layers cover a η < 0.9 range and the full azimuthal angle and grant a good performance in track separation and de/dx measurement capability. The functioning principle is to measure the drift time of the electrons created by a particle traversing the active region. Each SDD layer is composed of modules, 84 and 176 for the inner and outer layers, respectively; each module is split in two drift regions separated by a central cathode strip. The cathode strips provide the electric field needed for 73

76 CHAPTER 2. The ALICE experiment at LHC charge drifting (intensity of approximately 500 V/cm). On each drift region, 256 anodes provide the charge collection. Three rows of MOS charge injectors are also used to monitor online the drift speed. Thus, when a particle crosses the active region of one module, generating e-h pairs, the electrons move from the generation points to the anodes, located at the edge of the modules. From the time needed to collect all the generated electrons, it is possible to retrieve the rφ coordinate of the track crossing point. The z coordinate can be obtained from the centroid of the collected charge distribution. In addition, since the collected charge is proportional to the energy release of the crossing particle, the SDD has also particle identification capabilities. The SDD subsystem has an intrinsic spatial resolution of 35 µm along rφ, slightly worse than SPD, and 20 µm along z, the best of the ITS subsystems for this coordinate. Figure 2.6 shows the structure of an SDD module. Figure 2.6: Left: basic structure of an SDD module. Right: principle of functioning of a linear SDD detector, with charge production, drifting and collection. Silicon Strip Detector The Silicon Strip Detector (SSD), composed of 1698 double-sided microstrip silicon sensors, comprises the two outermost layers of the ITS. It has the same azimuthal and pseudorapidity coverage of the SDD with a very good intrinsic spatial resolution in the rφ direction (20 µm), while due to the strip length and the stereo angle it has a poorer resolution along the z direction (about 830 µm). Being the outer ITS subsystem, the SSD plays a fundamental role in the prolongation of the tracks from the ITS to the TPC or vice-versa. Each microstrip sensor has a surface of mm 2 and is read by two hybrid circuits. A microstrip with its two readout circuits constitutes the basic SDD structure, called module. In the sensor area of each module 768 strips are implanted on each side; each strip is 40 mm long and there is a 95 µm pitch between two adjacent strips. The strips are not perpendicular to the sensor edges, but are slightly tilted, leading to a stereoscopic angle of 35 mrad between the strips on the two sides. This 74

77 CHAPTER 2. The ALICE experiment at LHC particular configuration was chosen to remove the ambiguities in the event reconstruction (ghost hits). The structure of an SSD module and of its sensor is shown in Fig The working mechanism of the SSD relies on the collection at the edges of the strips of the e-h pairs created by the passage of a charged track in the sensors, providing a two dimensional measurement of the position of the track crossing point. Also for this subsystem it is possible to relate the quantity of charge collected to the energy deposited by the crossing particle, allowing particle identification via de/dx measurement. Figure 2.7: Left: picture of an SSD module, showing the sensor and its readout hybrid circuits. Right: scheme of an SSD sensor structure. The alignment of the ITS modules was performed by using survey information, cosmic ray tracks and pp data, as described in [110]. A r.m.s. of approximately 8 µm and 15 µm was estimated for the residual misalignment along rφ of SPD and SSD modules, respectively. For the SDD, with the calibration level of the 2010 pp data taking, the space point resolution along rφ was estimated in about 60 µm for the modules which did not suffer of drift field non-uniformities. The precision of the alignment along z was estimated to be 50 µm for SPD and SDD and a few hundred µm for SSD [110, 111]. To take into account the residual misalignment, in the detector simulation the ITS modules were randomly displaced with respect to their ideal positions according to the estimated precision of the alignment Time Projection Chamber The Time Projection Chamber is the main tracking detector of ALICE. It is a cylindrical gas chamber, located at outer radii from the ITS, with a full azimuthal geometrical acceptance and a rapidity coverage of η < 0.9 for tracks completely trespassing the detector. The TPC is capable of three-dimensional reconstruction of charged particles with an extremely high number of points and with an outstanding spatial resolution. For this reason, the TPC is fundamental for event reconstruction and track finding (up to p T = 100 GeV/c), both in pp and Pb-Pb events. This detector also helps to reconstruct vertices and can provide particle identification in the 75

78 CHAPTER 2. The ALICE experiment at LHC low and intermediate p T region via de/dx measurement, plus statistical measurement of pion, kaon and proton yields at high p T exploiting the de/dx relativistic rise. The TPC was optimized to work properly with a number of tracks in its volume per event as high as 20000, as it was expected to occur in central Pb-Pb collisions at the time of ALICE design. A scheme of the TPC structure is shown in Fig. 2.8, while Tab. 2.4 reports some of its basic parameters and its performance [107, 112]. The inner radius, of 80 cm, was chosen on the basis of the maximum hit density sustainable by the detector (0.1 hits/cm 2 ), while the outer radius was set to 250 cm to grant a resolution better than 10% on the de/dx measurement; the length along the z direction is of 500 cm. The active volume of the detector is of 88 m 3, and it is filled with a gas mixture of Ne/CO 2 /N 2 with a 85.7/9.5/4.8 proportion 2, kept at atmospheric pressure. This particular mixture was studied in order to grant a quite high drift velocity of the charges (to keep under control the pile-up issue), a low diffusion coefficient and negligible Coulomb multiple scattering (to increase the spatial resolution). Due to the strong dependence of the drift velocity on temperature, the detector temperature has to be kept constant and uniform along the whole drift volume. The TPC cage is divided in two sections by a high voltage electrode, which generates a drift electric field of about 400 V/cm. A field cage grants an excellent uniformity of the field along the z axis. A charged track which traverses the detector creates e-h pairs along its path; these charge drift toward the endcaps of the cylinder due to the presence of the electric field. The electric signal is amplified through an avalanche cascade, which occurs when the charges approach the anode wires, located in the readout chambers. The readout chambers are MWPC with segmented cathode, which allow a bidimensional measurement, while the third coordinate is obtained by measuring the drift time. They are located on the TPC endcaps, which in turn are segmented in 18 sectors around the azimuthal angle of 20 each. The presence of a small gap between each MWPC limits the azimuthal acceptance to about 90%. The major TPC limitation comes from the distortion of the electric field produced by the ionized gas in high multiplicity environments. This leads to errors in spatial measurements up to few mm. To avoid this issue it is necessary to limit the interaction rate to a value which consents the full drift of the charges in the active volume. At the average drift velocity of 2.7 cm/µs, the maximum drift time to cover the detector length is about 92 µs, a value which defines the maximum event rate sustainable by the TPC. The material budget of the TPC is 3.5% of X 0 at central rapidity growing to about 5% at η = 0.9. The resolution on the de/dx determination, for tracks crossing the entire detector, was measured to be about 5.5% by using cosmic ray tracks and pp data [113]. This grants good PID capabilities from 200 MeV/c up to almost 1.5 GeV/c, allowing in some cases to statistically separate species also in 2 The N 2 gas was added to the mixture during the prototyping phase, but then removed from 2010 onwards, leading to a Ne/CO2 gas with 90/10 proportion. 76

79 CHAPTER 2. The ALICE experiment at LHC the relativistic rise region of the Bethe-Bloch curve. The resolution on the track momentum is as low as 1% for low momentum tracks (p T 1 GeV/c), worsening for increasing momenta (about 3.5% for p T 100 GeV/c). Figure 2.8: Layout of the Time Projection Chamber Time Of Flight The main goal of the TOF detector is the identification of charged particles produced at central rapidity in momentum regions where it is no longer possible to exploit the de/dx measurements, i.e. above momenta of about 1 GeV/c. The TOF covers the full azimuthal angle and has the same pseudorapidity coverage as ITS and TPC ( 0.9 < η < 0.9), which allows a study of the interesting observables on an event-by-event basis. The TOF is located 3.7 m far from the beams axis, covering a surface of about 150 m 2. It is segmented in 18 sectors along φ; each sector lies in the z direction and is composed of 5 modules, which are the basic structures of the detector. On the modules a certain number of Multigap Resistive Plate Chamber (MRPC) strips is placed (15 to 19, depending on the position of the module). The MRPC come in a total number of 1638, with an active area of cm 2 each. Their role is to detect the passage of tracks through the module, providing the time information of the passage. This is obtained by collecting the avalanche charges produced immediately after the track crossing. Since there is no drift time for these elements, the only time jitter comes from fluctuations in the avalanche production and growth. It is also necessary to reduce the transverse path of the particles through the strip, which could cause a sharing effect of the signal among adjacent pickup pads and increase the time jitter of the signals. This is fulfilled by varying the angle that the strips form with the axis of the TOF cylinder; this angle increases from 0 in the 77

80 CHAPTER 2. The ALICE experiment at LHC Table 2.4: Main geometrical and performance parameters of the TPC detector. Quantity Value Pseudorapidity coverage 0.9 < η < 0.9 for full radial track length 1.5 < η < 1.5 for 1/3 radial track length Azimuthal coverage 2π Radial position (active volume) 845 < r < 2466 mm Radial size of vessel 780 < r < 2780 mm Length (active volume) 5000 mm Segmentation in φ 18 sectors Segmentation in r Two chambers per sector Segmentation in z Central membrane, readout on two end-plates Total number of readout chambers = 72 Detector gas Ne/CO 2 90/10 Gas volume 88 m 3 Drift length mm Drift field 400 V cm 1 Drift velocity 2.84 cm µs 1 Maximum drift time 88 µs Total HV 100 kv Diffusion D L = D T = 220 µm cm 1/2 Material budget X/X 0 = 3.5 to 5% for 0 < η < 0.9 Position resolution In rφ µm (inner/outer radii) In z µm de/dx resolution Isolated tracks 5.5% dn/dy 6.9% central part of the sector up to 45 in the external parts (at the end of the barrel). An overlap of 2 mm between adjacent strips in the same module avoids the presence of dead areas. Each strip is endowed with 96 readout pads, for a total number of readout channels, granting extreme granularity and the possibility to operate in an environment with high track density like the Pb-Pb collisions. A drawing of a TOF sector and of the structure of a TOF module is shown in Fig Tab. 2.5 summarizes some of the main specifics of the TOF detector, together with its capabilities and merit parameters. As described in Section 2.4.1, the particle identification is performed by measuring the time of flight of the particles from the primary vertex to the TOF detector, by combining the arrival time information extracted from the TOF itself and the T0 detector, which gives the start time. In high-multiplicity collisions, however, also the start time is evaluated with the TOF, using the information from the other particles produced in the event. It is therefore crucial to achieve an excellent precision in tagging the moment in which the tracks cross the detector. 78

81 CHAPTER 2. The ALICE experiment at LHC The time resolution of a MRPC has been measured to be less than 50 ns, leading to a total time resolution of approximately 160 ps for the whole TOF. This guarantees a 3σ separation up to 1.9 GeV/c for K/π and up to 3.2 GeV/c for p/k. This momentum range is crucial for heavy flavour studies, since most of the products of heavy flavour hadron decays, mainly pions and kaons, exhibit momenta inside this region. Results from the TOF commissioning using cosmic ray particles can be found in [114]. Figure 2.9: Left: representation of a TOF sector, segmented in 5 modules along the z axis. Right: scheme of a TOF module; it is possible to see the strips and the interface cards located on them. 2.4 ALICE Performance PID capabilities in central barrel ALICE experiment is capable of discriminating different particle species produced at central rapidity by using various detectors, which exploit all the known PID techniques. Figure 2.10 describes the p T range in which separation among various species is possible for each ALICE PID detector. In the following, the particle identification techniques and performance will be described in detail for each detector. In most of the cases the best PID performance is achieved in the p T region from 0.1 GeV/c up to few GeV/c; for some particular species, in addition, ALICE grants a good degree of separation up to even some tens of GeV/c. PID with the ITS Four out of the six ITS layers (those of the SDD and SSD) allow particle identification by measuring the energy released by the crossing particle in the active 79

82 CHAPTER 2. The ALICE experiment at LHC Table 2.5: Basic parameters of TOF detector. Quantity Value Pseudorapidity coverage 0.9 < η < 0.9 Azimuthal coverage 2π Radial position 3.70 < r < 3.99m Length 7.45 m Segmentation in φ 18-fold Segmentation in z 5-fold Total number of modules 90 Central module (A) dimensions cm 2 Intermediate module (B) dimensions cm 2 External module (C) dimensions cm 2 Detector active area 141 m 2 Detector thickness (radially) X/X 0 = 20% Number of MRPC strips per module 15 (A), 19 (B), 19 (C) Number of readout pads per MRPC strip 96 Module segmentation in φ 48 pads Module segmentation in z 30 (!), 38 (B), 38 (C) pads Readout pad geometry cm 2 Detector gas C 2 H 2 F 4 (90%), i-c 4 F 1 0(5%), SF 6 (5%) Gas volume 16 m 3 Total flow rate 2.7 m 3 h 1 Working pressure < 3 mbar Fresh gas rate m 3 h 1 Occupancy for dn ch /dη = % (B = 0.4 T), 16% (B = 0.2 T) Occupancy for pp π, K identification (with contamination < 10%) GeV/c p identification (with contamination < 10%) GeV/c e identification in pp (with contamination < 10%) GeV/c Event size for dn ch /dη = 8000 Event size for pp 100 kb < 1 kb area of the detector. This is possible due to the analog readout of drifts and strips, while the binary output does not allow PID with the SPD. The energy deposit of a particle is evaluated by considering the truncated mean of the cluster charges collected in the four layers. In particular, an average of the lowest two values is taken if all the four layers gave a signal, or a weighted average is considered if only three are available. The compatibility with a given particle hypothesis is then computed in units of sigma from the difference between the measured energy deposit and the expected de/dx value, extracted from the Bethe-Bloch formula. This PID approach can be combined with other techniques from outer barrel detectors (for the tracks at higher momenta, which are able to exit the ITS), or can be used in a standalone approach (usually for the low p T tracks, which do not get out of the ITS). In the latter case, the ITS PID provides fairly good performance for p, K and π of low momenta, granting π/k separation up to about GeV/c 80

83 CHAPTER 2. The ALICE experiment at LHC Figure 2.10: p T ranges for separation of different species in the ALICE barrel detectors with PID capabilities. and K/p separation up to nearly 1 GeV/c, corresponding to the 1/β 2 region of the Bethe-Bloch curve. The left panel of Fig shows the specific energy deposit for charged tracks reconstructed with the ITS standalone versus the track momentum, in pp collisions at s = 7 TeV. The points are mainly aggregated in distinct regions, corresponding to proton, kaon and pion species. The parameterizations evaluated from the Bethe- Bloch curve are superimposed. This allows a separation of the three different species, plus electrons for p < 200 MeV/c. The right panel shows the resolution on the specific energy deposit versus the track p T in pp collisions at s = 7 TeV. Data and Monte Carlo simulation results are plotted, for three or four total clusters produced in the SDD and SSD layers. The resolution is slightly worse than 10% in the whole p T range from 200 MeV/c up to 2 GeV/c. PID with the TPC Similarly to the ITS, the TPC detector exploits the measurement of the specific energy deposit for particle identification. The energy deposit is evaluated by collecting the charge that is produced in the ionization of the gas by the passage of a charged particle and drifts through the detector toward the readout MWPC. The amount of collected charge is proportional to the energy released from the particle crossing the active area of the detector. Thanks to the large number of samples, the TPC grants a better energy resolution on the de/dx measurement with respect to the ITS, with values of about 5.5% in pp collisions and 6.5% in Pb-Pb collisions. Separation of pions, kaons and protons is possible in the 1/β 2 region of the Bethe-Bloch curve (but up to higher momenta values than in ITS) and, partially, in the relativistic rise region, while at the intermediate momenta the three species exhibit a similar energy deposit. 81

84 CHAPTER 2. The ALICE experiment at LHC Figure 2.11: Left: specific energy deposit in the ITS versus track momentum for charged tracks reconstructed in pp collisions at s = 7 TeV. Parameterizations for pions, kaons and protons from the Bethe-Bloch curve are superimposed. Right: energy resolution on the de/dx measurements in the ITS versus track p T. Results are shown for data and Monte Carlo simulations, for three or four clusters obtained in the four outermost ITS layers. The left panel of Fig shows the de/dx of charged tracks as a function of their momentum in pp collisions at s = 7 TeV. The bands for e, π, K, p and deuterons are clearly visible and distinguishable at low momenta; the Bethe-Block parameterizations for the five different species are superimposed. The plot in the right panel of Fig depicts the distribution of the difference between the energy deposit of charged tracks in pp collisions at 7 TeV and the expected value for pions, in the p T range between 4 and 4.5 GeV/c. A fit with different Gaussians provides the fraction of pions, kaons and protons. Figure 2.12: Left: specific energy deposit in TPC detector versus track momentum for charged tracks reconstructed in pp collisions at s = 7 TeV. Parameterizations for e, π, K, p and d from the Bethe-Bloch curve are superimposed. Right: difference between specific energy deposit of charged tracks and expected value for pions with same momenta, for 4 < p T < 4.5 GeV/c. The fit function is the sum of different Gaussian functions. 82

85 CHAPTER 2. The ALICE experiment at LHC PID with the TOF Using the time-of-flight technique, the particle velocity is obtained by measuring the time of flight t of the particle to cover a known length L: v = L/t. From kinematic relations, the mass of the particle can be consequently determined: m = p βγ = p c2 t 2 1, (2.9) L2 where β = v/c. The PID performance depends on the resolution on the track length, momentum and time of flight. The difference in the time of flight of two particles with different mass m 1 and m 2 and same momentum p is obtained by: t = t 1 t 2 = L [ ] (m 2 1 m 2 2)c 2. (2.10) 2c p 2 This relation defines the upper limit on the momentum of the particles for their separation, depending on their species. It is worth noticing that if the p of the particles doubles, it would be necessary to increase L by a factor 4 to get the same t. The TOF detector, being 3.7 m far from the beam axis and having an overall time resolution of 160 ps, grants a 2σ separation for π/k up to 2.2 GeV/c and for K/p up to 4 GeV/c. The association between tracks and time of flight values is performed by using an algorithm which propagates tracks reconstructed in inner detectors to the TOF. For low-multiplicity pp events, the time of flight is determined in combination with the T0 detector, which supplies the start signal from the time measurement. In Pb-Pb collisions (and for high-multiplicity pp collisions), instead, TOF is used to evaluate the start time as well, by analyzing the distribution of the arrival times of the particles produced in the event. It is therefore crucial to achieve an excellent precision in tagging the moment in which the tracks cross the detector. Fig shows the velocity β of tracks measured with the TOF versus the corresponding track momentum, divided by its charge (signed momentum). It is possible to distinguish the bands for pions, kaons, protons and deuterons, with positive and negative charges, consequently granting a separation of the different species. Other detectors In the ALICE central barrel other detectors can perform particle identification, exploiting additional techniques, namely TRD, HMPID, EMCal and PHOS. The TRD is located just outside the TPC and allows one to identify electrons (and positrons) with momentum higher than 1 GeV/c (corresponding to γ > 1000) by detecting the transition radiation (TR) emitted from these particles when crossing the detector. Each detector module is composed of a radiator and a drift chamber with a Xe/CO 2 mixture (85%/15%). When a particle over the threshold crosses the foils present in the radiator, it emits photons which enter the conversion and 83

86 CHAPTER 2. The ALICE experiment at LHC Figure 2.13: Particle β measured by the TOF versus signed momentum in pp collisions at s = 7 TeV. drift region of the readout chamber. Here photons are converted in electron-positron pairs, which drift in the electric field and are collected at the readout pads, producing a signal. Fig shows the difference between the specific energy deposit in the TPC for charged tracks of 2 GeV/c momentum and the expected value for electrons. When applying the TRD rejection, most of the hadron contribution is removed, while rejecting much less electrons; this increases the purity of electron samples at high p T. The HMPID is a Ring Imaging Cherenkov detector which allows an extension of the momentum range in which it is possible to identify hadrons (up to 3 GeV/c for π and K and up to 5 GeV/c for p). It consists of seven modules of proximity focusing Ring Imaging Cherenkov (RICH) counters, covering a limited acceptance region but representing, with an active area of 12 m 2, the largest detector ever built exploiting this detection technique. Cherenkov radiation is emitted when a charged particle with β > c/n traverses the radiator, made of a 15 mm thick layer of liquid C 6 F 14. The Cherenkov photons exit from the radiator, with an angle depending on the particle mass and momentum, and after traversing a proximity gap they are detected by a photon counter, consisting of a thin layer of CsI deposited onto the pad cathode of a MWPC. From the radius of the photon rings, the Cherenkov angle can be measured with an accuracy of few mrad. Fig shows the measured angle for Cherenkov photons as a function of the momentum of the emitting tracks, in pp collisions at s = 7 TeV. The expected curves of the angle for pions, kaons and protons are superimposed to the data and are found to be in good agreement with the measurements. Finally, it is possible to use information from the two electromagnetic calorimeters, EMCAL and PHOS, to separate photons from neutral pions for momenta higher than 1 GeV/c. PHOS detector grants photon detection performance, with 84

87 CHAPTER 2. The ALICE experiment at LHC Figure 2.14: Distribution of the difference between the specific energy deposit in TPC and the expected value for electrons, for tracks with 2 GeV/c momentum, without (red points) and with (blue points) the TRD electron selection. Figure 2.15: HMPID Cherenkov angle as a function of track momentum for pp collisions at s = 7 TeV, with expected Cherenkov angle values for π, K, p superimposed on data. an energy resolution of a few percent at 1 GeV/c, decreasing to 1% above 10 GeV/c momentum. EMCal provides the same features over a wider acceptance, but with an energy resolution a factor 2-3 lower than PHOS calorimeter. With the help of the PMD detector, a pre-shower calorimeter, it is also possible to count the number of photons produced in the 2.5 < η < 3.5 pseudorapidity region. In addition, EMCal is capable of electron identification, by means of the E/p ratio of the particles, where E is the energy released in the EMCal and p the reconstructed track momentum. This approach relies on the fact that electrons deposit all their energy in the EMCal (E/p = 1), while hadrons release, on average, only a small fraction of their energy in it (E/p < 1) Vertex reconstruction A good performance in the reconstruction of the primary vertex is important for the ALICE physics programme. It allows putting constraints on the trajectories of the primary particles, making the track reconstruction easier. It also helps in identifying heavy flavour particles, which decay on average hundreds of µm far from the primary vertex, making possible to measure the displacement of the decay vertex from it and improving the resolution of the impact parameters of the decay tracks. At the online level, a correct estimation of the primary vertex position is mandatory to keep under control the beam position inside the interaction region and to measure its spread along the x, y and z coordinates; this spread is typically of about 50 µm along x and y and about 5 cm along the z direction for pp collisions at s = 7 TeV. The SPD detector is the most suitable system for online primary vertex reconstruction in ALICE: it is the closest detector to the interaction region and, ow- 85

88 CHAPTER 2. The ALICE experiment at LHC ing to its high granularity, it grants the best spatial resolution in the transverse plane. Three different algorithms for primary vertex reconstruction are available in ALICE [115]: 1. VertexerSPDz: it allows measuring the z coordinate of the vertex by using only the SPD detector; it needs the knowledge of x and y coordinates. 2. VertexerSPD3D: it allows measuring the three coordinates of the primary vertex by using only the SPD detector. 3. VertexerTracks: it allows measuring the three coordinates of the primary vertex by using the reconstructed tracks. The first two algorithms provide a worse resolution, but they do not need prior reconstruction of the tracks in the event, and grant better efficiency for very low multiplicity events. For this reason, during the event reconstruction a first 3-dimensional measurement of primary vertex is performed through VertexerSPD3D algorithm, then track reconstruction is performed (cf. Section 2.4.3) and finally a more precise evaluation of the vertex is obtained by means of the VertexerTracks algorithm. Further details on the three vertexing algorithms are given in the following. VertexerSPDz algorithm This algorithm is based on SPD tracklets, i.e. associations of two clusters in the inner and outer SPD layers. It provides a measurement of the z coordinate of the primary vertex if the other two coordinates are known with an accuracy of at least 200 µm (e.g. from the knowledge of the transverse position of the beams). For each tracklet i, the intersection point z i with the beam axis is evaluated. At first, a Region of Interest (ROI) is defined around the peak of the z i distribution; then a first determination on the z position of the vertex is computed by a weighted average (z mean ) of the z i coordinates which fall in the ROI. The calculation of the z coordinate is reiterated re-centering the ROI on the last z mean position, repeating the procedure until a symmetric region around z mean is found. This allows us to minimize the bias caused by asymmetries in the tails of the z i distribution. VertexerSPD3D algorithm SPD tracklets are the starting point also for this algorithm, which allows the measurement of all the three coordinates of the primary vertex. In this case only tracklets satisfying some requirements are used for vertex reconstruction. Tracklets must cross a cylindrical fiducial region in which the vertex is expected to be found, and the two points composing each tracklet must be inside a given ϕ window relative to the transverse position of the beams. Then all the possible tracklet pairs are built and a selection on these pairs is performed: after a cut on the distance of closest approach between the two tracklets (DCA < 1 mm), the crossing point 86

89 CHAPTER 2. The ALICE experiment at LHC c ij of the pair is computed, and only the pairs with their crossing point inside the cylindrical fiducial region are kept. As a last selection step, a 3D histogram is constructed from all the c ij points; all the tracklets too far from the peak of this distribution (more than 1 mm along x and y and more than 8 mm along z) are removed from the vertexing process. After completing the tracklet selection, vertex reconstruction begins. As a first estimate, the vertex is determined as the point of minimum distance between all the tracklets passing the selection. Then, the vertex coordinates are recalculated after an additional selection on the tracklets based on their displacement from the first vertex estimate (removing tracklets farther than 1 mm). The full procedure described above is repeated twice. In the second iteration the tracklet selection cuts are tightened and the cylindrical fiducial region is reduced and centered on the position of the vertex evaluated in the first iteration. At the end of the procedure, an additional check on the vertex position (which must be inside the beam pipe) and on the number of contributing tracklets (at least one) is performed. The evaluation of the vertex position from a given sample of selected tracklets is performed by minimizing the quantity: D 2 = N d 2 i, (2.11) where N is the number of the contributing tracklets and d i the displacement of the tracklet i from the vertex (x 0,y 0,z 0 ) weighted by the errors on the tracklet: i ( ) 2 ( ) 2 ( ) 2 d 2 xi x 0 yi y 0 zi z 0 i = + +. (2.12) σ xi If VertexerSPD3D algorithm fails to reconstruct the primary vertex, the reconstruction is performed calling the VertexerSPDz, avoiding the rejection of the event. This case is most likely in low multiplicity pp interactions, for which vertex reconstruction efficiency is larger for the VertexerSPDz algorithm than for the VertexerSPD3D one. σ yi σ zi VertexerTracks algorithm The VertexerTracks algorithm grants a measurement of the primary vertex with higher precision than the previous algorithms, but it requires a former reconstruction of the full tracks inside the barrel. The algorithm starts with a preselection on the tracks, removing tracks with an insufficient number of associated clusters or tracks which do not point to a cylindrical fiducial region with r < 3 cm and z < 30 cm. After this preselection, a first estimate of the vertex is performed, used as a starting point for the rest of the reconstructing procedure. 87

90 CHAPTER 2. The ALICE experiment at LHC The algorithm then continues with three more steps, which are repeated for two times: 1. Track selection: in this step the algorithm removes secondary tracks (from strange hadron decays or from interactions in the material of the detector) and fake tracks, obtained by wrongly associating points from different particles; 2. Vertex finding: here the vertex position is evaluated as the point of minimum distance among the selected tracks; in the first iteration, the tangent to the tracks at the nominal beam position is used, while in the second iteration the tracks are prolonged backwards to the primary vertex found in the previous iteration. 3. Vertex fitting: in the last step the tracks are extrapolated back to the vertex position estimated in the previous step and the best estimate of the vertex position as well as the vertex covariance matrix are obtained by a fitting algorithm [116]. The value of the χ 2, approximating the tracks as straight lines around the vertex position, is given by: χ 2 ( r v ) = i ( r v r i ) T V 1 i ( r v r i ), (2.13) where r v is the position of the track i and V i its covariance matrix. The vertex position obtained from the minimization is then: ( ) 1 ( r v = W i i i W i r i ) 1, (2.14) where W i = V 1 i. Fig shows the width (sigma) of a Gaussian fit to the distributions of the x (circles) and y (triangles) coordinates of the primary vertex, as a function of the tracklet multiplicity of the event, for pp collisions at s = 7 TeV. The vertex is reconstructed using SPD tracklets (open markers) or the reconstructed tracks (closed markers). The sigma value accounts for the spread of the primary vertex position in the interaction region and on the resolution on the reconstructed primary vertex position. In the track case a fit function is superimposed, whose asymptotic value represents the size of the luminous region Track reconstruction Reconstructing the charged tracks produced in the collisions is a tough challenge in heavy ion collisions, where track density is high. Particles produced at central rapidity are reconstructed by the ITS and the TPC, the core of the ALICE tracking system, and eventually propagated to the outer barrel detectors. 88

91 CHAPTER 2. The ALICE experiment at LHC Figure 2.16: Values of the width of a Gaussian fit applied to the distribution of x (circles) and y (triangles) coordinates of primary vertex versus tracklet multiplicity, for pp collisions at s = 7 TeV. The vertex position is evaluated by using reconstructed tracks (closed markers) or SPD tracklets (open markers). More details on the sigma value are found in the text. The starting point is constituted by raw data, which contain the outputs of the channels of each detector. Signals produced from adjacent elements of the detector sub-systems are grouped in clusters; a cluster identifies the passage of a charged track through the active area of the corresponding sub-detector. By evaluating the cluster centroid it is possible to estimate the track crossing point in the subdetector, named rec point. The rec points position is registered using the local coordinate frame of each sub-detector. This frame has the z axis coincident with the z axis of the ALICE frame (described in Section 2.2), the x axis perpendicular to the sensitive plane of the sub-detector and pointing outwards, while the y axis is perpendicular to the other two axis forming a right-handed system. With this choice it is possible to move from the local coordinates frames to the ALICE global frame with a simple rotation around the z axis. Starting from the rec points, tracks are reconstructed with the Kalman algorithm [117, 118], which aggregates rec points from the various detectors into tracks, reproducing the trajectory of the charged particles inside the barrel. The Kalman filter is a local reconstruction algorithm; it re-evaluates the best parameterization of a track after adding each rec point, increasing at each time the quality of the fit, and it performs the extrapolation of the tracks when passing through materials and from a detector to another (e.g. going from the TPC to the ITS). Each track is parameterized as an helix, using 5 free parameters: two of them describe the track geometry along the beam direction, while the other three parameterize it in the transverse plane (along rφ). The errors on the parameters are stored in a 5 5 covariance matrix, which is also re-evaluated at each rec point addition as the five track parameters. The track reconstruction starts from the outer part of the TPC, since there 89

92 CHAPTER 2. The ALICE experiment at LHC clusters have lower density and are more displaced one from the others. Track seeds are evaluated by trying different combinations of the rec points in the TPC outer region, using the SPD vertex information. After finding the seeds, the Kalman algorithm propagates them inside the whole TPC, associating for each seed the rec points likely generated from the passage of the same particle. Rec point association starts from the tracks with lower bending (higher p T ), which also resent less of the Coulomb multiple scattering effects. TPC tracks are then extended in the ITS, starting again from higher p T tracks. All the rec points in the outer ITS layer inside a fiducial region are associated to the TPC tracks, track parameters are recalculated for each case and the new tracks are propagated to the next ITS layer. This procedure is repeated until the inner ITS layer is reached. Only at this point, the track having the best χ 2 is selected, discarding all the other possibilities created by the algorithm and freeing the corresponding rec points. The rec points used for the chosen track are instead removed and cannot be associated to other tracks, which facilitates the reconstruction of the following tracks, with lower p T. The track finding is subsequently repeated for all the TPC tracks. After this procedure, tracking is repeated inside ITS only, where the algorithm tries to reconstruct tracks from the rec points not associated to any TPC track. This allows us to reconstruct tracks either with very low p T, which are confined inside the ITS, or without any rec point in TPC, due to TPC dead zones, or decaying before exiting the ITS. Track fitting comes in two steps. In the first, a constraint for primary vertex (calculated from SPD information) is set, to increase the tracking efficiency for primary tracks; during the second step, this constraint is removed, allowing the reconstruction of tracks which are not produced in the primary vertex. Afterwards, Kalman algorithm is repeated again in the opposite direction, starting from the vertex and going outwards through the ITS and then the TPC. When the outer radius of the TPC is reached, parameter errors are small enough to allow track extrapolation to the outer barrel detectors (TRD, TOF, and possibly HMPID and PHOS). In this step, reconstructed tracks acquire also PID information from the detectors. In the conclusive step the reconstructed tracks are refitted in the inward direction with the Kalman filter going backwards to the primary vertex (and, for secondary tracks, to their innermost measured point). Fig shows the tracking efficiency versus track p T in pp collisions at s = 0.9, 2.76 and 7 TeV, evaluated on Monte Carlo samples. Tracking efficiency is defined as the ratio between the number of reconstructed tracks (passing certain quality criteria) and the number of the primary tracks suitable for reconstruction (i.e. entering the ALICE barrel with a high enough momentum). Tracking efficiency is shown separately for positive and negative charge tracks. In the simulation at 2.76 TeV, the SDD detector was excluded from the track reconstruction process. Among the quality criteria, the selection on the tracks requires a minimum of 120 crossed 90

93 CHAPTER 2. The ALICE experiment at LHC rows in the TPC, a minimum of two hits in the whole ITS, with at least one of them in the SPD, a maximum distance of closest approach to primary vertex of 2 cm in the z direction and a value of pseudorapidity in the range η < 0.8. Figure 2.17: Tracking efficiency for positive and negative tracks, in Monte Carlo simulations of pp collisions at s = 0.9, 2.76 and 7 TeV. Details on the track selection are described in the text. The left panel of Fig shows the fraction of TPC tracks for which it is possible to associate ITS rec points (ITS prolongation efficiency) as a function of the track p T in pp collisions at s = 7 TeV. Prolongation efficiency is reported for data at first reconstruction pass and for Monte Carlo, requiring at least 2 hits in the ITS or at least 1 hit in the SPD. TPC tracks are required to satisfy standard quality selection. Requiring 2 ITS hits, the prolongation efficiency is close to 1, with only a slight decrease at very low p T ; it degrades by 15% on average if at least one SPD hit is required. A very good agreement between data and Monte Carlo simulations is found over the full p T range. The right panel of the same figure shows the resolution on the track p T measurement, estimated from the track covariance matrix, for tracks reconstructed combining ITS and TPC information, in Pb-Pb collisions at s NN = 2.76 TeV. p T resolution is better than 1% at about 1 GeV/c and stays below 10% up to almost 50 GeV/c. A crucial performance parameter for heavy flavour analysis is the resolution on the measurement of the track impact parameter (i.e. the minimum distance between the primary vertex and the backward prolongation of the track), since heavy flavour particles are reconstructed exploiting the distance travelled from the primary vertex before decaying. Impact parameter resolution involves both tracking and vertexing performance, since it mainly depends on the spatial resolution on the primary vertex position and on the spatial resolution on the reconstruction of the tracks. Fig shows the impact parameter (d 0 ) resolution in the transverse direction as a function of p T in pp collisions at s = 7 TeV. The left panel compares the d 0 rφ resolution for charged tracks in data and in Monte Carlo simulations; in the 91

94 CHAPTER 2. The ALICE experiment at LHC Figure 2.18: Left: data-monte Carlo comparison for ITS prolongation efficiency in pp collisions at s = 7 TeV. TPC tracks were selected requiring at least 70 clusters, η < 0.8, distance of closest approach to primary vertex of 2.4 cm (z direction) and 3.2 cm (in transverse plane). Right: p T resolution for tracks reconstructed combining ITS and TPC in Pb-Pb collisions at s NN = 2.76 TeV. right panel the impact parameter resolution is shown separately for pions, kaons and protons. The difference on the resolution for the three species at low p T is due to the different influence of the Coulomb multiple scattering. In all the cases, ALICE grants excellent performance on the determination of the impact parameter, with a resolution better than 100 µm for tracks with p T > 700 MeV/c and performance only slightly worse than that expected from Monte Carlo simulations. Figure 2.19: Left: data (red) and Monte Carlo (black) impact parameter resolution for pp collisions at s = 7 TeV. Right: impact parameter resolution plotted separately for pions (red circles), kaons (magenta squares) and protons (purple triangles). Data points are represented with closed markers, Monte Carlo with open markers. 92

95 Chapter 3 Measurements of charm with ALICE 3.1 Introduction ALICE can study charm and beauty quark production by reconstructing the quark hadronization products, in both open and hidden heavy flavour sectors. This can be done exploiting a series of techniques, as it will described in this chapter. The ALICE heavy flavour analyses performed using the detectors in the central barrel and in the forward muon spectrometer are listed in Table 3.1. In the barrel, it is possible to reconstruct D mesons through their hadronic decays in kaons and pions (studies are ongoing also for the charmed baryon Λ c, reconstructed from its decays in pkπ and pk 0 s). Measurements of charm and beauty production can be also performed by analyzing semileptonic decays of heavy flavour hadrons into electrons; in addition, the J/Ψ state can be studied from its decay into dielectrons. In the muon arm, charmonium and bottomonium states can be studied by reconstructing their dimuonic decays, while open charm and beauty production can be measured from the inclusive muonic decays of heavy flavour hadrons. First results in pp collisions at s = 7 TeV and s = 2.76 TeV have been published by ALICE for most of the analyses presented above. In some cases, results have been published also for Pb-Pb collisions at s NN = 2.76 TeV; all the channels are also being studied in the sample of p-pb collisions at s NN = 5.02 TeV collected in the first months of The analysis of D mesons from the reconstruction of their hadronic decay channels in the central barrel constitutes a basic ingredient for the D-hadron angular correlation analysis described in the next chapter. The reconstruction and the selection of the D mesons, used as trigger particles for the correlations, exploit indeed the strategy and the instruments of this analysis. For this reason, it will be described in detail. Only a quick overview of the other heavy flavour analyses will be given, presenting the main results obtained in pp collisions at s = 7 and 2.76 TeV. The results for the R AA and v 2 observables obtained from the study of Pb-Pb collisions 93

96 CHAPTER 3. Measurements of charm with ALICE at s NN = 2.76 TeV will be also discussed. Table 3.1: List of the main heavy flavour analyses performed by ALICE. Probe Decay channel Acceptance η < 0.9 D 0, D +, D, D + s D + K π + π + D + D 0 π + D 0 K π +, K π + π π + D + s φπ + K K + π + B mesons J/Ψ e + e η < 0.9 J/Ψ, Ψ, Υ, Υ, Υ e + e η < 0.9 J/Ψ, Ψ, Υ, Υ, Υ µ + µ 2.5 < η < 4 c, b quarks e+x η < 0.9 c, b quarks µ+x 2.5 < η < D meson reconstruction from hadronic decays in pp collisions The charmed mesons produced at central rapidity in pp, p-pb and Pb-Pb collisions can be studied by reconstructing their hadronic decay channels, exploiting a selection based on the topology of the decays and on the identification of the daughter charged tracks. At present, p T -differential production cross sections and their ratios in pp collisions at s = 7 TeV [26, 119] have been evaluated for four species of charmed mesons, D 0, D +, D + and D + s. In addition, p T -differential cross sections have also been measured in pp collisions at s = 2.76 TeV [81], in a smaller data sample with respect to that available at s = 7 TeV. The basic properties of the D meson species studied in these analyses are summarized in Tab. 3.2 [46]. The hadronic decay channels used for D meson reconstruction are: D 0 K π + (with branching ratio BR = 3.87%±0.05%), D + K π + π + (BR = 9.13%±0.19%), D + D 0 π + (strong decay, BR = 67.7% ± 0.5%), D + s φπ + K K + π + (full decay chain has BR = 2.28% ± 0.12%). Table 3.2: Basic properties of the D mesons reconstructed in ALICE [46] Meson qq Mass [MeV/c] I J P S C Mean lifetime [s] D 0 cu ± / (4.101 ± 0.015) D + cd ± / (1.040 ± 0.007) D + s cs ± (5.00 ± 0.07) D cd ± / (6.9 ± 1.9)

97 CHAPTER 3. Measurements of charm with ALICE D meson reconstruction and selection The D 0, D + and D + s mesons 1 undergo weak decays, where the c quark is transformed into a lighter quark. Their life time is thus relatively long, allowing them to travel for long distances before decaying (proper decay lengths are cτ 123 µm for D 0, cτ 312 µm for D + and cτ 150 µm for D + s ). Hence, their decay vertices (secondary vertices) are generally displaced by a few hundred µm from the primary vertex of the event. The strategy for the analysis of D mesons consists in performing a selection on the separation between primary and secondary vertices and on other variables related to the topology of the decay. For the D + meson, which is subject to strong decay, the analysis is performed by reconstructing the decay vertex of the daughter D 0 and associating a low momentum charged pion to it. The pion has low momentum because the mass difference m = m D + m D MeV/c 2 is very close to the pion mass and the D 0 takes away the largest fraction of the available Q-value of the reaction. After the selection of the D meson candidates, the yield was extracted in different p T ranges via a fit to the invariant mass distributions. The procedure for reconstructing and selecting the D candidates is described in the following. D meson candidates were reconstructed by combining all the possible pairs (for the D 0 ) or triplets (for D + s, D + ) of tracks with the proper charge signs (e.g. a positive and a negative track for the D 0 ). For each combination, the position of the secondary vertex of the candidate D meson was evaluated from the tracks composing the candidate, using the same algorithm used to calculate the position of the primary vertex from reconstructed tracks. The combination was stored as a D meson candidate if some loose selection criteria on the tracks and on the secondary vertex were satisfied. Each D meson candidate had then to pass a selection on: (i) reconstruction quality of the daughter tracks; (ii) kinematics and topology of the decay; (iii) particle identification of the daughter tracks. The selection criteria are here described for the D 0, which is the meson that has been studied in this thesis; the criteria for the other D species are in any case based on a similar strategy. Only events with the z coordinate of primary vertex satisfying the condition z vtx < 10 cm were used in the analyses, at both energies. The D 0 meson daughter tracks had to satisfy some requirements on the quality of their reconstruction in the ITS and TPC detectors: at least 70 associated space points in the TPC (out of a maximum number of 159) and χ 2 /ndf < 2 for the momentum fit in the TPC, minimum 2 hits in the ITS, out of which at least one in either of the two SPD layers, η < 0.8 and p T > 0.4 GeV/c. Then, topological cuts were applied to the D 0 candidates (see Fig. 3.1 for a graphical reference). To exploit the large decay length of the D 0 meson, the displacement of the secondary vertex from the primary vertex was requested to be of at least From now on, when referring to a given meson (e.g. the D 0 ), also its antiparticle (D 0 ) will be considered. 95

98 CHAPTER 3. Measurements of charm with ALICE µm, with a distance of closest approach between the two tracks of at most 300 µm. The product of the track impact parameters in the rφ direction had to be negative and large in magnitude: d π 0 d K 0 < 120 (µm) 2. This was requested since the impact parameters d π 0 and d K 0 are expected to have large and opposite sign values in displaced decays. The D 0 momentum was required to point to the primary vertex, i.e. a small value of the pointing angle θ pointing (the angle between the D 0 momentum and the flight line connecting primary and secondary vertices) was requested. A cut on the cosine of the angle θ between the direction of the kaon momentum in the D 0 rest frame and the direction of the D 0 momentum ( cos θ < 0.8) was imposed to reject candidates not coming from real two-body decays. Background D 0, indeed, commonly show higher values of cos θ, while due to the isotropic decay in the D 0 rest frame the cos θ distribution for true D 0 is rather flat. Finally, a minimum value on the p T of the two daughter tracks was required. The values of the topological cuts depended on the D 0 p T and were chosen as a compromise to (i) optimize the statistical significance of the signal peaks in the invariant mass S distributions, defined as S+B ; (ii) grant a sufficiently high value of the D meson reconstruction and selection efficiencies; (iii) preserve a high fraction of prompt D mesons in the sample of the selected candidates. A fiducial acceptance cut was also applied to the D 0 candidates, excluding candidates with y D < y fid (p T ), with y fid smoothly increasing from y fid = 0.5 at p T = 0 to y fid = 0.8 at p T = 5 GeV/c. Figure 3.1: Scheme of the D 0 K π + decay. Particle identification selection was applied to the two D 0 decay tracks, in order to check their compatibility with the pion or kaon hypotheses. PID information was extracted from the TPC (the π/k separation is effective up for tracks with momentum up to GeV/c) and from the TOF (for tracks with momentum below 1.5 GeV/c) detectors. For each track, the compatibility with kaon or pion mass was checked in both detectors by evaluating the difference between the measured and the expected signal. The global PID response (identification, compatibility or rejection) was determined by combining the responses from the two detectors. In case no TOF information was available, only the TPC was used to perform PID. For tracks showing opposite TPC and TOF responses for a given mass hypothesis, compatibility with that hypothesis was assumed. The whole D 0 candidate was accepted if the PID output for the two tracks was compatible with a K ± π hypothesis. 96

99 CHAPTER 3. Measurements of charm with ALICE A similar procedure was adopted for the PID selection of D + and D + s, checking the compatibility of the daughter tracks with the corresponding final states. For the D + case PID selection was not performed on the soft pion tracks, while for the D + s meson it was also required that the invariant mass of the two tracks tagged as kaons was compatible with the mass of the φ resonance. For all the D meson species, the effect of the PID selection was to reduce the combinatorial background by a factor 2-3 at low p T, with a small rejection of the D meson signal (about 95% of the signal was preserved). The raw yields of the D 0, D + and D + s mesons were extracted in different p T intervals by fitting the corresponding candidate invariant mass distributions; the fit function was the sum of a Gaussian function and an exponential, reproducing respectively the signal peak and the combinatorial background. For the D + the fit was applied to the mass difference between the Kππ and Kπ combinations, using a slightly different fit function for the background [120]. Examples of invariant mass distributions with the fit functions superimposed are shown in Fig. 3.2 for D 0, D + and D + mesons. Figure 3.2: Fit of invariant mass distributions for D 0 (left), D + (middle) and D + (right) candidates, in the 4 < p T < 5 GeV/c transverse momentum range. The values of mean (µ) and width (σ) of the Gaussian peaks and the extracted raw yields (S) are also quoted Corrections and systematic uncertainties The production cross section of prompt D mesons can be calculated in each p T interval from the raw yields N D/D (p T ) as follows: dσ D dp t = 1 1 f prompt (p T ) N D/D (p T ) y <yfid, (3.1) y <0.5 2 y p T (Acc ɛ) prompt (p T ) BR L int where y = 2y fid is the width of the rapidity interval, p T is the width of the p T interval, f prompt is the fraction of prompt D mesons in the extracted raw yield, (Acc ɛ) prompt factorizes the acceptance and the efficiency for prompt D mesons, accounting for vertex reconstruction, track reconstruction and D meson reconstruction and selection efficiencies, BR is the branching ratio of the decay 97

100 CHAPTER 3. Measurements of charm with ALICE channel chosen for the reconstruction and L int is the integrated luminosity. The factor 1/2 is relative to the contribution of the corresponding antiparticle, since the raw yield is the sum of particle and antiparticle, while the cross section is given for particle only. Equation 3.1 implicitly assumes that the rapidity distribution of the D mesons is flat inside the y range. This was verified using both PYTHIA [83] Monte Carlo simulations and FONLL pqcd calculations [20], where flat rapidity distributions were obtained, with deviations of less than 1%. The (Acc ɛ) prompt factor was evaluated using a Monte Carlo simulation based on GEANT3 [121] transport code, in which the ALICE detectors and their conditions during the data taking were described in great detail. Simulations of pp collisions were performed using PYTHIA event generator [83], with Perugia0 tune [122]. Figure 3.3 shows the acceptance times efficiency for D 0, D + and D + mesons as a function of p T, separately for prompt and feed-down D mesons. For the prompt case the efficiency without the PID selection is also shown, being almost the same as with the full selection including the PID. This shows that the adopted PID selection strategy keeps about the 95% of the signal. (Acc ɛ) prompt exhibits a clear rising trend versus p T for all the mesons, since the presence of less combinatorial background at high p T allows us to loosen the selection cuts. In addition, D mesons with higher p T travel farther before the decay: the secondary vertex is hence more displaced, giving higher probability to pass the topological cuts. A similar consideration also explains the higher efficiency for feed-down mesons with respect to that of prompt mesons, especially at low p T (B mesons have significantly larger lifetimes than D mesons). Figure 3.3: Acceptance times efficiency as a function of p T for D 0 (left), D + (middle) and D + (right), shown for prompt mesons (red circles), prompt mesons without PID selection (green closed squares) and feed-down mesons (blue open squares). The fraction of prompt D mesons was evaluated by using FONLL pqcd calculations [20] for the production cross section of B mesons at LHC energies and the B D decay kinematics from the EvtGen package [123], in association with the 98

101 CHAPTER 3. Measurements of charm with ALICE acceptance times efficiency correction for feed-down D mesons extracted from Monte Carlo as described above. f prompt was then calculated, for each p T interval, as: N feed down D raw f prompt = 1, (3.2) N D raw where: N feed down D raw y <yfid = 2 dσfeed down D FONLL dp T T (Acc ɛ) feed down BR L int y <0.5 y p (3.3) The value of f prompt is shown as a function of p T in the left panel of Fig. 3.4 (solid line), together with the value obtained using a different approach (dashed line). This alternative approach exploits FONLL cross section calculations for both prompt and feed-down D mesons and their respective reconstruction and selection efficiencies. The systematic uncertainty on feed-down contribution is also shown in the figure (red box). It was evaluated by varying, for both approaches, the quark masses and the QCD factorization and renormalization scales and by taking the envelope of all the results thus obtained. Finally, the black circles of Fig. 3.4 show the f prompt values evaluated with a data-driven approach, using a fit to the impact parameter distribution of D mesons. The distribution was obtained considering the candidates in the signal region of the invariant mass distribution, after removing the background contribution evaluated from the sidebands. The fit function was the sum of two terms: the first was a detector resolution term, composed of a Gaussian and an exponential functions, describing the impact parameter of prompt D mesons; the second accounted for the impact parameter distribution of D from B decay and was a convolution of the same detector resolution term with a double-exponential function describing the true impact parameter of secondary D mesons [26]. An example of fit to the impact parameter distribution for D 0 mesons in the 2 < p T < 3 GeV/c range is shown in the right panel of Fig Several other sources of systematic uncertainties were also considered, in addition to the feed-down contribution: D meson yield extraction, estimated by varying the background fit function (polynomial instead of exponential), the range of the fit and extracting the signal via a bin counting approach 2. The uncertainty was taken as the maximum variation in the yields obtained with the different approaches; Tracking efficiency, estimated by varying the criteria for the track selection and checking the difference in the results; the different efficiency for the track propagation from the TPC to the ITS in data and Monte Carlo was also considered; D meson selection efficiency, due to residual discrepancies between data and Monte Carlo simulations for the cut variables used for the D meson selection. It was estimated by repeating the analysis with different topological 2 With the bin counting procedure, the yield is evaluated by summing the entries of the bins in the peak region and subtracting the integral of the background function in the same region. 99

102 CHAPTER 3. Measurements of charm with ALICE Figure 3.4: Left: fraction of prompt D 0 mesons in the measured raw yield as a function of p T evaluated with standard FONLL approach (solid line), alternative FONLL approach (dashed line) and D 0 impact parameter fit method (black circles). Red boxes show the systematic uncertainties for f prompt evaluation with the FONLL-based methods. Right: example of impact parameter distribution for D 0 meson with 2 < p T < 3 GeV/c; the distribution is fitted with the two components for prompt and feed-down D 0 mesons described in the text; the resulting prompt fraction is written as a label; the top-right inset shows also the negative entries, resulting from the background subtraction. cuts (using looser and tighter values) and taking the difference with respect to the results obtained using the standard selection; PID efficiency, evaluated by repeating the analysis without this selection and with tighter PID cuts, taking as uncertainty the variation in the corrected yields; Simulated D meson p T shape, estimated by using a different p T shape, extracted from FONLL calculations, for the D mesons in the Monte Carlo simulations used to evaluate the efficiencies. The evaluation of the corrections and of the cross sections was then repeated and a comparison with the standard results was performed; Branching Ratio value, defined according to the PDG uncertainty [46]; Normalization, arising from the uncertainty on the minimum-bias trigger cross section (3.5% contribution) Cross sections and ratios Figure 3.5 shows the p T -differential cross sections for prompt D 0, D +, D + [26] and D + s [119] mesons at central rapidity in pp collisions at 7 TeV. The error bars represent the statistical uncertainties, while the boxes quote the total systematic uncertainties. Results are compared to predictions from pqcd calculations, using FONLL [20, 124] and GM-VFNS [23, 125] schemes for D 0, D + and D + mesons and 100

103 CHAPTER 3. Measurements of charm with ALICE GM-VFNS and k T -factorization at LO schemes [28 30] for the D + s meson (FONLL framework does not have a prediction for the D + s ). Ratios of data points over theoretical predictions are shown in the bottom panels, denoting a good agreement between data and models within the uncertainties for all the D meson species. In particular, data lie on the upper edge of FONLL uncertainty band, confirming a feature already observed at CDF [77]. Figure 3.5: p T -differential inclusive cross section for prompt D 0, D +, D + and D + s meson production in pp collisions at s = 7 TeV compared to pqcd calculations (FONLL and GM-VFNS schemes for D 0, D + and D +, GM-VFNS and k T -factorization at LO schemes for D + s ). Statistical and systematic uncertainties are displayed with error bars and black boxes, respectively. The bottom panels show the ratios of data over theoretical predictions. The 3.5% normalization uncertainty is not shown. Figure 3.6 [26] shows the ratios of the cross sections for prompt production of the different D meson species in pp collisions at 7 TeV, with statistical (error bars) 101

104 CHAPTER 3. Measurements of charm with ALICE and systematic (boxes) uncertainties, in different p T intervals. Data are compared to calculations using FONLL (except for cases involving the D + s ) and GM-VFNS schemes 3 and with expectations from PYTHIA [83] simulations with Perugia0 tune [122]. A substantial agreement is found between data and predictions. Data do not show a visible p T dependence of the ratios within the uncertainties, denoting no big differences between the fragmentation functions of charm quark into the four considered species of D mesons. Figure 3.6: Ratios of D meson production cross sections as a function of p T, compared to predictions from FONLL, GM-VFNS and PYTHIA with Perugia0 tune. For FONLL and GM-VFNS the lines show the ratio of the central values of the theoretical cross section, while the shaded area is defined by the ratios computed from the upper and lower limits of the theoretical uncertainty band. The p T -integrated ratios of D meson production cross sections are shown in Fig. 3.7 [26]. The measured cross sections for the different D mesons were extrapolated to the full p T range by using the FONLL theoretical predictions for D meson production at central rapidity. The extrapolation factor was evaluated from these 3 Neither FONLL nor GM-VFNS calculations directly predict the relative abundances of the D meson species (i.e. the absolute values of the ratios), since those calculations use fragmentation fractions f(c D) extracted from data measurements. It is worthy, however, to compare the p T behaviour of the ratios as observed from data and as predicted by these calculations. This feature, indeed, depends on the fragmentation functions used in the calculations (specific to each D meson specie). 102

105 CHAPTER 3. Measurements of charm with ALICE predictions as the ratio between the total D production cross section and the cross section integrated in the p T interval where the measurement was performed. The ratios obtained by ALICE are compared to measurements from LHCb [82], ep data in photoproduction from ZEUS [126], deep inelastic scattering results from H1 [126] and a compilation of e + e measurements [127]. For ALICE data, error bars are the sum in quadrature of statistical and systematic uncertainties, not including the uncertainty on the branching ratios (common to all the experiments). Predictions from PYTHIA simulations and from Statistical Hadronization Model (SHM) [128] are also included in the figure. Figure 3.7: p T -integrated ratios of D meson production cross sections, compared to results from other experiments [82, 126,127, 129] and to expectations from PYTHIA simulations and SHM [128]. Error bars represent the quadratic sum of statistical and systematic uncertainties, excluding the uncertainty on the branching ratios, common to all the experiments. The D meson reconstruction analysis was carried out also in pp collisions at s = 2.76 TeV. The analysis strategy is the same as that described above for the 7 TeV collisions. The p T -differential cross sections for prompt D 0, D + and D + production at central rapidity were measured and are shown in Fig. 3.8 [81]. Comparison with FONLL and GM-VFNS pqcd calculations and ratios between data and theoretical predictions are also shown and indicate a substantial agreement, with the FONLL central values slightly underestimating the data results and GM- VFNS central predictions slightly overestimating them. The measurements at 7 TeV were also extrapolated with a scaling procedure to 2.76 TeV energy to allow a comparison with measurements performed at this energy [130]. The 7 TeV data points were scaled by a factor equal to the ratio of FONLL calculations for the cross sections at the two energies; the uncertainty on the scale factor was evaluated by varying the pqcd calculation parameters and taking the envelope of the resulting predictions. The comparison between the p T - 103

106 CHAPTER 3. Measurements of charm with ALICE Figure 3.8: p T -differential cross sections for prompt D 0, D + and D + production at central rapidity in s = 2.76 TeV collisions, compared to FONLL and GM-VFNS pqcd calculations. Ratios between data and predictions are shown in the bottom panels. differential cross sections at 2.76 TeV and the rescaled 7 TeV cross sections is shown for D 0, D + and D + in Fig. 3.9 and indicates compatibility within the statistical uncertainties only. Ratios of the two measurements are also shown in the bottom panels of the same figure. This compatibility allows us to use the rescaled 7 TeV cross sections as the reference for the evaluation of the D meson nuclear modification factor. 3.3 Measurement of the D 0 p T -differential cross section in pp collisions at s = 7 TeV with the channel K π + π π + During the first part of the PhD studies, my research activity was devoted to study an alternative approach to reconstruct the D 0 meson at central rapidity with ALICE. With this approach, the D 0 meson is reconstructed from the hadronic decay channel into four charged mesons (i.e., the 4-prong decay mode) D 0 K π + π π +. This channel grants a series of advantages: it has a branching ratio larger than the K π + channel (8.07% ± 0.21% against 3.87% ± 0.05%); the secondary vertex of the decay can be reconstructed with higher precision, due to the presence of four daughter particles (since secondary vertex res- 104

107 CHAPTER 3. Measurements of charm with ALICE Figure 3.9: Comparison of p T -differential cross sections for prompt D 0, D + and D + meson production at central rapidity in s = 2.76 TeV collisions and in s = 7 TeV collisions rescaled to 2.76 TeV energy based on FONLL predictions. Ratios between 2.76 TeV and rescaled 7 TeV measurements are shown in the bottom panel. For the ratios, filled boxes represent scaling uncertainties, empty boxes show the systematic uncertainties on the measurements. 105

108 CHAPTER 3. Measurements of charm with ALICE olution increases with the number of reconstructed tracks coming from the vertex); 66% of the decays occurs through an intermediate resonant state, the ρ 0 (770): D 0 K π + ρ 0 (770) K π + π π +. This allows us to exploit an additional cut for the D 0 candidate selection, requiring to have, among the daughter tracks, a pair of opposite charge pions compatible with the ρ 0 (770) mass. The main drawback of the K π + π π + decay channel is the presence of a large combinatorial background. The D 0 candidates in an event were indeed built combining all the possible quadruplets of two positive and two negative tracks, starting from a pair of a positive and a negative track, then adding another positive track, obtaining a triplet, and finally adding another negative track, producing the D 0 candidate. This procedure leads to a number of candidates equal to: B 4 = N +(N + 1) 2! N (N 1), (3.4) 2! where N + and N are respectively the number of positive and negative tracks reconstructed in the event and passing the track quality selection. In high multiplicity events, the number of candidates B 4 is much larger than the number of D 0 candidates B 2 = N + N obtained exploiting the K π + decay channel. The data sample used for this analysis contained minimum-bias events collected during the 2010 pp data taking at s = 7 TeV, corresponding to an integrated luminosity of L int = 5 nb 1. Only events with the z coordinate of primary vertex satisfying the condition z vtx < 10 cm were considered. The minimum-bias trigger was based on the SPD and VZERO detectors: minimum-bias collisions were triggered by requiring at least one hit in either of the VZERO counters or in the SPD ( η < 2), in coincidence with the arrival of proton bunches from both directions. This trigger was estimated to be sensitive to about 87% of the pp inelastic cross section [131]. It was verified on Monte Carlo simulations based on the PYTHIA event generator [83] with Perugia0 tune [122] that the minimum-bias trigger is 100% efficient for D 0 mesons with p T > 1 GeV/c and y < 0.5. Contamination from beam-induced background was rejected offline using the timing information from the VZERO detector and the correlation between the number of hits and the tracklets in the SPD detector D 0 candidates selection and invariant mass distributions The sample of D 0 and D 0 candidates 4 was studied in the 3 < p T < 25 GeV/c transverse momentum range. The lower p T limit was due to the high combinatorial 4 In the analysis, both D 0 and D 0 were reconstructed; from now on both particle and antiparticle will be indicated with D 0 for brevity, when not differently specified. 106

109 CHAPTER 3. Measurements of charm with ALICE background for p T < 3 GeV/c, which made not possible to extract the signal yield in that range; in addition, due to the kinematics of the decay, only in few cases all the four decay particles of a D 0 with p T < 3 GeV/c could satisfy the conditions on the minimum p T and pseudorapidity acceptance (e.g., this occurred only for the 11.6% of the D 0 with 2 < p T (D 0 ) < 3 GeV/c). The limit for the high p T reach depended on the limited statistics of the analyzed data sample. The rapidity range in which the candidates were reconstructed was a fiducial interval (y fid ), whose range increased quadratically with p T, from y fid = 0.5 at p T = 0 up to y fid = 0.8 for p T 5 GeV/c. The analysis was performed in six p T intervals, as summarized in Tab Table 3.3: p T interval limits (in GeV/c) for the D 0 to 4-prong reconstruction analysis. Bin1 Bin2 Bin3 Bin4 Bin5 Bin6 3 < p T < 5 5 < p T < 6 6 < p T < 8 8 < p T < < p T < < p T < 25 Selection of the D 0 candidates Each reconstructed D 0 candidate had to pass a set of selection criteria to reduce the combinatorial background in the invariant mass distributions. The selection comprised three different types of cuts, similarly to the D 0 K π + analysis, but with different cut variables and values: reconstruction quality of the D 0 daughter tracks; kinematics and topology of the decay; particle identification of the daughter tracks. For the reconstruction quality selection, the tracks tagged as D 0 daughters had to satisfy the following requirements: p T > 0.3 GeV/c, η < 0.8, χ 2 /ndf < 2 for the track momentum fit in the TPC, at least four hits in the ITS, one of which had to be in either of the SPD layers. The topological selection was defined on the basis of Monte Carlo studies [132]. The cut variables are listed in the following: Distance of closest approach between opposite charge tracks (DCA). For a D 0 candidate, built from four tracks, there are four pairs of opposite charge tracks, and consequently four DCA values. For a true D 0, neglecting the detector resolution, all the DCA would be 0, while DCA values of background candidates have a broader distribution, because there are cases in which some of the tracks come from a decay vertex and some from the primary vertex. The candidate had to pass the cut for all the four DCA variables, i.e. all the four DCA values had to be lower than the cut value, in order to be selected. 107

110 CHAPTER 3. Measurements of charm with ALICE Distance between primary vertex and vertex of the pair (Dist2). The pair is an intermediate state in the construction of the candidate, obtained by combining the first two tracks. Since a D 0 has a mean proper decay length of cτ 123 µm, a true D 0 is more displaced from the primary vertex than a background candidate; this reflects in a wider distribution of this variable for the true D 0. Distance between primary vertex and vertex of the triplet (Dist3). Once a third track is associated to the pair, a triplet is obtained and its vertex is computed. Also in this case, for a true D 0 this variable assumes an average value larger than for background candidates. Distance between primary vertex and vertex of the quadruplet (Dist4). Here the quadruplet corresponds to the final D 0 candidate, after having added the fourth track. As before, a true D 0 has on average a larger distance from the primary vertex than background candidates. Cosine of pointing angle (cos θ point ). It is defined as the angle between the flight line (i.e. the vector connecting primary and secondary vertex) of the candidate and the direction of its momentum. Neglecting the detector resolution, the distribution of this variable for true D 0 should be peaked at 1 (θ point = 0), while for background candidates it should be much flatter. ρ 0 (770) compatibility. As previously stated, about the 66% of the decays occurs through the intermediate state K π + ρ 0 (770), with the ρ 0 (770) eventually decaying into a pair of pions (BR 100%). A topological cut was thus introduced to select mainly the D 0 decaying through this resonant mode, allowing for an effective background rejection. In particular, the candidate was required to have at least a pair of tracks with opposite charge which, under the pion mass assumption, had a mass compatible with that of the ρ 0 (770). Except for the ρ 0 (770) compatibility cut, the values of the cut variables depended on the p T of the candidate. They were tuned in order to maximize the statistical significance of the signal peaks in the invariant mass distributions, keeping at the same time the selection efficiency high enough. Anyway, the values were defined in order to have smooth transitions of the cut value from a p T interval to the following one. This avoided to define specific values which could result in an artificial enhancement of statistical fluctuations under the signal peak. The values of the cut variables for the different p T intervals are listed in Tab The particle identification on the daughter tracks was performed using the specific energy deposit (de/dx) in the TPC and the time-of-flight information from the TOF. In both cases, the measurements were compared to the expected values for a given particle (π or K) having the same momentum of the track. This comparison was performed on each daughter track and for both mass hypotheses (kaon 108

111 CHAPTER 3. Measurements of charm with ALICE Table 3.4: Summary of selection criteria for the six p T intervals of the analysis. Variable Condition Values Bin1 Bin2 Bin3 Bin4 Bin5 Bin6 DCA (µm) upper cut Dist2 (µm) lower cut Dist3 (µm) lower cut Dist4 (µm) lower cut cos θ point lower cut M(π + π ) m ρ 0 (770) (MeV/c 2 ) upper cut 100 or pion), producing for each case one of the following responses: identification, compatibility or exclusion. In particular, for the TOF, identification of tracks with p T < 1.5 GeV/c was claimed if the measured time-of-flight was inside 3σ from the expected value, otherwise the response was exclusion ; if the track had a p T > 1.5 GeV/c, a compatibility response was always given inside 3σ, since it was no longer possible to discriminate K and π. For the TPC, identification was assumed if the measured de/dx was within 2σ from the Bethe-Bloch reference for p T < 0.6, and within 1σ for 0.6 < p T < 0.8; if it was not, but the track was within 3σ from the reference for any p T, the hypothesis was considered as compatible, otherwise the response was exclusion. Outputs from TPC and TOF were combined, and if the two detectors gave opposite responses (i.e. one identification and one exclusion ) on a track for a given specie, the track was considered to be compatible with that specie. In case of compatibility output from only one detector, the other one determined the global response. PID was performed by means of the TPC only, which is always available, in case TOF information was missing. Since a D 0 candidate is composed of four tracks, each candidate generates four different mass hypotheses, differing in the daughter tagged as the kaon. In the analysis, each D 0 mass hypothesis passed the PID selection if all the four tracks were at least compatible with the specie assigned by that hypothesis. The ρ mass cut could help in removing some of the hypotheses, requiring the pair of tracks satisfying it to be pions. This, however, did not exclude that multiple hypotheses could be accepted for the same D 0 candidate, resulting in a contribution to the background, called reflection from here on. Subtraction of reflection contribution A Monte Carlo study, based on the PYTHIA event generator [83] with Perugia0 tune [122], showed that a non-negligible amount of entries in the invariant mass distributions consisted of reflections, i.e. wrong mass hypotheses for track quadruplets coming from a true D 0 decay. Differently from the combinatorial background, well described by a 2 nd order polynomial function, the distribution of these reflections showed a structure with a concentration of candidates near the D 0 nominal mass; in this region, the presence of reflections could introduce a bias in the raw 109

112 CHAPTER 3. Measurements of charm with ALICE yield extraction. The reflection candidates had to be removed from signal counting. To do so, an analysis was performed on a Monte Carlo sample to extract, in each p T interval, the invariant mass distribution of reflections which had passed the candidate selections. These distributions were fitted with a polynomial plus Gaussian function (FuncRefl in the following), in order to have a precise description of their shape. The invariant mass distributions of reflections are shown in Fig with the fit functions superimposed. For each p T interval, the fit function was then rescaled by a normalization factor N and added to the function used to fit the invariant mass distributions in the real data analysis. The normalization factor was calculated as follows. From the data analysis, the signal S data was extracted by fitting the invariant mass distributions; the Monte Carlo invariant mass distributions were also produced by running the analysis on the same Monte Carlo sample used to determine the reflection distributions, and the signal from the Monte Carlo sample was extracted as well (S MC ). N was thus defined as the ratio S data /S MC. Figure 3.10: Invariant mass distributions of reflection contribution extracted from the Monte Carlo analysis, in the six transverse momentum intervals. The polynomial plus Gaussian fit functions (FuncRefl) are superimposed to the distributions. Invariant mass distributions The invariant mass distributions obtained after the selection of the D 0 candidates are shown in Fig for the six p T intervals in which the sample was divided. The distributions were fitted using the following fit function, which is superimposed to the data distributions in the figure: Ax 2 + Bx + C + D e (x µ)2 2σ 2 + N FuncRefl. (3.5) 110

113 CHAPTER 3. Measurements of charm with ALICE The 2 nd order polynomial (Ax 2 + Bx + C) described the combinatorial background; the Gaussian was used to fit the signal peak and all its parameters were left free; FuncRefl, rescaled by the factor N, accounted for the reflections close to the D 0 mass peak as described above. Both FuncRefl and N were p T -dependent. The background function, composed of the 2 nd order polynomial and the reflection function component, is also shown superimposed to the distributions in Fig The reflection peak, under the D 0 mass peak, can barely be seen in most of the p T intervals. The values of the signal (S) and of the background (B) were extracted from the integral of the Gaussian component of the fit in the range [µ 3σ, µ + 3σ], allowing to evaluate the statistical significance of the signal peak. A summary of the values for these quantities is reported in Table 3.5. To extract the yields used for the cross sections evaluation, however, the full integral of the Gaussian component of the fit was considered. 111

114 CHAPTER 3. Measurements of charm with ALICE Figure 3.11: Invariant mass distributions of the selected D 0 candidates, for the six pt intervals in which the data sample was split. In each panel, the overall fit function (blue curve) and the background fit function (red curve) are superimposed to the data, as described in the text. The µ and σ values of the Gaussian function, together with the signal value S, are also reported. 112

115 CHAPTER 3. Measurements of charm with ALICE Table 3.5: Values of signal (S), background (B), statistical significance, mean (µ) and sigma (σ) of the Gaussian peaks, with the corresponding uncertainties, in the six p T intervals. Quantity Values for the various p T intervals 3 < p T < 5 5 < p T < 6 6 < p T < 8 8 < p T < < p T < < p T < 25 S 129 ± ± ± ± ± ± 27 B 1140 ± ± ± ± ± ± 14 Significance 3.6 ± ± ± ± ± ± 0.5 µ (GeV/c 2 ) ± ± ± ± ± ± σ (MeV/c 2 ) 6.6 ± ± ± ± ± ± 4.2 The functional form of the combinatorial background was chosen to be a 2 nd order polynomial after a study on Monte Carlo simulations. Compared to the 1 st order polynomial and to the exponential, this function granted, on average, lower χ 2 /ndf and widths of the signal peaks closer to those expected from Monte Carlo simulations. The reflections under the D 0 mass, which were accounted for by the reflection function in the fit, amounted to about 5-8% of the signal value and their contribution decreased with increasing D 0 p T. This contribution was calculated from the ratio between the value of the signal extracted with the overall fit function and the signal obtained from a fit function without the reflection component (i.e. fitting the background with a 2 nd order polynomial only). The mean and the sigma values of the Gaussian peaks extracted from the fits were compared, respectively, to the PDG value of the D 0 mass and to the mass resolution obtained from Monte Carlo simulations, as shown in Fig For the mean value, a few intervals showed a higher value than the nominal mass of the D 0, probably due to large statistical fluctuations of the background. For the sigma value, compatibility within the uncertainties was obtained in most of the p T intervals, with only two of them showing a larger sigma than in Monte Carlo simulations Corrections Starting from the raw yields extracted from the fits to the invariant mass distributions, the cross section for prompt D 0 production can be obtained for each p T interval by means of the following formula, similarly to the other D meson analyses described in Section 3.2: dσ D0 dp T 0 = 1 1 f prompt(p T ) N D0/ D y <yfid, (3.6) y <0.5 2 y p T (Acc ɛ) prompt (p T ) BR L int where N D0 / D 0 is the raw yield, which includes both D 0 and D 0, p T and y are the widths of the p T and rapidity intervals, respectively, (Acc ɛ) prompt (p T ) is the efficiency times acceptance for prompt D 0 and D 0, f prompt (p T ) is the fraction of prompt D 0 and D 0 in the raw yield, BR is the branching ratio of the K π + π π + 113

116 CHAPTER 3. Measurements of charm with ALICE Figure 3.12: Left: comparison between the means of the Gaussian peaks (data points) and the PDG mass of the D 0 (dashed line). Right: comparison between the σ of the Gaussian peaks and the σ values predicted by a Monte Carlo simulation. decay mode and L int is the integrated luminosity. Since the cross section refers to D 0 only (not including D 0 ), a factor 1/2 is also present in the formula. The integrated luminosity was calculated as the ratio N pp,mb /σ pp,mb, where N pp,mb is the number of pp events selected by the minimum-bias trigger used in the analysis and σ pp,mb = 62.2 mb is the cross section of the minimum-bias process, with a 3.5% systematic uncertainty, as obtained from a Van der Meer scan [131]. The efficiency and acceptance, merged in the (Acc ɛ) prompt factor, were calculated separately. The efficiency ɛ is the fraction of reconstructed and selected D 0 over the total number of D 0 in the fiducial acceptance y fid with all the four decay tracks entering the acceptance of the central barrel. All the decay modes leading to the K π + π π + final state were considered in computing the efficiency correction, with the decay mode with the ρ 0 (770) in the intermediate state being dominant because of the ρ 0 (770) mass cut. The efficiency correction was determined from a Monte Carlo sample enriched with charm quarks and in which D mesons were forced to decay into the hadronic modes under study. This simulation described in detail the geometry, the experimental setup and the conditions of all the ALICE detectors during the 2010 data taking. The collisions were simulated using PYTHIA event generator [83], with Perugia0 tune [122]. The acceptance Acc can be defined as the ratio between the number of D 0 generated in y fid with all the four decay tracks in the barrel acceptance and the number of D 0 generated in y < 0.5, without any acceptance cut on the decay particles. With this definition, the y in Eq. 3.6 is equal to 1. Fig shows the overall (Acc ɛ) values for the six p T intervals, for both prompt and feed-down D 0. In both cases, as also noticed for the other D meson analyses, the value of the efficiency grows with increasing p T. This is expected since at low p T tighter cuts were applied to remove the large combinatorial background, while for higher values of p T the background was less abundant and the cuts could be released. The efficiencies for feed-down D 0 are a factor 2-3 higher than for prompt 114

117 CHAPTER 3. Measurements of charm with ALICE Figure 3.13: Efficiency times acceptance correction as a function of p T for prompt D 0 (red points) and feed-down D 0 (blue points). mesons (the factor decreases with increasing p T of the D 0 ), because B mesons have on average a large proper decay length, thus making feed-down D 0 decay vertices more displaced from primary vertex than for prompt D 0. Therefore, it is more likely for feed-down D 0 to pass the Dist2, Dist3 and Dist4 topological cuts, especially at low p T. The f prompt factor is the fraction of prompt D 0 present in the sample of selected candidates. It was determined with a method, called N b approach, that exploits the FONLL calculation for the B meson production, which describes well the beauty production data collected at Tevatron [133] and at the LHC. The B D 0 decay kinematics was described with the EvtGen package [123]. The number of feed-down D 0 in the raw yields obtained from the mass distributions, N feed-down D0 raw, was obtained as: N feed-down D0 D0 raw dσfeed-down FONLL y <yfid = 2 dp T y p T (Acc ɛ) feed-down BR L int. y <0.5 (3.7) In detail, the p T -differential cross section predicted by FONLL calculations was normalized to the width of the p T and rapidity intervals, it was then multiplied by the acceptance times efficiency for feed-down D 0 and rescaled by the branching ratio of the decay channel and by the integrated luminosity. An additional factor of 2 was included to account for the antiparticle too, since FONLL calculations consider only the D 0 particle. The fraction of prompt D 0 in the yields was then obtained as: f prompt (N b ) = N D0 raw N feed-down D0 raw. (3.8) N D0 raw The f prompt evaluation was performed separately in each p T interval. To estimate the systematic uncertainty on the feed-down subtraction, the results 115

118 CHAPTER 3. Measurements of charm with ALICE obtained with N b approach were compared to those obtained from an alternative method, called f c approach. This approach uses both the FONLL charm and beauty predictions, together with the (Acc ɛ) corrections for prompt and feeddown D 0. With this method, the fraction of prompt D 0 in the yield was obtained as follows: f prompt (f c ) = 1 + (Acc ɛ) feed-down (Acc ɛ) prompt dσfeed-down D0 FONLL dp T y <0.5 prompt D0 dσfonll dp T y < (3.9) which is equivalent to evaluate the ratio of prompt D 0 over the sum of prompt and feed-down D 0, with all the predictions multiplied by the respective (Acc ɛ) factors. Fig shows the values of f prompt for each p T interval evaluated with both approaches, together with their uncertainties. N b results are slightly higher than f c ones. This feature occurs because the central value of FONLL predictions underestimates the prompt D 0 meson cross section points (as it will be seen in the final results); the farther the predictions from the data points, the higher the discrepancy. The N b method was taken as reference for the cross section calculation because FONLL theoretical predictions describe beauty production better than charm production [120, ]. The uncertainties on the results are due to the theoretical uncertainty on the FONLL predictions. These, in turn, derive from the uncertainties on the PDFs, on the renormalization (µ R ) and factorization (µ F ) scales and on the beauty and charm quark masses. The larger error at low p T depends on the wider uncertainty band of the FONLL predictions in this region of transverse momentum. As systematic uncertainty for the feed-down correction evaluation, the envelope of N b and f c results was taken Systematic uncertainties evaluation In this section the various sources of systematic uncertainties are enlisted and the methods used to evaluate their contributions are described. The values of the uncertainties were computed separately for each p T interval. A first source of systematic uncertainty deals with the yield extraction from the invariant mass distributions. Its amount was estimated in different ways. A first approach was to obtain the value of the signal by counting the entries in the bins under the peak instead of integrating the Gaussian component of the fit (bin counting approach). More precisely, all the entries in the bins closer than 3σ from the centre of the peak were summed, considering also the bins containing the edges of the interval, and the integral of the background function in the same range was subtracted. Width and mean values were taken from the Gaussian fit of the signal peak. A second test consisted in changing the function used to fit the combinatorial background. Instead of the 2 nd order polynomial, a straight line was used in the fit, together 116

119 CHAPTER 3. Measurements of charm with ALICE Figure 3.14: Fraction of prompt D 0 in the raw yield, estimated with N b (blue triangles) and f c (red squares) approaches as described in the text, for the six p T intervals. with the Gaussian and reflection functions. The fit procedure was performed fixing the Gaussian widths to the values obtained with the 2 nd order polynomial fit, since in some p T intervals the fit with a straight line for the combinatorial background gave rise to Gaussian peaks with a too large width with respect to Monte Carlo predictions, thus biasing the signal extraction. The raw yields were then extracted by integrating the Gaussian component of the fit function. For each approach, the value of the uncertainty was defined as the relative difference between the values of the yields obtained with the procedures described above and the standard procedure. For each p T interval, the highest discrepancy with respect to standard results from the two approaches was chosen as systematic uncertainty for the raw yield extraction. Another source of uncertainty on the cross section measurement derives from the residual differences between data and Monte Carlo simulations for the variables used for the D 0 selection. To estimate this contribution, two other sets of cut values were defined, having respectively looser and tighter values than standard cuts. In order to have sufficiently different statistical samples, the cut values were varied by more than 15%, except for a few variables for which such a variation strongly suppressed the signal peaks in the invariant mass distributions. For p T < 12 GeV/c, where the cuts were most selective, the different cut values produced a variation of the raw yield of at least 20%. The cross sections were computed with the alternative cut values, using the corresponding acceptance and efficiency corrections, and their ratios over the standard cross section, obtained using the default cut values, were evaluated. For each p T interval the systematic uncertainty was assumed as half of the maximum difference from unity of the ratios. An additional source of uncertainty derives from different efficiency of the PID selection in data and Monte Carlo samples. In order to give an estimation of this discrepancy, the analysis was repeated not using the particle identification selection. When trying to extract the raw yields from the invariant mass distributions without 117

120 CHAPTER 3. Measurements of charm with ALICE Table 3.6: Values of systematic uncertainties from the sources described in the text and overall systematic uncertainty. Contribution Estimated values Bin1 Bin2 Bin3 Bin4 Bin5 Bin6 Cut efficiency 20% 20% 20% 20% 10% 10% PID efficiency 15% 15% 15% 10% 10% 10% Yield extraction 20% 15% 15% 20% 20% 20% Feed-down subtraction +6% 20% +6% 15% +4% 11% +5% 9% +5% 10% +3% 11% MC p T shape 10% 5% 5% 5% 5% 5% Tracking efficiency 16% Branching ratio 2.5% Normalization 3.5% Total (w/o normalization) +37% 42% +34% 36% +33% 35% +34% 35% +30% 31% +29% 31% PID selection, however, no clear signal was observed in the first two p T intervals (for p T < 6 GeV/c); indeed, at low p T particle identification was crucial to distinguish the signal peak from the combinatorial background. In these two intervals, this systematic contribution could not be evaluated directly, so the value was taken as the same of the third p T interval (6 < p T < 8 GeV/c). The shape of the D 0 p T spectrum in the Monte Carlo simulation used to compute the reconstruction and selection efficiencies could lead to another systematic uncertainty. To evaluate its contribution a comparison of the D 0 efficiencies obtained using PYTHIA and FONLL p T shapes to describe the D 0 spectrum was performed. The variation of the efficiency was used to assign a systematics uncertainty of 10% at low p T, decreasing to 5% at intermediate and high p T. The uncertainty on the feed-down subtraction was estimated, as discussed before, by taking the envelope of the f prompt values obtained with N b and f c methods, including their errors. The uncertainty due to tracking efficiency and track selection criteria was estimated to be about 16% (coming from a 4% for the uncertainty on the single track) by varying the track selection and comparing data and Monte Carlo simulations. Other additional sources of uncertainties are the branching ratio uncertainty, for which the value from the 2010 PDG [46] was considered, and the uncertainty on the cross section of the pp minimum-bias trigger, used for the normalization, estimated as 3.5%. The values of all the systematic uncertainties described above are reported in Tab. 3.6, while a comprehensive plot in which all contributions are displayed as a function of p T is shown in Fig

121 CHAPTER 3. Measurements of charm with ALICE Figure 3.15: Systematic contributions from the sources described in the text and overall systematic uncertainty on the measurement of the prompt D 0 meson production cross section in the K π + π π + channel as a function of the transverse momentum Cross section and comparison with D 0 K π + results The p T -differential cross section for prompt D 0 production at mid-rapidity ( y < 0.5) is shown in Fig. 3.16, compared to the FONLL [20,124] and GM-VFNS pqcd calculations [125] evaluated in the same p T intervals used for the analysis. In these calculations the CTEQ6.6 PDFs are used [136] and the unknown parameters are varied independently in the following ranges: 1.3 < m c < 1.7 GeV/c 2, 0.5 < µ F /m t < 2, 0.5 < µ R /m t < 2, with the constraint 0.5 < µ F /µ R < 2, with m t = p 2 T + m2 c. The values of the measured cross section are also given in Table 3.7, together with statistical and systematic uncertainties. The results show a good compatibility between data and theoretical calculations within the uncertainties, with the central values of GM-VFNS and FONLL predictions slightly overestimating and underestimating, respectively, the data. In particular, data results lie on the upper edge of FONLL uncertainty band, reflecting what had already been observed in pp collisions at RHIC ( s = 200 GeV) [ ] and in p p collisions at Tevatron ( s = 1.96 TeV) [120]. The cross section was also compared to the measurements obtained by reconstructing the D 0 meson from its K π + decay [26] (as described in Section 3.2), rebinned in the same p T intervals of this analysis. The comparison is shown in Fig Figure 3.18 shows the ratio between the cross section measurements from this analysis and those obtained by reconstructing the D 0 in the channel K π + ; the error bars show the statistical uncertainties only. The ratio is compatible with unity within the uncertainties in all the intervals, denoting a good agreement between the two measurements. The value for the 16 < p T < 25 GeV/c interval is not present 119

122 CHAPTER 3. Measurements of charm with ALICE Figure 3.16: Comparison between measurements for prompt D 0 meson production cross section, with statistical errors (bars) and systematic uncertainties (boxes), and FONLL (red boxes) and GM-VFNS (blue boxes) predictions, rebinned in the p T intervals of the analysis. In the bottom panels, the ratios of data over theoretical predictions are displayed. 120

123 CHAPTER 3. Measurements of charm with ALICE Table 3.7: Values of the prompt D 0 meson production cross section, with statistical and systematic uncertainties, for the six D 0 p T intervals used in the analysis. p T range (GeV/c) dσ dydp T ± stat. ± syst. (µb/gev/c) ± ± ± ± ± ± since no results are available in that p T range for the K π + analysis. Fitting the five points of the ratio with a constant results in an overall ratio of ± 0.133, compatible with unity within 1σ. Figure 3.17: Comparison between prompt D 0 production meson cross sections measured via the K π + π π + (blue points) and the K π + (red points) decay modes. 121

124 CHAPTER 3. Measurements of charm with ALICE Figure 3.18: Ratio between prompt D 0 meson production cross sections from K π + π π + and K π + analyses in the five common p T intervals, with a constant fit superimposed (solid line). 3.4 Other charm analyses in pp collisions Measurement of charm and beauty hadron production from e+x decays Most of charm and beauty hadrons have large branching ratios to semielectronic decays. This allows us to measure heavy flavour production by studying the contribution of these decays to the inclusive electron p T distributions. ALICE measured the production of single electrons from charm and beauty hadron decays in the 0.5 < p T < 8 GeV/c transverse momentum range at central rapidity ( y < 0.5) in pp collisions at s = 7 TeV [140]. The analysis relies on the electron identification and on the determination of all the other sources of electrons in the inclusive distributions, which can be considered as background for the heavy flavour decay electron measurements. Excellent capabilities for the identification of the electrons among the reconstructed tracks are therefore required. The electron identification was performed through two complementary approaches. Both used specific energy loss measurements from the TPC detector. The first approach used the TPC together with TOF and TRD responses, while the second in combination with E/p information from the EMCal. After selecting the electrons from the reconstructed tracks via PID selection, the residual contamination from misidentified hadrons was estimated by fitting the measured TPC de/dx distributions with functions modelling hadron and electron contributions. This contamination, of few percents, was subtracted from the sample of selected electrons. A series of corrections was then applied to the inclusive electron p T distributions, taking into account the detector geometrical acceptance, the track 122

125 CHAPTER 3. Measurements of charm with ALICE reconstruction efficiency and the PID efficiency for the selection of the electrons. The background to the heavy flavour decay electrons in the inclusive electron p T distribution comprises a series of contributions, the most important being: electrons from Dalitz decays of light neutral mesons and from conversions of their decay photons in the detector material; electrons produced in weak decays of K mesons and dielectron decays of light vector mesons; electrons from e + e decays of quarkonium states; electrons produced in partonic hard scattering processes and electrons related to the production of prompt photons. Monte Carlo simulations were used to describe the relative electron contributions of the different background sources, with a cocktail approach. The cocktail distribution was subtracted from the measured inclusive electron distribution, leaving only the heavy flavour decay electron component. After an overall normalization performed using the cross section of minimum-bias pp collisions, the final production cross section for heavy flavour decay electrons was calculated as the weighted average of the measurements with the two PID strategies, using as weights the sum in quadrature of statistical and uncorrelated systematic uncertainties of each procedure. The left panel of Fig shows the p T -differential cross section of electrons from heavy flavour decays, in the rapidity range y < 0.5, in pp collisions at s = 7 TeV, together with predictions from FONLL calculations. Theoretical predictions well reproduce the data, as shown in the ratio in the bottom panel. ALICE results are also found to be compatible with measurements by ATLAS [141] in a complementary p T range and in the rapidity interval y < 2, (excluding the 1.37 < y < 1.52 regions) in pp collisions at the same energy, as shown in the right panel of Fig FONLL calculations for both rapidity intervals are also shown in the same panel, while the bottom panel plots the ratios between measurements and theoretical predictions. Preliminary results for heavy flavour decay electron measurements are also available for pp collisions at s = 2.76 TeV energy, as shown in Fig Here the p T -differential cross section for heavy flavour decay electrons with η < 0.7 is presented, together with FONLL theoretical calculations. The ratio between data and theoretical calculations is shown in the bottom panel. FONLL predictions match very well data except for the highest p T interval. Measurements of beauty contribution to electrons from heavy flavour decays The measurement of azimuthal correlations between heavy flavour decay electrons and charged hadrons can be exploited to quantify the beauty contribution to the spectrum of heavy flavour decay electrons. In addition to providing a reference for Pb-Pb measurements, this analysis allows us to test perturbative pqcd calculations and is complementary to the D-hadron correlation analysis described in Chapter 4. The relative beauty contribution can be evaluated by considering that the correlation shapes for electrons coming from B mesons and D mesons are differ- 123

126 CHAPTER 3. Measurements of charm with ALICE Figure 3.19: Left: p T -differential cross section of electrons from heavy flavour decays measured at central rapidity in pp collisions at s = 7 TeV, compared to FONLL predictions. The ratio of data over pqcd calculations is shown in the bottom panel. Error bars and boxes represent statistical and systematic uncertainties on the measurements, respectively. Right: p T -differential cross section of electrons from heavy flavour decays measured by ALICE and ATLAS [141] in pp collisions at s = 7 TeV, at central rapidity but for different y intervals. FONLL pqcd calculations for the corresponding rapidity intervals are also shown for comparison. The bottom panel shows the ratios of data over pqcd calculations. 124

127 CHAPTER 3. Measurements of charm with ALICE Figure 3.20: p T -differential cross section of electrons from heavy flavour hadron decays with η < 0.7 in pp collisions at s = 2.76 TeV, compared to FONLL predictions. Error bars represent the statistical error, empty boxes show the systematic uncertainty. The ratio of data over pqcd calculations is shown in the bottom panel. ent, due to the different decay kinematics of the hadrons. The greatest difference is related to the width of the near side peak (for ϕ 0), which is larger for beauty electrons. Figure 3.21 shows ALICE preliminary results for the e-h azimuthal correlations in several p T intervals, in pp collisions at s = 7 TeV (black points). The correlation distributions from beauty (blue points) and charm (red points) electron contributions only, obtained from Monte Carlo simulations, are superimposed to data results. A fit to the data distribution is performed in the range 1.5 < ϕ < 1.5 rad. The fit function is composed of the sum of the Monte Carlo distributions for beauty and charm electron ϕ correlations, leaving their relative weights as a free parameter, plus a constant to account for the uncorrelated background. This allows us to extract the relative contribution from beauty electrons up to p e T = 18 GeV/c. These results extend the p T range of other ALICE measurement for the beauty contribution to heavy flavour decay electrons [142]. In this analysis, electrons from beauty hadron decays were selected studying the displacement of the decay vertex from the collision vertex, in the p T range 1 < p e T < 8 GeV/c. The fraction of beauty electrons contributing to the heavy flavour decay electron spectra obtained combining the two approaches is shown in Fig Although performed in different p T intervals, the results show a compatible p T trend of the beauty contribution. Predictions from FONLL [20] pqcd calculations are in agreement with ALICE measurements in the whole p T range. 125

128 CHAPTER 3. Measurements of charm with ALICE Figure 3.21: Azimuthal correlation distributions for heavy flavour decay electrons (black points) in pp collisions at s = 7 TeV, shown for different p T intervals. Distributions for electrons from D (red points) and B (blue points) meson decays, obtained from Monte Carlo simulations, are superimposed on data. A fit to the data results is also shown for the range 1.5 < ϕ < 1.5 rad (details in the text). 126

129 CHAPTER 3. Measurements of charm with ALICE Figure 3.22: Relative beauty contribution to the heavy flavour decay electron yield, measured by ALICE in pp collisions at s = 7 TeV. Results are obtained exploiting impact parameter (red points) and e-h azimuthal correlation methods (black points). Predictions from FONLL calculations are superimposed to data. Error bars and boxes represent statistical and systematic uncertainties, respectively Measurement of charm and beauty hadron production from µ+x decays ALICE has measured the p T -differential production cross section of single muons from heavy flavour decays in the transverse momentum range 2 < p T < 12 GeV/c with the forward muon spectrometer (rapidity range 2.5 < y < 4), in pp collisions at s = 7 TeV [143]. The single muon analysis was performed on events selected with a specific muon trigger, while minimum-bias trigger events were used to translate the muon production yield into a p T -differential cross section. A series of cuts was applied to the tracks reconstructed in the muon spectrometer in order to remove the contamination from other particles. A selection on the pseudorapidity (actually the radial coordinate of the tracks at the end of the absorber) was applied to accept only tracks in the spectrometer geometrical acceptance. Tracks reconstructed in the tracking chambers were required to match the ones detected in the trigger chambers, to reduce the hadronic contamination of the sample. In addition, the correlation between the distance of closest approach to the primary vertex of the track (DCA) and its momentum was exploited to exclude tracks not pointing to the interaction vertex. Muons produced from charm and beauty hadron decays were obtained by studying the p T distribution of the selected tracks. Three main background contributions had to be removed from the muon sample: 127

130 CHAPTER 3. Measurements of charm with ALICE decay muons, produced from decays of primary light hadrons (i.e. π, K) and other hadron decays (like J/Ψ and lower mass resonances); secondary muons, coming from decays of secondary light hadrons produced inside the front absorber; punch-through hadrons, misidentified as muons, which are hadrons escaping the front absorber and then crossing the tracking chambers and reaching the trigger chambers. The p T distributions of all these contributions were evaluated via Monte Carlo simulations produced using PYTHIA [83] and PHOJET 1.12 [144]. The results indicate a negligible residual contribution from hadrons and fake tracks, while the heavy flavour contribution dominates the inclusive muon sample for p T > 4 GeV/c. All the background distributions in the Monte Carlo simulations were fitted to remove statistical fluctuations, which are due to low statistics at high p T. The normalization of the background distributions was performed by assuming that the fraction of decay muons was the same in data and Monte Carlo simulations, in the p T region where this contribution is dominant (i.e. for p T < 1 GeV/c). The average of PYTHIA and PHOJET simulations was then subtracted from the inclusive p T spectrum of the muons. The yield of heavy flavour decay muons was corrected for acceptance and for reconstruction and trigger efficiencies, extracted from a Monte Carlo simulation implementing the forward spectrometer response. The resulting distribution was finally normalized to the integrated luminosity to obtain the cross section. Fig shows the differential production cross section of single muons produced in heavy flavour decays as a function of p T in the rapidity range 2.5 < y < 4 (left panel) and as a function of rapidity for the transverse momentum range 2 < p T < 12 GeV/c (right panel), in pp collisions at s = 7 TeV. FONLL predictions for muons from charm and beauty decays (and their sum) are superimposed to data, showing a substantial agreement within the uncertainties. The ratio of data over theoretical predictions is shown in the bottom panels. FONLL calculations were found to slightly underestimate the data in the whole p T and y ranges. A similar conclusion was drawn also for the D meson [26] and the single heavy flavour decay electron [140] measurements at central rapidity. The analysis was also performed on the sample of pp collisions at s = 2.76 TeV, using the same methodology [145]. The p T -differential production cross section for heavy flavour decay muons in the range 2.5 < y < 4 is shown in Fig together with expectations from FONLL theoretical calculations, while the bottom panel shows the ratio of data over FONLL predictions. A similar slight underestimation of data as for the 7 TeV analysis is found for the theoretical predictions J/Ψ reconstruction from dileptonic decays ALICE can reconstruct heavy quarkonium states through their dileptonic decays, namely the e + e decay channel at mid-rapidity ( y < 0.9) and the µ + µ 128

131 CHAPTER 3. Measurements of charm with ALICE Figure 3.23: p T -differential (left) and y-differential (right) production cross sections of single muons from heavy flavour hadron decays in pp collisions at s = 7 TeV, compared to FONLL predictions for charm (violet), beauty (blue) and total heavy flavour (gray band) contributions. Error bars (too small to be visible for most of the points) represent statistical errors, empty boxes show the systematic uncertainties. Ratios of data results over FONLL calculations are shown in the bottom panels. decay channel in the forward spectrometer (2.5 < y < 4). The results for the J/Ψ differential production cross section in both rapidity ranges in pp collisions at s = 7 TeV [146] and at s = 2.76 TeV [147] will be discussed. The dielectron analysis was performed on a sample of minimum-bias events with the z coordinate of primary vertex satisfying the z vtx < 10 cm condition. A set of quality cuts for tracks reconstructed in ITS and TPC was applied to select only good tracks, requiring also a minimum p T of 1 GeV/c and η < 0.9. Electrons from γ conversions were reduced by requesting a hit in at least one of the SPD layers. PID selection was applied to reject hadrons: a 3σ inclusion cut around the electron hypothesis and a 3.5σ (3σ) cut for exclusion of pions (protons) were applied, based on the TPC de/dx measurements. The invariant mass distribution of oppositesign (OS) electrons was built. To remove the large combinatorial background, the invariant mass distribution for like-sign (LS) electrons was calculated too. After rescaling the latter to the integral of the OS distribution in the 3.2 < M ee < 5.0 GeV/c 2 mass interval, the LS distribution was subtracted from the OS distribution. Integration of the signal in the J/Ψ mass range was performed to extract the value of the yield. For the dimuon analysis a specific muon trigger (µ-mb trigger) was requested, in order to analyze events with at least one muon reconstructed in the forward spectrometer and with at least one interaction vertex reconstructed with the SPD. 129

132 CHAPTER 3. Measurements of charm with ALICE Figure 3.24: p T -differential production cross section of single muons from heavy flavour hadron decays in pp collisions at s = 2.76 TeV, compared to FONLL predictions for charm (violet), beauty (blue) and total heavy flavour (gray band) contributions. Error bars and empty boxes represent statistical and systematic uncertainties, respectively. The ratio of data over FONLL calculations is shown in the bottom panel. Only muon pairs in the 2.5 < y < 4 rapidity range were selected, to exclude muons reconstructed at the edge of the spectrometer. To reject hadrons passing through the absorber, it was requested that at least one of the two muon candidates matched the corresponding hits produced in the trigger chambers, located after the iron wall where hadrons are stopped. In addition, a lower cut on the track radial coordinate at the end of the front absorber was applied. This allowed to reject muons produced at small angles, which had crossed a large part of the beam shield. The invariant mass distribution of the muon pairs was built in the mass region 1.5 < m µµ < 5 GeV/c 2. Both J/Ψ and Ψ(2S) peaks were visible in the spectrum, on top of a large combinatorial background continuum. The J/Ψ yield was extracted from a fit to the distributions, using Crystal Ball functions [148] for the two peaks and a sum of two exponentials for the background. For both the dielectron and dimuon analyses, the J/Ψ raw yields were corrected for detector acceptance, track reconstruction and selection efficiencies and triggering efficiencies. Corrections were evaluated exploiting a Monte Carlo simulation with a p T distribution of J/Ψ extrapolated from CDF measurements [134] and a rapidity distribution evaluated from Color Evaporation Model calculations [149]. Production cross sections were then obtained by normalizing the yields to the integrated luminosity, using the measured minimum-bias trigger cross section. 130

133 CHAPTER 3. Measurements of charm with ALICE Fig [146] shows the double differential production cross section of J/Ψ as a function of p T (left) and the y-differential cross section for J/Ψ with p T > 0 (right), for both mid-rapidity and forward rapidity analyses, in pp collisions at s = 7 TeV. In the y-differential distribution, the forward rapidity measurements are reflected about mid-rapidity (open markers). Statistical and systematic errors are summed in quadrature and shown as error bars, while boxes represent the uncertainty on the luminosity. Results are compared to measurements from other LHC experiments [ ], showing an overall agreement within the uncertainties. A comparison between these results and the cross sections measured in pp collisions at s = 2.76 TeV [147] is shown in Fig The left panel shows the cross sections at forward rapidity, with superimposed NLO NRQCD calculations [153, 154] for p T > 3 GeV/c. The right panel shows the comparison of the measurements at the two energies for both e + e and µ + µ analyses. Figure 3.25: Left: double differential cross section for J/Ψ production at mid-rapidity and at forward rapidity as a function of p T, in pp collisions at s = 7 TeV. Results are compared to measurements from the other LHC experiments [ ] in similar rapidity ranges. Right: y-differential cross sections for J/Ψ production (for p T > 0) for midrapidity and forward rapidity measurements in pp collisions at s = 7 TeV. Comparison with results from the other LHC experiments is shown [151, 152]. In both panels error bars represent the sum in quadrature of the statistical and systematic uncertainties, while the luminosity systematic uncertainties are shown as empty boxes. All the results shown above refer to inclusive J/Ψ production, i.e. both prompt J/Ψ (directly produced in the pp collision or coming from decays of higher charmonium states) and non-prompt J/Ψ, obtained from B hadron decays. Nonetheless, it could be possible to separate the prompt and non-prompt contributions to J/Ψ production by studying the J/Ψ pseudoproper decay length, a kinematical variable defined as follows: x = c L xy m J/Ψ, (3.10) p J/Ψ T 131

134 CHAPTER 3. Measurements of charm with ALICE Figure 3.26: Left: double differential cross sections for J/Ψ production versus p T in the 2.5 < y < 4 rapidity range, in pp collisions at s = 7 TeV and s = 2.76 TeV. The measurements are compared to NLO NRQCD calculations for both energies [153, 154]. Right: y-differential cross sections for J/Ψ production (p T > 0) in pp collisions at s = 7 TeV and s = 2.76 TeV. Measurements from e + e (at mid-rapidity) and µ + µ (at forward rapidity) decay channels are shown. In both panels error bars and boxes show respectively the statistical and systematic uncertainties, while the uncertainty on luminosity (1.9%) is not included. where m J/Ψ is the J/Ψ mass and L xy = L p J/Ψ T /pj/ψ T is the signed projection of the J/Ψ flight distance L in the direction of its transverse momentum p J/Ψ T. As resulting from Monte Carlo studies, with the current performance of ALICE detectors it is possible to determine the fraction of non-prompt J/Ψ in pp collisions at s = 7 TeV by properly fitting the distribution of the J/Ψ pseudoproper decay length under the invariant mass peak, in the e + e analysis, for J/Ψ p T > 1.3 GeV/c. Further details on this topic and the results of this analysis can be found in [155]. 3.5 Results in Pb-Pb collisions Heavy flavour production in Pb-Pb collisions at s NN = 2.76 TeV was studied with ALICE exploiting the techniques previously described for the pp collisions. In this section a selection of the main results will be presented, with the focus on the two observables introduced in Section for the study of QGP properties: the nuclear modification factor R AA and the elliptic flow coefficient v R AA measurements The nuclear modification factor of prompt D mesons was measured as the ratio of D meson yields at central rapidity in Pb-Pb collisions at s NN = 2.76 TeV 132

135 CHAPTER 3. Measurements of charm with ALICE and the s-scaled cross section in pp collisions, multiplied by the nuclear overlap function (T AA ). Measurements of the average R AA of D 0, D + and D + mesons in the most central events (0-20% centrality class) [156] exhibit a suppression by a factor 3-4 of the D meson production in Pb-Pb collisions for p T > 4 GeV/c, as shown in Fig In the left panel of the figure, the D meson R AA at central rapidity for 0-20% centrality class is compared to ALICE results for the R AA of charged particles [157] and of non-prompt J/Ψ with p T > 6.5 GeV/c, measured by CMS [158], in a wider rapidity range. The comparison shows compatibility between D meson and charged particle R AA within the systematic uncertainties. The D meson R AA uncertainties are not fully correlated against p T, though, and some hints on a D meson R AA higher with respect to that of charged particles can hence be obtained, since D mesons R AA central values are constantly above charged particle R AA measurements. The comparison with non-prompt J/Ψ R AA, though being not conclusive with the current statistics, gives indications for R AA (B) > R AA (C). This hierarchy is also confirmed by the comparison between ALICE results for D meson R AA and CMS measurements for B meson R AA, already shown in Fig In the right panel of Fig D meson R AA is compared to predictions from several theoretical models which also evaluate the D meson v 2 coefficient [ ]. Some of the models describe well the p T dependence and the value of the nuclear modification factor, but for all of them it is challenging to properly reproduce at the same time both R AA and v 2 measurements. Figure 3.27: Left: average R AA of D mesons (black circles) at central rapidity in the 0-20% centrality class, compared to R AA measurements for charged particles [157] (open circles) and for non-prompt J/Ψ [158] (orange squares). The three normalization uncertainties shown as boxes at 1 are almost fully correlated. Right: comparison between ALICE measurements for D meson R AA and several theoretical models [ ]. Error bars and boxes represent the statistical and systematic uncertainties, respectively. The ALICE Collaboration has measured the nuclear modification factor also for 133

136 CHAPTER 3. Measurements of charm with ALICE heavy flavour decay leptons. The left panel of Fig shows preliminary results for the R AA of heavy flavour decay electrons with y < 0.6, for the most central events (0-10% centrality class). R AA was evaluated by using as pp reference the 7 TeV rescaled cross section at low p T and FONLL pqcd predictions at high p T, where pp measurements were not available. Data are compared to measurements by the PHENIX Collaboration for electrons with a p T up to 9 GeV/c, in a smaller rapidity range ( y < 0.35), in Au-Au collisions at s NN = 200 GeV [169]. Despite the large uncertainties, the comparison indicates a similar suppression in the overlapping p T region. The right panel of the same figure shows ALICE measurements for R AA of heavy flavour decay muons in the most central events (0-10%, red squares) and in peripheral collisions (40-80%, blue triangles) [170]. In central events a strong suppression is observed, by a similar factor as for D mesons and heavy flavour decay electrons. The suppression is flat with p T and it reduces when considering peripheral collisions. Figure 3.28: Left: ALICE measurements of R AA of heavy flavour decay electrons with y < 0.6, in the 0-10% centrality class. Data are compared to PHENIX measurements of heavy flavour decay electron R AA in the same centrality class, in Au-Au collisions at snn = 200 GeV [169]. Right: nuclear modification factor of heavy flavour decay muons in 2.5 < y < 4 as a function of p T in central (0-10%, red circles) and peripheral (40-80%, blue triangles) collisions. In both plots, vertical bars are the statistical uncertainties and open boxes are the p T -dependent systematic uncertainties. The normalization uncertainties are displayed as boxes at R AA = 1. Finally, ALICE has also measured the inclusive J/Ψ nuclear modification factor, for J/Ψ reconstructed in the µ + µ channel at forward rapidity (2.5 < y < 4) [171] and in the e + e channel at central rapidity ( η < 0.8). The results are shown in Fig as a function of the number of participants in the Pb-Pb collision (left panel). A clear suppression is observed at forward rapidity, independent of the centrality of the collision; at central rapidity, despite the larger uncertainties on the 134

137 CHAPTER 3. Measurements of charm with ALICE results, a suppression is observed too. The J/Ψ R AA values measured with ALICE in the integrated 0-90% centrality class are 0.57 ± 0.01 (stat) ± 0.09 (syst) and 0.72 ± 0.06 (stat) ± 0.10 (syst) at forward and central rapidity, respectively. A comparison of the ALICE results with theoretical models including a contribution to J/Ψ production from regeneration is shown in the right panel of the same figure. Here, J/Ψ R AA measurements are shown along with predictions from the Statistical Hadronization Model [ ], where J/Ψ production totally comes from cc combination at the hadronization, and from two transport models, where a rate equation controlling dissociation and regeneration of J/Ψ in the medium is introduced. Both SHM and Transport Model I predictions are found to be in good agreement with the data. This could suggest that a component of the Pb-Pb J/Ψ yield at LHC energies comes from J/Ψ regeneration from deconfined charm quarks in the medium. Figure 3.29: Left: inclusive J/Ψ R AA measured with ALICE as a function of the number of participating nucleons, reconstructing the J/Ψ in the µ + µ channel at forward rapidity (red squares) [171] and in the e + e channel at central rapidity (blue circles). Statistical errors are shown as vertical bars, uncorrelated systematic uncertainties as boxes. Global correlated systematic uncertainties are written as text. Right: comparison between inclusive J/Ψ R AA measured with ALICE and predictions by Statistical Hadronization model [172], Transport model I [173] and II [174] v 2 measurements In addition to the R AA measurements, the analyses described above also produced results for the elliptic flow coefficient of heavy flavour hadrons, namely D mesons, heavy flavour decay leptons and J/Ψ. Results for prompt D meson v 2 coefficient are shown in Fig The left panel of the figure shows the comparison between the average v 2 of prompt D 0, D + and D + mesons and the v 2 of charged particles [175] as a function of p T, in the 30-50% centrality class. Although uncertainties are large for the D mesons, the v 2 is similar for charm hadrons and light flavour hadrons, which dominate the charged particle sample. This suggests that low momentum charm quarks participate in the collective 135

138 CHAPTER 3. Measurements of charm with ALICE motion of the system. The right panel of Fig shows a comparison between the measured D meson v 2 and predictions from several theoretical models, which simultaneously also try to describe the D meson R AA [159, ,167,168, ]. Some models are able to reproduce the v 2 measurements but, as previously noted, a simultaneous description of both observables is presently a challenge. Figure 3.30: Left: comparison of the v 2 coefficient of prompt D mesons with unidentified charged tracks v 2, in the 30-50% centrality class. Right: prompt D meson v 2 compared to predictions from several theoretical models [159, , 167, 168, ], for events in 30-50% centrality class. For both panels, error bars, empty boxes and gray boxes show statistical uncertainties, uncorrelated systematic uncertainties and the asymmetric systematic contribution for feed-down subtraction, respectively. Measurements of the elliptic flow coefficient were performed also for heavy flavour decay leptons, by reconstructing electrons in the central barrel ( y < 0.5) and muons at forward rapidity in the muon spectrometer (2.5 < y < 4). The left panel of Fig shows the v 2 results obtained with ALICE for heavy flavour decay electrons reconstructed in y < 0.7, for the centrality class 30-50%, compared to results from PHENIX, which are relative to heavy flavour decay electrons in y < 0.35 in a lower p T range, produced in Au-Au collisions at s NN = 200 GeV. The values of v 2 from the two measurements are compatible inside the overlapping p T region, and are also well described by predictions from BAMPS model [179], a transport model which simulates the QGP evolution by solving the Boltzmann equation for on-shell partons, evaluated for s NN = 2.76 TeV. In the right panel of the same figure measurements of heavy flavour decay muon v 2 as a function of p T, in the 20-40% centrality class, are compared to the corresponding predictions from BAMPS [179] (in a slightly different centrality class) and Rapp et al. [180] theoretical models. As for the electrons, BAMPS model is able to reproduce the trend of the measurements. Although the uncertainties are very large, the v 2 of heavy flavour decay electrons and muons in the different rapidity ranges show a similar trend and compatible values. 136

139 CHAPTER 3. Measurements of charm with ALICE Figure 3.31: Left: measurements for heavy flavour decay electron v 2 performed with ALICE in the 20-40% centrality class, compared to results from PHENIX experiment, for heavy flavour decay electrons in a lower p T range. Predictions from BAMPS model [179] are also shown. Right: comparison of v 2 coefficient for heavy flavour decay muons measured with ALICE in 20-40% centrality class to predictions from BAMPS [179] (yellow dashed line) and Rapp et al. [180] (orange dashed line). In both panels the error bars represent statistical uncertainties, while empty boxes represent systematic uncertainties. Measurements of elliptic flow coefficient were carried out also for inclusive J/Ψ, reconstructed at forward rapidity in the dimuonic decay channel [181]. Fig shows the results for J/Ψ v 2 as a function of p T, in the 2.5 < y < 4 rapidity range, for events in the 20-60% centrality class. Results are compared to predictions from two transport models [182,183] including a J/Ψ regeneration component from deconfined c quarks in the medium ( 30% in the 20-60% centrality range). Despite the large uncertainties, there are hints of non-zero v 2 (a combined 2.9σ effect). This favors again a scenario where recombination mechanism is at play and the J/Ψ produced by cc recombination inherit the anisotropy of the c and c quarks, consistently with the physics message obtained from the R AA measurements. 3.6 D meson preliminary results in p-pb collisions During the last year, ALICE has studied the heavy flavour quark production also in p-pb collisions at s NN = 5.02 TeV, delivered in the first months of This is mandatory to separate, in the results extracted from Pb-Pb collisions, the cold nuclear matter effects from the final state effects, since QGP is not produced in p-pb collisions. While many analyses are still ongoing, some preliminary results are already available. In the following only the main results from the D meson reconstruction analysis will be presented, as they are strictly related with the D-hadron correlation analysis subject of this thesis work. The analysis strategy is similar to 137

140 CHAPTER 3. Measurements of charm with ALICE Figure 3.32: Measurements of inclusive J/Ψ v 2 coefficient as a function of p T, at forward rapidity, in the 20-60% centrality class. Results are compared to predictions from two different transport models [182, 183]. Error bars and boxes represent statistical and systematic uncertainties, respectively. that employed for the other collision systems, described in detail in Section 3.2. Figure 3.33 shows the inclusive cross section for prompt D 0, D +, D + and D + s meson production as a function of p T, in the rapidity range 0.04 < y cms < 0.96, in p-pb collisions at s NN = 5.02 TeV. The results are compared to a pp reference for the same energy. The reference was obtained by scaling the s = 7 TeV pp measurements for the prompt D meson production cross section by using the ratio of FONLL [20] predictions at s = 5.02 TeV and s = 7 TeV, as described in [130]. A scaling by the number of nucleons in the Pb nucleus is applied as well. A quantitative comparison between p-pb measurements and the pp reference can be obtained by evaluating the value of the D meson R pa. The value of this observable as a function of p T is shown in Fig for the four mesons separately (right panels) and for the average of D 0, D + and D + results (left panel). In the latter case, the results are compared to predictions from a theoretical model based on the Color Glass Condensate [184] and from pqcd calculations based on the HVQMNR code [16], combined with a parametrization of the shadowing effect from the EPS09 parameterizations of the PDFs [62]. Both the theoretical predictions provide a good description of the average of D meson R AA. The R pa measurements of the four mesons are in agreement with one another, and they are compatible with unity within the uncertainties over the full p T range. No suppression of the D meson yields is visible from the p-pb measurements. This allows us to conclude that the suppression of D meson production observed in Pb-Pb collisions is mainly due to final state effects, i.e. to the formation of a QGP state. 138

141 CHAPTER 3. Measurements of charm with ALICE Figure 3.33: p T -differential inclusive cross sections for prompt D 0, D +, D + and D + s meson production in p-pb collisions at s NN = 5.02 TeV. The measurements are compared to the pp rescaled reference. The vertical error bars represent the statistical uncertainties, the open boxes the data systematic uncertainties, the filled boxes the uncertainties from feed-down subtraction. The normalization uncertainties are written as text, the BR uncertainties are not shown. 139

142 CHAPTER 3. Measurements of charm with ALICE Figure 3.34: Left panel: ALICE measurements for the average R pa of D 0, D + and D +, compared to predictions from two theoretical models [16, 184]. Right panels: R pa of D 0, D +, D + and D + s mesons as a function of p T. In all the panels, vertical bars and empty boxes represent the statistical uncertainties and the total systematic uncertainties, respectively. The uncertainties related to the pp reference are also reported as vertical square brackets for the individual R pa measurements. 140

143 Chapter 4 D-hadron azimuthal correlation analysis 4.1 Introduction Two-particle angular correlations play a fundamental role in investigating the process of high p T parton fragmentation into jets, both in pp and in Pb-Pb collisions. As it was discussed in Section 1.4, at the LHC it is possible to extend these studies to the heavy flavour domain. In pp collisions, this allows us to probe our understanding of QCD in the perturbative regime. The azimuthal correlations between a charmed hadron trigger and the charged particles produced in the same event allow us to gain further insight into the underlying charm production mechanism. In particular, prompt heavy quark pair production, a leading order pqcd process, leads to back-to-back production in the azimuthal angle. Heavy quarks produced by splitting of massless gluons, a NLO process, are instead preferentially produced with small ϕ. A third production process, flavour excitation, may lead to a large separation in rapidity and most of the times one of the two quarks is emitted in the forward region, with no preferred angle along ϕ. Therefore, the azimuthal correlation analysis enables to study not only the fragmentation and hadronization of charm quarks, but their production as well. Since D mesons are correlated not only with tracks coming from other charm hadrons, but with all the tracks with a p T higher than a threshold value, a direct access to charm quark information is not possible. Anyway, information on the charm production mechanism can be inferred by analyzing the azimuthal correlation peaks at ϕ = 0, π and comparing their features with the expectations from Monte Carlo simulations. In more complex systems, like p-pb and Pb-Pb collisions, heavy flavour correlations allow us to investigate the in-medium modification of the structure of charm jets, as it was already done for hadron-hadron correlation studies in heavy ion collisions at RHIC and LHC. In particular, these studies can help to quantify the parton 141

144 CHAPTER 4. D-hadron correlation analysis energy loss effects on heavy quarks due to the presence of the QGP, providing complementary information to R AA and v 2 measurements. Figure 4.1: Left: typical D meson production in a pp collision. Right: graphical definition of the interesting regions for the D-hadron correlation analysis. In this chapter the analysis of azimuthal correlations between D mesons and unidentified charged tracks in pp collisions at s = 7 TeV is described. The analysis was performed using the D 0 as charmed meson, reconstructed from its K π + hadronic decay, as sketched in Fig A similar analysis, based on similar algorithms than those used for the D 0 K π + channel, is currently pursued within the ALICE Collaboration by exploiting the D + and the D + mesons. A full description of the analysis strategy and of its steps will be specifically given for the D 0 case. The strategy of the other analyses is very similar to the D 0 one. Both the D 0 results and a weighted average of D 0 and D + results will be presented. In both cases, the distributions were approved by the ALICE collaboration. Status and perspectives of the analyses in p-pb and Pb-Pb central collisions will be also described. In these systems the same analysis steps as in pp events are performed. It will be shown that, while the first results in p-pb are promising, in Pb-Pb collisions the large track density and the huge combinatorial background in the D 0 invariant mass distributions severely reduce the possibility of extracting significant results from the analysis. A further study has been performed, considering the expected performance with the ALICE upgrade programme [108,185], with improved resolution on the track parameters and much larger statistics. The outcome is that the performance achievable after the ALICE upgrade should allow us to extend the D-hadron correlation studies to the Pb-Pb collision system too. 142

145 CHAPTER 4. D-hadron correlation analysis 4.2 Analysis strategy The analysis target is to produce fully corrected azimuthal correlation distributions of D mesons (trigger particles) and charged primary hadrons (associated particles) in different ranges of transverse momentum of the trigger particle, at central rapidity. Differently for common correlation analyses, the trigger particle is defined by the identity of the particle rather than by a momentum cut (i.e. p trig T > pmin T ). Therefore the momentum range of the associated particles is not constrained by that of the trigger particle, but only a minimum p T threshold is set. The definition of primary particles used for the analysis comprises any charged particle coming from the primary vertex, including also particles from strong and electromagnetic decays and particles deriving from the decay of heavy flavour hadrons. Particles coming from weak decays of strange hadrons and particles produced in interactions with the detector material are instead excluded from this criterion and are considered as secondaries. The corresponding contribution to the ϕ correlations, therefore, was removed from the results. The analysis was performed through the following steps: D meson selection and signal extraction Charged track selection Correlation of D candidates with associated tracks Subtraction of correlations of background candidates exploiting the sidebands of the invariant mass distribution Corrections for: Detector effects (local inhomogeneities and limited acceptance) via Event Mixing Associated track reconstruction efficiency D meson reconstruction and selection efficiency Contamination from secondary tracks Contribution due to feed-down from beauty hadron decays Evaluation of systematic uncertainties Fit of azimuthal correlation distributions Comparison with models For the D 0 analysis, the correlation distributions were evaluated in seven fine D 0 transverse momentum ranges, integrating then the results in three wider p T intervals to reduce the statistical fluctuations: 3 < p T (D 0 ) < 5 GeV/c, 5 < p T (D 0 ) < 8 GeV/c and 8 < p T (D 0 ) < 16 GeV/c. The associated particle p T threshold was set to the following values: p assoc T > 0.3, 0.5, 1 GeV/c. The data sample used for the analysis was composed of about minimumbias (MB) pp events at s = 7 TeV, corresponding to an integrated luminosity of L int = 5 nb 1. The events were collected during the year 2010, in distinct data taking periods, defined as LHC10b, LHC10c, LHC10d and LHC10e, each with quite 143

146 CHAPTER 4. D-hadron correlation analysis homogeneous conditions of the ALICE detectors. The minimum-bias trigger was based on the SPD and VZERO detectors, by requiring at least one hit in either of the VZERO counters or in the SPD (with pseudorapidity coverage η < 2), in coincidence with the arrival of proton bunches from both directions. Only events with the z coordinate of the primary vertex satisfying the condition z vtx < 10 cm were used for the analysis. Contamination from beam-induced background was removed exploiting the VZERO timing information and the correlation between the numbers of hits and tracklets reconstructed in the SPD. 4.3 Evaluation of D 0 -hadron correlations D 0 meson selection and signal extraction The reconstruction and selection strategy for D 0 mesons at central rapidity has been described in Section It relies on the selection of displaced vertex topologies, achieved by imposing kinematical and topological cuts on the D 0 candidates, e.g. by requiring a significant distance between the secondary and the primary vertices (decay length) and a good alignment between the reconstructed D 0 meson momentum and the flight-line joining the primary and secondary vertices. Selection cuts were also applied to the daughter tracks of the reconstructed D 0, based on the quality of the track reconstruction in the ITS and TPC. Finally, the identification of the charged kaon in the TPC and TOF detectors helped to further reduce the background at low p T. The topological cut values, slowly varying with p T, were made uniform inside the three p T ranges in which the final correlation results were produced. This was necessary since these ranges are wider than the seven p T intervals in which the D 0 meson signal was extracted from the invariant mass distributions, and the D 0 selection efficiency must not have sudden variations inside these intervals. The list of the main topological cut values used for the D 0 meson selection is reported in Tab Furthermore, the D 0 mesons were accepted only if inside a rapidity range y D < y fid, with y fid varying with the D 0 transverse momentum, from y fid = 0.5 at p T = 0 up to y fid = 0.8 for p T 5 GeV/c. The D 0 raw yields were extracted from an invariant mass analysis on the selected D 0 candidates. The invariant mass distribution in each p T interval was fitted using the sum of a Gaussian function for the signal and an exponential for the combinatorial background (the same function used in [26]). Figure 4.2 shows the invariant mass distributions for the seven fine p T intervals used in the analysis, with the fit function superimposed to the data distributions. The values of signal, signal over background (S/B) ratio, statistical significance and the parameters of the Gaussian peaks are also shown in the panels. 144

147 CHAPTER 4. D-hadron correlation analysis Figure 4.2: Invariant mass distributions for the seven fine D 0 p T intervals exploited in the analysis. For each panel the fit function is superimposed to the data (total fit function in blue, combinatorial background in red). Values of signal (S), statistical significance (Signif.), signal over background ratio (S/B) and mean (µ) and sigma (σ) of the Gaussian peak are also shown in each panel. 145

148 CHAPTER 4. D-hadron correlation analysis Table 4.1: Values of the main topological cuts for the D 0 selection in the three p T ranges used in the correlation analysis. See for the definition of the selection variables. Topological cut Typology Low p T value Intermediate p T value High p T value 2 5 GeV/c 5 8 GeV/c 8 16 GeV/c DCA (µm) upper cut cos θ upper cut K p T (GeV/c) lower cut π p T (GeV/c) lower cut d π 0 d K 0 (cm 2 ) upper cut cos θ pointing lower cut Charged track selection A selection was performed on the sample of associated tracks found in each event. Cuts on the number of associated clusters in the tracking detectors (ITS and TPC) and on the quality of the track momentum fit were imposed to reject poorly reconstructed tracks. The secondary tracks were removed by using a cut on the distance of minimum approach to the primary vertex (DCA cut in the following). A pseudorapidity cut η < 0.8 was also applied to define a precise acceptance range and to exclude tracks too close to the edges of the barrel. The criteria used for the track quality selection are listed in the following: a minimum of 3 clusters was required in the ITS; a minimum of 70 clusters was required in the TPC; the maximum χ 2 per TPC cluster was set to 4; a successful fit of the track with the Kalman filter during the last inward tracking step in the TPC was required (TPC refit); DCA to primary vertex along z: DCA z < 1 cm; DCA to primary vertex along xy: DCA xy < 0.25 cm; pseudorapidity acceptance: η < 0.8. In addition, the tracks forming a D 0 candidate were excluded from the correlations with that D 0 candidate (but they were accepted for other D 0 candidates in the event). The tracks compatible with being pions produced in D + D 0 π decays ( soft pions ) were also removed by applying an invariant mass selection on the M(Kππ) M(Kπ) value Correlation evaluation In each event, pairs were formed by associating each selected D 0 meson with the other charged primary particles passing the track selection described above. For each particle pair, the pseudorapidity difference η = η trig η track and the azimuthal angle difference ϕ = ϕ trig ϕ track were evaluated and used to build a two-dimensional correlation distribution. As the difference in the azimuthal angle is 146

149 CHAPTER 4. D-hadron correlation analysis periodic, the ϕ range in these distributions was limited to the interval [ π/2, 3π/2], which provides a good visibility of the correlation pattern, peaked around 0 and π. The transverse momentum value of the associated track was stored for each pair as well. Each correlation entry in the distributions was also weighted by a value depending on the trigger and track reconstruction and selection efficiencies, as it will be described in Section 4.4. The two-dimensional correlation distributions were independently evaluated for each of the seven transverse momentum intervals in which the D 0 invariant mass distributions were produced. For each D 0 transverse momentum interval, the correlation distribution was evaluated both inside the invariant mass region of the signal ( signal region) and in the sidebands. The signal region was defined as the invariant mass range inside 2σ from the centre of the Gaussian peak in the invariant mass distribution. The sidebands were defined as the two regions on the left and on the right sides of the Gaussian peak, between 4σ and 8σ from its centre. The signal region and the sidebands are shown in Fig. 4.3 superimposed to an invariant mass distribution. Figure 4.3: Example of signal (red+yellow) and sideband (green) regions, highlighted on a D 0 candidate invariant mass distribution Subtraction of the background correlations Inside the signal region, the correlation distributions include also correlations of tracks with background candidates which passed the D 0 selection cuts. Their contribution was subtracted using, for each p T interval, the correlation distribution evaluated for the D 0 trigger particles located inside the sidebands of the invariant mass distributions, containing only background D 0. The sideband correlation distribution was normalized by a factor, defined from the mass fits, being the ratio of the background integral in the signal region over the 147

150 CHAPTER 4. D-hadron correlation analysis integral in the sidebands (the red area over the sum of the green areas in Fig. 4.3). This normalized background correlation distribution was then subtracted from that in the signal region to obtain the signal correlation distribution. This subtraction was performed after performing the Event Mixing correction (cf. Section 4.4.1). Figure 4.4 shows an example of the two-dimensional ( ϕ, η) correlation distributions in the signal region (panel a ) and in the sidebands (panel b ). It was verified, using Monte Carlo simulations, that frequently the background D 0 are built by using, as one of their two daughters, decay tracks from a real D 0. In other cases, high p T tracks belonging to jets, in jet events, are misidentified as D 0 daughters. This feature can explain the similar shapes of the correlation plots in the signal region and in the sidebands, as obtained in several p T intervals. 4.4 Correction of the correlation distributions Besides the background subtraction, the correlation distributions had to be corrected to remove effects from detector acceptance and efficiency, the residual contamination from secondary tracks and the contribution coming from D 0 from beauty hadron decays (feed-down). Due to the limited statistics available in the correlation distributions, especially in the high p T interval, it was necessary to project the distributions on the ϕ axis, integrating over the η variable. The projections were performed after having applied the acceptance and efficiency corrections, which depend on the η value. The corrections for the secondary contamination and the feed-down contribution subtraction were instead applied to the one-dimensional ( ϕ) azimuthal distributions. In addition, after the ϕ projection, the correlation plots for the seven D 0 p T intervals were merged in the three wider p T ranges introduced before, namely 2 5, 5 8 and 8 16 GeV/c. This reduces the statistical fluctuations in the correlation pattern. The various corrections will be discussed in the following subsections Event Mixing correction The angular correlation distributions may be affected by structures not due to physical effects, but originating from the limited detector acceptance or from angular inhomogeneities in the trigger and track reconstruction efficiencies as a function of ϕ or η. In particular, it can be proven that the presence of a dead or inefficient area in the coverage of the detectors produces an excess of correlations in the near side of the ϕ distribution. Effects of this kind were removed using the Event Mixing technique. In detail, the analysis was executed on the same data sample as the standard analysis (called same event analysis, SE, from now on because D 0 trigger particles were correlated with charged particles from the same collision), but D 0 trigger particles found in each event were correlated to charged particles reconstructed in different events (mixed event analysis, ME). The resulting correlation distribution contained 148

151 CHAPTER 4. D-hadron correlation analysis no physical correlations, since trigger and associated tracks are independently produced. They exhibit, instead, the features related to the detector inhomogeneities and limited acceptance, which affect in the same way the distributions of both ME and SE analyses. For this reason, the ME correlation distributions can be used to correct the SE results, removing the detector effects and preserving the physical correlation patterns. For each trigger particle p T interval, the correction was applied by dividing binby-bin the correlation distribution from the same event analysis by the one from the mixed event analysis, the latter normalized to its value in ( ϕ, η) = (0, 0): dn corr ( ϕ, η) d ϕd η = dn SE ( ϕ, η) d ϕd η dn ME ( ϕ, η) d ϕd η dn ME (0, 0) d ϕd η. (4.1) This particular normalization, used also in the analysis of hadron-hadron correlations, was adopted since at ( ϕ, η) = (0, 0) the trigger and the associated particle experience the same detector effects. However, it should be noted that in the D meson case this is a correct assumption only on average and not for very low p T of the trigger particles, since D mesons are reconstructed from daughter tracks, which can cross different detector regions. ( ϕ, η) = (0, 0) is in any case the bin with maximum efficiency for the pairs (both correlated and uncorrelated), thus the same convention as for hadron-hadron analysis was adopted. In the mixed event analysis the correlations between D 0 mesons and charged particles were evaluated only if the corresponding events had similar features. In particular, they were required to have similar multiplicity and position of the z coordinate of the primary vertex. This was aimed at avoiding to bias the correction by introducing additional structures due to the different properties of the events that were mixed together. In particular, during the ME analysis the events were classified in pools of multiplicity (number of SPD tracklets in the following ranges: [0, 20], [20, 40], [40, ]) and z position of the vertex ([ 10, 2.5] cm, [ 2.5, 2.5] cm, [2.5, 10] cm) 1. Each time a D 0 meson candidate was found in an event, only the events contained in the same pool as the event under analysis were used to evaluate the correlations for the event mixing correction. The mixed event correlation distributions were built in both signal and sideband regions. The Event Mixing correction was applied separately in the two invariant mass regions before the background subtraction, i.e. following this procedure: normalization of the sidebands correlation distribution; Event Mixing correction for the signal region (SE/ME ratio); Event Mixing correction for the sidebands (SE/ME ratio); subtraction of the normalized sideband distribution from the signal region correlation distribution; Anyway, it was verified that by inverting the order of the event mixing correction and of the background subtraction, the final correlation distributions were not modified. 1 It was not possible to classify the events in finer pools due to the limited statistics available for the analysis. 149

152 CHAPTER 4. D-hadron correlation analysis Figure 4.4 shows examples of mixed event distributions for the signal region (panel c ) and the sidebands (panel d ). Panels e and f show the correlations distributions in the signal region and in the sidebands, respectively, after the Event Mixing correction, while panel g represents the background subtracted and Event Mixing corrected correlation distribution. Although it was possible to cover a maximum η region of η < 1.6, the correlation distributions were limited to the interval η < 1. This reduced range was imposed to avoid the so-called wing effect, i.e. the wing-like structures appearing in the corrected correlation distributions at large η, as well as to reduce the large statistical fluctuations appearing there, due to the limited entries present in those regions of the correlation plots. In an ideal case, the mixed event distributions are expected to present a flat distribution along ϕ (no detector inhomogeneities) and a triangular shaped distribution in η, due to the finite acceptance of the detector. From the distributions in the figure, the triangular shape is present along η as expected, while no particular structures are visible along ϕ. This result points toward the absence of any influence on the correlation distributions from the inefficient regions of the tracking detectors. This is confirmed by looking at the ϕ distribution of all the associated tracks used to build the correlation distributions. As shown in the left panel of Fig. 4.5, this distribution is compatible with a flat shape. For completeness, the p T -integrated ϕ distribution of the D 0 candidates is shown in the right panel of the same figure. In this case, relevant structures are visible, mainly due to the request that the tracks forming a D 0 candidate must have a point in the SPD. 150

153 CHAPTER 4. D-hadron correlation analysis Figure 4.4: Examples of two-dimensional ( ϕ, η) correlation distributions between D 0 trigger particles and charged tracks, for 5 < pt(d 0 ) < 8 GeV/c and p assoc T > 0.3 GeV/c: (a) signal region, same event analysis; (b) sidebands (normalized), same event analysis; (c) signal region, mixed event analysis; (d) sidebands (normalized), mixed event analysis; (e) signal region, event mixing corrected; (f) sidebands (normalized), event mixing corrected; (g) signal region, background subtracted and event mixing corrected. 151

154 CHAPTER 4. D-hadron correlation analysis Figure 4.5: p T -integrated azimuthal angle distributions of associated tracks (left) and D 0 candidates (right) used to build the correlation distributions Tracking efficiency correction While building the correlation distributions, it is necessary to account also for the correlations with tracks not reconstructed, or not passing the quality selection due to a poor reconstruction. The amount of lost tracks depends on the track reconstruction efficiency in the ITS and TPC. From the shape of the mixed event correlation plots it is already evident that the tracking efficiency has no strong dependence on the ϕ and η variables. Its value, however, is lower than 1, since not all the charged tracks produced in the event are reconstructed and pass the quality selection criteria. The correlation distributions, thus, need to be corrected. Since the tracking efficiency depends on the transverse momentum of the associated track, the correction must be applied before integrating on the associated track p T. It was hence directly applied to the two-dimensional distributions during the execution of the analysis. When filling the correlation distributions both in the signal and sideband regions, each correlation entry was weighted by the inverse of the associated track reconstruction efficiency. The efficiency value was extracted from an efficiency map, which was parameterized using the transverse momentum of the track, its pseudorapidity and the z coordinate of the primary vertex of the event. The efficiency map was evaluated from a Monte Carlo simulation of minimumbias events, generated using the PYTHIA event generator [83] with Perugia0 tune [122]. To grant sufficient statistics to the efficiency map, the efficiency was evaluated for all the events, independently of whether a D 0 was produced in the event or not. It was anyway verified that there were no relevant differences in the tracking efficiencies for the events containing at least a D 0 and the ones that are used in the data analysis. Figure 4.6 shows the value of the track reconstruction efficiency as a function of p T and η of the track, obtained by projecting the efficiency map for two ranges of the primary vertex z coordinate. The binning of the efficiency map was chosen as fine as possible, especially in the low p T region. The bin width was gradually increased at higher p T values to reduce the fluctuations due to the limited statistics. 152

155 CHAPTER 4. D-hadron correlation analysis As anticipated, a very mild dependence from the pseudorapidity was found in the η < 0.8 region considered, with the value of the efficiency lying everywhere at about No relevant differences are present comparing the efficiency map projections in the two ranges of the z vertex coordinate. A deeper insight into the p T dependence can be obtained by integrating the maps over the z and η variables to produce a one-dimensional map, as shown in Fig From the p T distribution, a rather flat trend is present at high p T, while for p T < 2 GeV/c a significant dependence on p T is found. Figure 4.6: Projection of the tracking efficiency map as a function of p T and η in two ranges of the primary vertex z coordinate (z [ 2, 0] cm, left; z [0, 2] cm, right). A weak dependence of the efficiency value from track p T and η is visible. Figure 4.7: p T dependence of track reconstruction efficiency D 0 meson efficiency correction In addition to the tracking efficiency, the correlation distributions are also influenced by the D 0 meson reconstruction and selection efficiency. In particular, the 153

156 CHAPTER 4. D-hadron correlation analysis p T dependence of the D 0 efficiency inside each p T interval has a relevant effect on the shape of the distributions. On the contrary, the average value of the efficiency inside each p T interval has no influence, due to the normalization of the correlation plots to the number of trigger particles. Figure 4.9 shows the p T dependence of the reconstruction and selection efficiency for prompt (left) and feed-down (right) D 0 mesons. The efficiency varies by a factor of about 5 among the seven fine D 0 p T intervals in which the analysis is performed, with big jumps between adjacent intervals. This occurs also when the two adjacent intervals have the same D 0 selection cuts. Since the p T ranges used for the D 0 - hadron correlations are composed by merging two or more fine D 0 p T intervals, the uncorrected correlation distributions show a bias toward the high p T region of each correlation p T range. In the higher p T part of each interval, indeed, a higher fraction of D 0 is reconstructed due to the higher efficiency value, while in the lower p T region the efficiency is smaller. This p T bias was corrected by applying a trigger efficiency correction. Figure 4.8: p T dependence of the reconstruction and selection efficiency of prompt (left) and feed-down (right) D 0 mesons. The plots include the D 0 acceptance correction. The correction was applied during the analysis execution, in the same way as the tracking efficiency correction. Each correlation entry in the two-dimensional distributions was weighted by the inverse of the reconstruction and selection efficiency of the trigger D 0, extracted from an efficiency map, assuming that the trigger was a prompt D 0. The total weight applied to each correlation entry, considering also the tracking efficiency correction, was hence (ɛ trig ɛ track ) 1. The D 0 efficiency map was evaluated by means of a Monte Carlo simulation, produced using the PYTHIA event generator [83] with Perugia0 tune [122]. Only the dependencies on D 0 p T and on the event multiplicity were considered to build the trigger efficiency map, while the dependence on the D 0 rapidity was neglected. This was decided in order to avoid large statistical fluctuations on the efficiency values, due to the limited size of the Monte Carlo sample. Although a significant 154

157 CHAPTER 4. D-hadron correlation analysis dependence of the D 0 efficiency on the multiplicity was found 2, studies of its impact on the correlation distributions resulted in an effect within 5%. Figure 4.9 shows the trigger efficiency maps for prompt (left panel) and feeddown (right panel) D 0 mesons. Only the prompt D 0 map was used to apply the trigger efficiency correction to the data distributions, while that for feed-down D 0 was used for the evaluation of the feed-down contribution and for the Monte Carlo closure test, as reported in the following sections. The trigger efficiency used for weighting the correlation entries also includes a correction for the D 0 acceptance. This additional correction accounts for the cuts applied on the pseudorapidity of the D 0 daughters. At the same time, it allows us to translate the p T -dependent fiducial acceptance rapidity range, used in the D 0 meson reconstruction, to a fixed p T -independent y < 0.5 range. Applying this correction does not bias the analysis, since it was verified that the shape of the correlation distributions has a negligible dependence on the y value of the D 0. Figure 4.9: D 0 reconstruction and selection efficiency as a function of D 0 p T and event multiplicity, for prompt (left) and feed-down (right) D 0. The maps include also the acceptance correction. The trigger efficiency correction strongly modifies the normalization of the correlation distributions. To recover the normalization to the number of trigger particles, it is necessary to properly scale the signal extracted from the invariant mass fits. For this reason, each D 0 meson entry in the mass distributions was weighted by the inverse of its efficiency. This allowed us to properly count the number of trigger particles. It was verified that the multiplicity dependence of the D 0 efficiency does not significantly modify the shape of the weighted invariant mass distributions with respect to the raw ones, for each of the seven D 0 p T intervals. 2 The multiplicity dependence of the D 0 efficiency derives from the multiplicity dependence of the primary vertex resolution. This, in turn, affects the evaluation of cut variables as decay length, pointing angle and impact parameter. 155

158 CHAPTER 4. D-hadron correlation analysis Subtraction of feed-down contribution The correlation distributions are composed of correlations between charged tracks and both prompt and feed-down D 0 mesons (the latter from the decay of beauty hadrons) with charged tracks. It was hence necessary to remove the feed-down contribution from them. The subtraction was performed after projecting the distributions on the ϕ axis and merging the distributions from the seven fine p T ranges in to the three p T intervals used for the D 0 -hadron correlations. It was based on the following equation: C prompt ( ϕ) = 1 [ ] p C inclusive ( ϕ) (1 f prompt )C MCtempl feed down f ( ϕ), (4.2) prompt where, for each p T interval, C inclusive ( ϕ) and C prompt ( ϕ) are the azimuthal correlation distributions before and after the feed-down subtraction, normalized to the number of trigger particles, f prompt is the fraction of prompt D 0 mesons, C MCtempl feed down ( ϕ) is a template of the azimuthal correlation distribution of the feed-down component and p is the purity of the associated track sample, i.e. the fraction of primary tracks correlated with the D 0 trigger particles (cf. Section 4.4.5). The f prompt fraction was estimated based on the FONLL calculations and using the reconstruction efficiency of prompt and feed-down D mesons, as described in Section 3.2 for the D meson reconstruction analysis [26]. Typical values of f prompt range from 80% to 95%, with a decreasing trend with the D 0 p T. The feed-down correlation template was obtained from Monte Carlo simulations of minimum-bias events. The simulations were performed using the PYTHIA event generator with different tunes, in particular the Perugia sets [122]. Varying the tuning of PYTHIA parameters mostly affects the process of parton fragmentation into hadrons, possibly influencing the shape of the correlation distribution. Figure 4.10 shows the comparison of the correlation distributions of feed-down D 0 mesons with charged tracks, from the simulations obtained with three different Perugia tunes, namely Perugia0, Perugia2010 and Perugia2011, in the transverse momentum range 8 < p T (D 0 ) < 16 GeV/c. A fit function composed of two Gaussians and a constant term is superimposed to the simulation results. Some differences are present between the distributions, mainly affecting the level of the baseline and the width of the away side peak, while the shape of the near side peak does not significantly vary among the different tunes. To remove the effect of the baseline mismatch among the different Monte Carlo tunes and between the Monte Carlo tunes and the data distributions, the templates were shifted to match the baseline value of data. The data baseline was extracted from a fit to the data distributions. Shifting the templates is not expected to influence the correction, since the prompt and feed-down correlation distributions primarily differ in the shapes of the near and away side peaks. The baseline level, instead, depends mainly on the underlying event and is very similar between the two cases (cf. for example the red and green points of Fig in Section 4.6). 156

159 CHAPTER 4. D-hadron correlation analysis Figure 4.10: Templates for feed-down D 0 meson correlations with charged hadrons, normalized to the number of trigger particles. The distributions were evaluated on minimumbias events simulated using the PYTHIA event generator with different tunes: Perugia0 (black), Perugia2010 (red), Perugia2011 (blue) [122]. A fit function composed of two Gaussians and a constant term is superimposed to the simulation results. Yields and σ values of the near side and away side peaks are shown in the boxes. Figure 4.11 shows the templates for feed-down correlations obtained with Perugia0 tune in the three D 0 p T ranges used for the correlation analysis (black markers) with the original position of the baseline. After matching the baseline to the data level, the templates were shifted upwards or downwards, as shown by the solid histograms. Figure 4.11: Templates for feed-down correlations obtained with Perugia0 tune for 3 < p T (D 0 ) < 5 GeV/c (left), 5 < p T (D 0 ) < 8 GeV/c (center) and 8 < p T (D 0 ) < 16 GeV/c (right). The raw templates are shown with black markers, together with the baseline position (dashed lines). The solid histograms show the templates after matching the baseline to the data height and after rebinning the ϕ axis. A systematic uncertainty related to the choice of the template used to perform the feed-down subtraction was considered. Another source of uncertainty for this correction was the uncertainty on the value of the f prompt fraction. This, in turn, 157

160 CHAPTER 4. D-hadron correlation analysis depended on the uncertainties on the quark masses and on the QCD scales employed in the FONLL theoretical calculations. It was decided to use, as default choices for the feed-down correction, the Perugia0 tune template and the value of f prompt obtained setting the default parameters in FONLL predictions [20]. The feed-down correction was also evaluated using the other templates, as well as the maximum and minimum f prompt values calculated by varying the parameters in the FONLL calculations. An example of the correlation distributions before and after the subtraction of the feed-down contribution, exploiting all the different Monte Carlo tunes and f prompt values, is shown in Fig for the 8 < p T (D 0 ) < 16 GeV/c interval. The differences among the various options on the final results are small, within few percent in most of the ϕ bins. Figure 4.13 shows the ratios between the corrected azimuthal distributions obtained with the various choices of f prompt and Perugia tunes and the results obtained with the standard choice (f prompt, Perugia0 tune), for the three correlation p T ranges. The envelope of the maximum variations among the various options, in both upward and downward directions, was taken as systematic uncertainty on the feed-down contribution subtraction. In the low and intermediate p T intervals the uncertainty is always below 5%, while at high p T it grows up to 10% in some ϕ bins, though being much lower on average. The values of these uncertainty are shown in Fig Figure 4.12: Azimuthal correlation distributions after the feed-down correction for the 8 < p T (D 0 ) < 16 GeV/c interval, using Perugia0 (left), Perugia2010 (center) and Perugia2011 (right) templates for the correction. For each template, results are shown for central (red squares), minimum (blue triangles) and maximum (red triangles) f prompt values. Central f prompt value and Perugia0 template are used for the final results Removal of secondary tracks contribution The DCA to primary vertex cut, applied during the associated track selection, has the role of removing the secondary particles from the associated track sample. Secondary particles are indeed produced either from long-lived strange hadrons or from interaction of particles with the detector material, far from the interaction 158

161 CHAPTER 4. D-hadron correlation analysis Figure 4.13: Ratio of the feed-down subtracted correlation distributions obtained using the different f prompt values and Perugia tunes over those obtained with central f prompt value and Perugia0 tune, for the three correlation p T intervals. Figure 4.14: Systematic uncertainty on the feed-down correlation subtraction for the three correlation p T ranges. For each range, the uncertainty is evaluated as the envelope of the ratios between the subtracted distributions with the different f prompt values and Perugia tunes choices and the default subtracted distribution. 159

162 CHAPTER 4. D-hadron correlation analysis vertex. No strong correlation is present between the particle momentum and the line-of-flight connecting the primary vertex and the point where the particle is produced: this results in large values of the DCA expected for these particles. Because of the non negligible decay length of charmed particles (cτ 123 µm for the D 0 meson), though, it is not possible to use too tight values for the DCA selection, otherwise tracks coming from charm decays would be rejected too. A residual contamination from secondary tracks is hence expected in the correlation distributions. This contamination was removed by correcting the distributions as described in the following. The amounts of primary and secondary tracks which survive the DCA selection or are rejected by it were evaluated with a Monte Carlo simulation of minimumbias collisions, generated using the PYTHIA event generator [83] with Perugia0 tune [122]. The azimuthal correlation distributions between trigger D 0 mesons and these subsamples of tracks were evaluated. From the results, it was possible to extract the correlation distribution of the secondary track residual contamination. This was obtained as the ratio of the accepted secondary track distribution over the distribution of all accepted tracks. The left panel of Figure 4.15 shows the number of primary tracks accepted or rejected by the DCA cut, as well as the number of secondary tracks accepted or rejected by it, in the whole D 0 p T range. It can be concluded that the DCA cut keeps the contamination of secondary tracks below 4%. In the right panel of the figure the residual contamination from secondary tracks as a function of ϕ is shown. The average contamination value is reported in the text box, inside the figure, and it is of 3.7%. A breakdown of this distribution in the three D 0 p T ranges used for the correlations is presented in Fig The secondary track contamination appears to be very small, with no dependence on the D 0 p T and rather flat along ϕ, if statistical fluctuations are taken into account. It was thus possible to correct the data correlation distributions by simply multiplying them by the average purity of the correlation sample (i.e., 1 minus the contamination value). 4.5 Evaluation of the systematic uncertainties The systematic uncertainties affecting the results of the azimuthal correlation analysis are discussed in this section. Each contribution was evaluated as described in the following, except for the beauty feed-down subtraction uncertainty, already discussed above. The different systematic uncertainties have the following origins: D 0 meson yield extraction Background subtraction Associated track efficiency D 0 meson efficiency Beauty feed-down subtraction Residual contamination from secondary tracks 160

163 CHAPTER 4. D-hadron correlation analysis Figure 4.15: Left: number of primary and secondary tracks which are accepted and rejected by the DCA selection. Right: residual contamination from secondary tracks in the correlation distributions as a function of ϕ. This is defined as the distribution of the secondary tracks surviving the DCA cut divided by the distribution of all the tracks (primaries+secondaries) passing the selection. The weighted average of the ratio is shown in the bottom-right inset. In both panels the whole D 0 p T range is considered. Figure 4.16: Residual contamination from secondary tracks in the correlation distributions as a function of ϕ, shown separately for the three p T ranges. For each panel, the weighted average of the distribution is shown in the bottom-right inset. 161

164 CHAPTER 4. D-hadron correlation analysis Rejection of D + decay pions D 0 meson yield extraction A first source of systematic uncertainty is related to the extraction of the D 0 meson yields from the invariant mass distributions. The standard procedure to obtain the yields is to integrate the Gaussian component of the mass fit in the signal region. To estimate the uncertainty on the yield extraction, the signal values were determined by modifying the default procedure as follows: changing the background fit function to 1st and 2nd order polynomials; changing the bin width of the invariant mass distributions (doubling it or reducing it by a factor of 2); narrowing the range of invariant mass in which the fit is performed; extracting the yield via bin counting instead of integrating the fit function. For each p T interval, both the value of the yield and the sideband normalization factor are affected by changing the yield extraction procedure. Apart from this difference, the procedure to obtain the fully corrected correlation distributions was performed in the same way as in the standard analysis. The ratios of the correlation distributions obtained with the default yield extraction procedure and the alternative ones were evaluated, as shown in Fig From a fit to these ratios with a constant (pol0) a 10% systematic uncertainty was estimated, with no ϕ or p T dependence. Figure 4.17: Ratios of azimuthal correlation plots produced with standard yield extraction procedure over results obtained with different approaches. The top-right inset in each panel shows the results of a fit to each ratio with a constant. Examples of ratios are shown for different correlation p T ranges and associated track p T thresholds. No statistical errors are shown, since the ratios are obtained from almost fully correlated samples. 162

165 CHAPTER 4. D-hadron correlation analysis Background subtraction The systematic uncertainty on the subtraction of background contribution includes effects due to statistical fluctuations in the sidebands of the invariant mass distributions and to the model used to fit the background. These can influence the subtraction of the background correlations from the distributions in the signal region, performed exploiting the correlations in the sidebands. To estimate the size of this uncertainty, the invariant mass range defining the sidebands was varied with respect to the default values. For the D 0 meson, the default range is 4σ to 8σ from the centre of the peak of the Gaussian fit of the invariant mass distributions; it was modified to: 4σ to 6σ from the position of the peak; 6σ to 8σ from the position of the peak. It was not possible to extend the sidebands further than 8σ from the peak because of some structures present in the invariant mass distribution of the D 0 candidates, while the limit in the direction of the D 0 mass was limited to 4σ by the presence of the Gaussian peak. No other differences were introduced in the procedure to extract the corrected azimuthal correlation distributions. The ratios of the standard correlation distributions over the distributions extracted with different sideband definitions were evaluated, as shown in Fig These ratio show no structures along ϕ. This implies that the uncertainty on the background subtraction has no effect on the correlation shape, but only on the normalization value. It is possible, hence, to assign a systematic uncertainty independent of ϕ. From a fit to these ratios with a constant, this systematic uncertainty was estimated at 5%, flat also in p T. Figure 4.18: Ratios of correlation plots produced with standard sideband definition over results obtained with different ranges for the sidebands. The top-right inset in each panel shows the results of a fit to each ratio with a constant. Examples of ratios are shown for different correlation p T ranges. No statistical errors are shown, since the ratios are obtained from almost fully correlated samples Associated track efficiency The systematic uncertainty on tracking efficiency includes the effects related to the quality selection on the charged tracks associated to the D 0 trigger particles. The influence of this uncertainty on the correlation distributions was estimated by 163

166 CHAPTER 4. D-hadron correlation analysis repeating the analysis using different criteria for the associated track selection. The alternative selections were: TPConly selection, i.e. TPC tracks with no requests on the number of hits in the ITS, and TPC+ITS selection, i.e. tracks with at least 3 points in the ITS, out of which at least one in the SPD, and successful refit in the ITS 3. In the default selection, at least 3 points are requested in the ITS and no further requests on the presence of points in the SPD are made. The other cuts applied to the tracks were not modified with respect to the default selection. A list of all the criteria for the three selections is reported in Tab. 4.2, while Fig compares the tracking efficiency maps obtained for the three cases. While the maps for the default and the TPConly selection are very similar, a substantial decrease of the efficiencies and a strong η asymmetry is found for the TPC+ITS selection. These features are due to the request of at least a hit in the SPD, which had several inactive modules during the data taking. As expected, the presence of inactive modules introduced modulations along the ϕ axis of the correlation distribution. These modulations were accounted for by means of the Event Mixing correction. The ME distributions, indeed, presented a non-flat ϕ distribution together with the typical triangular shape along η. Table 4.2: List of the criteria for the three different track quality selections. Topological cut Default TPConly Option 3 Minimum n. of ITS clusters Minimum n. of TPC clusters Requested ITS refit No No Yes Requested TPC refit Yes Yes Yes DCA to primary vertex (along z) 1 cm 1 cm 1 cm DCA to primary vertex (along xy) 0.25 cm 0.25 cm 0.25 cm Requested hits in SPD No No at least 1 Track typology TPC tracks TPC tracks TPC+ITS tracks Figure 4.19: Tracking efficiency maps for the three different track quality selections: default (left), TPConly (center), TPC+ITS (right), as a function of the track η and p T. The maps are shown for the 2 < z < 0 cm range of primary vertex z coordinate. 3 Requesting the ITS refit corresponds to requiring a successful fit of the track with the Kalman filter during the last inward tracking step in the ITS. 164

167 CHAPTER 4. D-hadron correlation analysis After performing the analysis, the ratios of the azimuthal correlation distributions with different associated track selections over the distribution with the standard selection were evaluated. These ratios are shown in Fig Since they showed no structures along ϕ, the results of a fit to each ratio with a constant were used to determine an asymmetrical systematic uncertainty of +10% 5%, flat in p T and ϕ. Figure 4.20: Ratios of correlation plots obtained with different associated track quality selections, for the three correlation p T ranges and different associated track p T thresholds. The top-right inset in each panel shows the results of a fit to each ratio with a constant. No statistical errors are shown, since the ratios are obtained from almost fully correlated samples D 0 meson efficiency A systematic effect can arise from residual discrepancies between data and Monte Carlo simulations for the variables used for D 0 selection. The size of this effect was quantified by repeating the correlation analysis using different sets of cuts to select the D 0 meson candidates. In these alternative selections, all the topological cuts were loosened or tightened with respect to their standard value. The trigger efficiency maps for the looser and tighter selections are shown in Fig It was verified that, also with the alternative selections, a signal peak with sufficient significance was obtained in the invariant mass distributions, for all the D 0 p T intervals used for the analysis. Furthermore, the D 0 yields extracted with the alternative selections were different enough from the yields obtained with the default selection. This granted that the correlation distributions were obtained from data samples at least partially different. 165

168 CHAPTER 4. D-hadron correlation analysis The correlation analysis was then performed without other changes. The ratios of the correlation distributions obtained using the tighter and looser selections over the results with the standard selection are shown in Fig An uncertainty of 5%, flat in p T and ϕ, was assigned to this systematic contribution from the results of a fit to each ratio with a constant. Figure 4.21: Trigger efficiency maps for looser (left) and tighter (right) selections for the D 0 candidates. Efficiencies are shown for prompt D 0 mesons only. Figure 4.22: Ratios of correlation plots obtained with looser and tighter D 0 selection over standard results, for the three D 0 p T ranges and different values of associated track p T threshold. The top-right inset in each panel shows the results of a fit to each ratio with a constant. No statistical errors are shown, since the ratios are obtained from partially correlated samples Residual contamination from secondary tracks The contamination from the secondary tracks surviving the DCA cut was subtracted by evaluating its contribution to the ϕ correlation distributions on a Monte Carlo simulation, as described in Section To evaluate the stability of the correlation distributions when varying the DCA cut and to check if this cut it has the same effects on Monte Carlo and on data, the following check was performed. The Monte Carlo analysis performed to extract the contamination contribution was repeated using different values for the cut on the DCA in the xy plane, where 166

169 CHAPTER 4. D-hadron correlation analysis a better resolution is achieved (1, 0.75, 0.50, 0.25 and 0.1 cm values were tested). For each value, the purity of the correlation sample and the ϕ distribution of the residual contamination due to secondary tracks were evaluated. Subsequently, the analysis was repeated on data, for the same DCA xy cut values. For each case, the correlation distribution was extracted and it was multiplied by the corresponding purity, estimated on Monte Carlo. The ratios of the correlation distributions obtained with the different cut values over the distributions obtained with the loosest cut value (1 cm) were evaluated. These ratios are shown in Fig They are flat along the ϕ axis within the uncertainties and the results of a fit to each ratio with a constant differs by only few percentage points from unity. The amount of tracks removed by the DCA cut is therefore consistent with that obtained with the Monte Carlo study. Based on these results, a 5% value was assigned as systematic uncertainty. This estimate also includes possible effects coming from a non-flatness of the ϕ distribution of secondary track contamination, which could be present in the distributions shown in Fig Figure 4.23: Ratio of correlation distributions obtained using different DCA xy cut values over the results with the loosest cut value, corrected for the purity, as a function of ϕ, for the three correlation p T ranges and associated track p T thresholds of 0.3 and 1 GeV/c. The top-right inset in each panel shows the results of a fit to each ratio with a constant. No statistical errors are shown, since the ratios are obtained from almost fully correlated samples. As a further check it was verified that, for the DCA cut value used in data analysis, the relative amounts of primary and secondary tracks accepted or rejected by the DCA cut did not depend on the track origin, i.e., if the track came from a light quark, a c quark or a b quark. Indeed, the same purity was found for the full track sample, for tracks coming from charm hadron decays and for tracks coming from beauty hadron decays. 167

170 CHAPTER 4. D-hadron correlation analysis Rejection of D + decay pions The low p T pions produced from D + D 0 π + decays were excluded from the correlation distribution via an invariant mass cut, as described in Section The possible bias introduced by applying this cut was evaluated through a Monte Carlo study. In the test, the number of pions from D + decays and of non-d + decay tracks which are accepted or rejected by the invariant mass cut was evaluated. This allowed us to estimate the efficiency of the cut and the residual contamination from D + decay pions in the sample of the tracks passing the selection. Figure 4.24 shows the number of rejected true D + decay pions, rejected non-d + decay tracks, accepted true D + decay pions and accepted non-d + decay tracks, for the whole D 0 p T range. From the relative amounts, the contamination from D + decay pions is below 1%; furthermore, the amount of non-d + decay tracks tagged as D + decay pions (and hence wrongly rejected) is much smaller than 1% of the number of accepted tracks. A negligible bias on the results is thus expected and no systematic uncertainty was consequently assigned for the D + decay pions rejection. Figure 4.24: Number of true/false D + decay pions which are accepted/rejected by the invariant mass cut, for the whole D 0 p T range. The ϕ correlation distributions for these track subsamples were also evaluated. Comparing the ϕ distribution of true D + decay pions and the one of all the rejected tracks, it was found that in both cases all the entries were concentrated in the bins close to ϕ = 0. Hence, the invariant mass cut removes tracks in the same ϕ region in which D + decay pions are expected to be found. By splitting the results in the three correlation p T ranges, the highest amount of D + decay pions was found in the high p T interval (8 < p T (D 0 ) < 16 GeV/c), when the lowest associated track p T threshold (0.3 GeV/c) was considered. This is expected, because for an high p T D 0 that come from a D + decay, the pion produced in the D + decay has 168

171 CHAPTER 4. D-hadron correlation analysis a significant boost and, hence, a higher probability to pass the associated track p T threshold. As an additional check, the data analysis was performed both disabling and keeping enabled the cut for the D + decay pions rejection. The ratio of the correlation distributions obtained without the cut over the standard results was then performed. With an associated track p T threshold of 0.3 GeV/c, a ratio compatible with 1 was found, perfectly flat in ϕ except for a slight excess in the two bins closest to ϕ = 0. For the highest threshold of 1 GeV/c, this excess disappeared as well, as shown in Fig The same behaviour was observed in the Monte Carlo simulation, confirming that the invariant mass cut produces the same effects on data and on Monte Carlo simulations. Figure 4.25: Ratio of azimuthal correlation distributions obtained on data without the invariant mass cut for removal of D + decay pions over the distributions obtained with the cut enabled. Results are shown for the whole D 0 p T range, for associated track p T threshold of 0.3 (left) and 1 (right) GeV/c. No statistical errors are shown, since the ratios are obtained from almost fully correlated samples Overall systematic uncertainty The overall systematic uncertainty for the three correlation p T ranges is shown in Fig In the figure the single contributions are also shown separately, with coloured bands. The overall amount of the uncertainty fully correlated along ϕ is shown with a black dashed line. This contribution comprises all the previous systematic sources except the ones for feed-down subtraction and for the MC closure test. The latter uncertainty will be described in the next section. 4.6 Monte Carlo closure test The following Monte Carlo samples were used to perform the corrections described in Section 4.4 and to estimate some of the systematic uncertainties: 169

172 CHAPTER 4. D-hadron correlation analysis Figure 4.26: Relative systematic uncertainty as a function of ϕ for the three correlation p T ranges. The black solid line describes the overall uncertainty, the black dashed line shows the uncertainty fully correlated in ϕ, while the single contributions are shown with bands of different colours. LHC10f6a+LHC10d4: comprise a total of 246 million minimum-bias pp events, reproducing the conditions of ALICE during the periods of data taking used for the analysis. LHC10f7a: comprises 30 million pp events requiring that either a cc or a bb pair are present in each event, with at least one of the heavy quarks of the pair generated in y < 1.5. In a subset of these events the D mesons are forced to decay through hadronic modes (D 0 K π +, D 0 K π + π π +, D + K π + π +, D + s K K + π + ). Both samples were produced using PYTHIA event generator [83], with Perugia0 tune [122]. As a consistency test, the complete analysis was performed both at kinematic level and at reconstructed level on the Monte Carlo set with enriched content of charm and beauty. In the analysis at kinematic level, only the acceptance cuts were applied to the associated particles and on the D 0 mesons, using the Monte Carlo information to identify them. At reconstructed level, the analysis was instead performed similarly as on data, i.e. applying the acceptance cuts, selecting the D 0 meson candidates with filtering cuts on their daughters, topological cuts and PID selection, and removing the non-primary particles by means of the DCA from primary vertex cut. Differently from the data analysis, however, only the true D 0 mesons were then used to build the correlation distributions, by looking at the Monte Carlo truth. No background subtraction was hence performed on the correlation distributions. Event mixing correction was applied both at reconstructed and at kinematic level. In the latter case, this correction only takes into account the effects of the acceptance cuts. In addition, at reconstructed level the other corrections were applied as well, except for the feed-down subtraction. Examples of correlation plots for the two analyses are shown in Fig and In the figures, the contribution of associated tracks and of D 0 mesons from different origins are shown separately, as described in the caption. 170

173 CHAPTER 4. D-hadron correlation analysis Figure 4.27: Examples of D 0 -hadron azimuthal correlation distributions obtained from Monte Carlo analysis at kinematic level on the sample with enriched content of charm and beauty. Black points: correlations between all D 0 and all tracks, normalized to the number of all D 0 trigger particles; red points: correlations between prompt D 0 and hadrons from charm, normalized to the number of prompt D 0 trigger particles; green points: correlations between feed-down D 0 and hadrons from beauty, normalized to the number of feed-down D 0 trigger particles; blue points: correlations between all D 0 and hadrons from light quarks, normalized to the number of all D 0 trigger particles. Figure 4.28: Examples of D 0 -hadron azimuthal correlation distributions obtained from Monte Carlo analysis at reconstructed level on the sample with enriched content of charm and beauty. The meaning of the different colours is the same as in Fig

174 CHAPTER 4. D-hadron correlation analysis It was then verified whether the corrected correlation distributions at reconstructed level were compatible with the results obtained at kinematic level. The ratios of reconstructed level over kinematic level distributions were evaluated in all the D 0 p T intervals and for the different associated track p T thresholds, keeping separated the contributions from the different origins of charged tracks and trigger particles. The ratios, shown in Fig. 4.29, are rather flat along ϕ. Their average values present a slight excess from unity (5% to 10%, depending on p T ) and only some structures are present on the near side for the beauty origin case, especially in the low p T interval. Figure 4.29: Ratios of corrected azimuthal correlation distributions from the Monte Carlo analysis at reconstructed level over the distributions from the analysis at kinematic level. Results are shown for the whole p T range (top-left) and separately for the three correlation p T ranges, with an associated track p T threshold of 0.3 GeV/c. The top-right inset in each panel shows the weighted average of each ratio. The meaning of the different colours is the same as in Fig This test was repeated on the Monte Carlo minimum-bias sample as well. The resulting ratios showed a slightly higher average than the results from the enriched sample (10% to 15%, depending on the p T ), but statistical fluctuations prevented a clear interpretation of the results. This occurred for all the D 0 and track origins and in all the D 0 p T intervals. Due to the limited statistics, no conclusions could be drawn on the near side structures for the b-origin case. 172

175 CHAPTER 4. D-hadron correlation analysis To check the effect of the D 0 meson efficiency correction on the correlations distributions at reconstructed level, this consistency test was also performed without applying the trigger efficiency correction. The resulting ratios presented higher divergencies from unity, with more pronounced structures on near side for tracks and triggers coming from beauty, and an additional enhancement on the away side for tracks and triggers coming from charm. The test was also repeated including again the D 0 efficiency correction at reconstructed level, but running both kinematic and reconstructed analyses on the same events, all containing at least a reconstructed D 0. This procedure reduces the effectiveness of the test, since it artificially selects only a subsample of events in the kinematic level analysis. The ratios obtained from this analysis denoted an excellent compatibility with 1; the structures previously present for the beauty origin contribution also completely disappeared. The only side effect present on these results was a small separation of the contributions from charm and beauty origins, whose averages were few percentage points below 1, while the contribution of correlations from light quark tracks was perfectly centered at 1. An additional test consisted in repeating the analysis at reconstructed level, on all the simulated events, stopping the selection of the D 0 meson candidates at the filtering level 4, i.e. not applying the topological cuts and the PID selection criteria defined for the analysis. The ratios of the correlation distributions were much flatter also in this case, showing no structures on the near side; the average heights of the ratios, for the contributions of the various origins, were compatible with the ones obtained with the standard selection (i.e. including also the topological and PID selections) of the candidates at reconstructed level. To spot possible effects of Event Mixing correction on the comparison of correlation distributions at reconstructed and kinematic level, the consistency test was performed without applying this correction on the results at both levels. The ratios of the correlation distributions presented the same discrepancies as the ratios obtained with the standard approach, suggesting that the Event Mixing was not a cause of the inconsistencies between the two levels. As a final test, the correlation distributions of tracks coming from heavy flavour quarks were split in two subsets. The first included only correlations of D 0 with associated tracks produced directly from heavy quark fragmentation. The second subset comprised correlations of D 0 with associated tracks produced from heavy flavour hadron decays. Since the daughters of the trigger D 0 meson were excluded, the latter subset contained decay tracks from other charmed and beauty hadrons produced in the event. Correlations were assigned to either of the two subsets by looking at the identity of the particles found going backwards in the decay chain of the associated track. The ratios of the correlation distributions showed a higher discrepancy with respect to standard results for the first subset of correlations, both 4 At this level the D 0 candidates are only requested to pass a very loose selection on some topological variables; this selection is directly applied while building the candidates from the combinatorial of the tracks reconstructed in the event. 173

176 CHAPTER 4. D-hadron correlation analysis for the baseline level and for the structures on the near side in the beauty origin case. For the second subset, a perfect compatibility was obtained: the resulting ratios were quite flat in ϕ, with baseline levels close to unity for all the track origins and in all the p T intervals. From this results it emerged that the differences between the two analyses did not affect all the tracks in the same way, but arose only when correlating tracks from heavy flavour hadron decays. A parallel analysis was performed on the enriched Monte Carlo sample by taking the D + as the trigger particle. It showed very similar features in the ratio of reconstructed over kinematic correlation distributions. Also in this case the ratios exceeded the level of 1 by about 10% and the beauty origin ratio showed an excess on the near side region. This brought to conclude that these effects were independent of the particular meson chosen as trigger particle. In addition, since the D + results were obtained using an independent analysis code, this reduced the possibility of errors in the analysis code. After performing all the tests previously described, the discrepancies still present in the ratio of the analyses at reconstructed and kinematic level (which were, even for b-origin case, always smaller than 20%) were still not fully understood. A probable cause could have been an effect of a residual dependence of the D 0 meson efficiency on variables not taken into account in the analysis and/or a different tracking efficiency for events containing D 0 candidates passing the selection cuts. For this reason, a further asymmetrical systematic uncertainty of +0% 8% was included in the data results, flat in ϕ, plus an additional contribution of +0% 4% in the bins near to ϕ = Fit to the correlation distributions The ultimate goal of the analysis is to extract physical observables from the corrected azimuthal correlation distributions. This is important both to quantitatively describe the charm fragmentation and hadronization processes in pp collisions and to compare these observables, in the future, with the p-pb and Pb-Pb results. For this reason, a fit procedure was performed on the ϕ correlation distributions. The fit function was composed of two Gaussians, with means fixed at ϕ = 0 and ϕ = π, plus a constant term, fixed to the weighted average of the 8 points in the range π/4 < ± ϕ < π/2 (transverse region). A periodicity condition was also imposed to the fit function to obtain the same value at the bounds of the 2π range. The expression of the fit function is reported below: f( ϕ) = C + Y NS exp ( ( ϕ µ ) NS 0 ) 2 + Y AS exp ( ( ϕ µ ) AS π ) 2 2πσ 2 NS 2πσ 2 AS 2σ 2 NS 2σ 2 AS (4.3) 5 The 4% values is due to the near side excess for the b-origin case, and it was estimated by considering that the highest contribution of feed-down correlations in the data sample is of about 20%. In turn, the near side excess obtained from the test accounts for a 20%, leading to an overall effect of no more than 4%. 174

177 CHAPTER 4. D-hadron correlation analysis From the best fit, the value of the constant C (called also baseline or pedestal value) and the values of yields (Y NS, Y AS ) and widths (σ NS, σ AS ) of the two peaks were obtained. Due to the large statistical fluctuations on the away side of the distributions, however, the away side peak parameters were affected by large statistical errors. To check the stability of the fit and, in addition, to take into account possible effects of statistical fluctuations on the fit results, the fit was repeated with slightly modified approaches. As alternative choices, it was tried to: use two Gaussian functions to fit the near side peak; do not fix the mean of the Gaussian functions; define the height of the baseline using the 2 (or 4) lowest points in the transverse region; extract the yields of the peaks with a bin counting approach. In addition, the fit with the default function was repeated after shifting all the points of the azimuthal distributions upwards and downwards, inside the uncorrelated systematic uncertainty. These checks allowed us to define a systematic uncertainty on the observables extracted from the fit as follows: the maximum variation of the parameters obtained by varying the fitting procedure and by shifting the position of the points within the uncorrelated systematic uncertainty were extracted; for the baseline and the near side yield, the previous value was added in quadrature to the ϕ-correlated systematics in the azimuthal correlation plots. σ syst fit param = Max( fit variation, point shift ) 2 + (σ syst correl )2. (4.4) This was not done for the near side width, since this parameter is not affected by the different normalization: The systematic uncertainty values extracted for baseline, near side yield and near side width are shown in Fig as a function of the D 0 p T. 4.8 Results from pp analysis D 0 -hadron azimuthal correlation distributions and p T trends Figure 4.31 shows the fully corrected azimuthal distributions of D 0 -hadron correlations, evaluated on the pp data sample used in the analysis. Results are shown for the three p T intervals 3 < p T (D 0 ) < 5 GeV/c, 5 < p T (D 0 ) < 8 GeV/c and 8 < p T (D 0 ) < 16 GeV/c, with an associated track p T threshold of 0.3 GeV/c. In Fig the values of baseline, near side yield and near side width for the three p T intervals are shown. These quantities are extracted using the default fit 175

178 CHAPTER 4. D-hadron correlation analysis Figure 4.30: Values of the total systematic uncertainties on the observables estracted from the fit functions, for the three D 0 p T ranges used for the correlation analysis (black solid line). The single contributions from the variation of the fit function and from the shift of the ϕ points are shown separately as coloured bands. 176

179 CHAPTER 4. D-hadron correlation analysis Figure 4.31: D 0 -hadron azimuthal correlation distributions for the three D 0 p T ranges used for the correlation analysis and an associated track p T threshold of 0.3 GeV/c. The statistical and uncorrelated systematic uncertainties are shown with error bars and boxes around the data points, respectively, while the correlated uncertainty is written in a text box. The default fit function (red solid line) and the baseline height (pink dashed line) are superimposed to the data distributions. 177

180 CHAPTER 4. D-hadron correlation analysis function and are shown together with their statistical and systematic uncertainties, defined above. No relevant dependence on D 0 p T is visible for the baseline and the width values, while hints of an increasing trend with increasing D 0 p T are present for the near side yield. The large values of the uncertainties, though, do not allow us to draw firm conclusions on these trends. Figure 4.32: Baseline, near side yield and near side width extracted from the fit to the azimuthal correlation distributions of Fig as a function of D 0 p T. Statistical errors are shown as error bars, systematic uncertainties as boxes Average of D 0 and D + results In Fig a comparison of the ϕ distributions for D 0 and D + -hadron correlation analyses is shown. The results are shown prior to the feed-down subtraction and the removal of residual secondary contamination, which in any case affect the distributions of the two mesons in the same way. A very nice agreement is seen in the p T ranges 5 < p T (D) < 8 GeV/c and 8 < p T (D) < 16 GeV/c. No comparison is shown for the 3 < p T (D) < 5 GeV/c range, instead, because in that range the D + results are not yet ready. Given the compatibility within the uncertainties of the D 0 and D + results and since no difference is visible in the correlations observed in Monte Carlo simulations, 178

181 CHAPTER 4. D-hadron correlation analysis Figure 4.33: D 0 -hadron azimuthal correlation distributions (red points) compared to those from D + -hadron correlation analysis (blue points), for the D meson p T ranges 5 < p T (D) < 8 GeV/c and 8 < p T (D) < 16 GeV/c, with an associated track p T threshold of 0.3 GeV/c. a weighted average (Eq. 4.5) of the azimuthal correlation distributions from the two mesons was performed. Although some correlation between the D 0 and D + could be present (about the 30% of the D 0 comes from D + decays), the selected D 0 and D + samples can be treated as uncorrelated. This can be assumed since: (i) the D 0 and D + selection cuts are quite different; (ii) the statistical error mainly comes from the background subtraction and the background is completely different for the two mesons. Performing the weighted average allowed us to reduce the overall uncertainties affecting the results. The inverse of the quadratic sum of the statistical uncertainty and of the part of the systematic uncertainty that is uncorrelated between the two mesons was used as weight. 1 dn assoc 1 dn i=d = 0,D + i w assoc i N D d ϕ 1, with w i = N D dp T D i=d 0,D w + i σi,stat 2 +. σ2 i,uncorr. syst. (4.5) The statistical uncertainty and the uncorrelated systematic uncertainty on the average were then recalculated according to: σ 2 = i=d 0,D + w i σ 2 i i=d 0,D + w i, (4.6) which, for σi 2 = 1/w i, coincides with the standard formula giving the uncertainty on a weighted average. The contribution from the correlated uncertainty sources to the average systematic uncertainty was evaluated via error propagation on the Eq. 4.5, resulting in the following equation: i=d σ = 0,D w + i σ i. (4.7) i=d 0,D w + i 179

182 CHAPTER 4. D-hadron correlation analysis In particular, the uncertainties on the associated track reconstruction efficiency, on the contamination from secondary tracks, on the feed-down subtraction, and that resulting from the Monte Carlo closure test were considered fully correlated between the D 0 and D + mesons. Those deriving from the yield extraction, the background subtraction and from the D meson reconstruction and selection efficiency were instead treated as uncorrelated. Figure 4.34 shows the average of D 0 and D + azimuthal correlations with associated tracks with p T > 0.3 GeV/c in the D meson p T ranges 5 < p T (D) < 8 GeV/c and 8 < p T (D) < 16 GeV/c. The same fit function used to fit the D 0 -hadron correlation distributions was used. Figure 4.34: D-hadron azimuthal correlation distributions, from a weighted average of D 0 and D + results, for 5 < p T (D) < 8 GeV/c and 8 < p T (D) < 16 GeV/c ranges and an associated track p T threshold of 0.3 GeV/c. The statistical errors are shown as error bars, the uncorrelated systematic uncertainties as error boxes. The ϕ correlated systematic uncertainty (±14%) is not shown. The p T trends of baseline, near side yield and near side width extracted from the fit function were evaluated also for the D 0 and D + averages. The same fitting procedure and the same criteria to evaluate the uncertainties were used as for the D 0 meson analysis. In the 3 < p T (D) < 5 GeV/c range, where D + results were not considered, only the D 0 correlation distributions were employed for the extraction of the observables. The results are shown in Fig and present the same features observed for D 0 -hadron correlations, with no relevant p T dependence for the baseline height and the near side width and hints of an increasing trend with p T for the near side yield. 180

183 CHAPTER 4. D-hadron correlation analysis Figure 4.35: Baseline, near side yield and near side width for the average of D 0 and D + results, extracted from the fit to the azimuthal correlation distributions of Fig. 4.34, as a function of D 0 p T. Statistical errors are shown as error bars, systematic uncertainties as boxes. For the low p T range only the D 0 results were used. 181

184 CHAPTER 4. D-hadron correlation analysis Results for higher associated track p T thresholds Fully corrected azimuthal distributions were also produced for higher thresholds on the associated track p T. For these results a thorough comparison of the distribution features for D 0 and D + triggers is still ongoing. The weighted average distributions are hence shown here only as complementary results of this thesis work. Figure 4.36 shows the ϕ distributions for the three D meson p T ranges, obtained by setting the charged track p T threshold at 0.5 and 1 GeV/c, together with their statistical and systematic uncertainties. For each panel, the default fit function is superimposed to the data results. Figure 4.36: D-hadron azimuthal correlation distributions, from a weighted average of D 0 and D + results, for the three D meson p T ranges and associated track p T thresholds of 0.5 GeV/c (top row) and 1 GeV/c (bottom row). The statistical errors are shown as error bars, the systematic uncertainties uncorrelated along ϕ as error boxes. The ϕ correlated systematic uncertainty (± 14%) is not shown Comparison with Monte Carlo A comparison of the azimuthal correlation distributions from D 0 and D + average with the expectations from Monte Carlo simulations is shown in Fig for the 8 < p T (D) < 16 GeV/c interval. The Monte Carlo samples were produced by generating events with the PYTHIA event generator [83], using three different Perugia tunes [122]. From the comparison one observes that an overall compatibility 182

185 CHAPTER 4. D-hadron correlation analysis within the uncertainties is found, although the Monte Carlo slightly underestimates the measured per-trigger yield. The best agreement with data is obtained using the Perugia2011 tune (blue circles). Figure 4.37: Comparison of fully corrected azimuthal distributions to expectations from Monte Carlo simulations, for the 8 < p T (D) < 16 GeV/c range. Data results are the weighted average of D 0 and D + distributions. Monte Carlo analysis was performed on minimum-bias events produced with PYTHIA with Perugia0 (red points), Perugia2010 (green points) and Perugia2011 tunes (blue points). The description of the event multiplicity by PYTHIA event generator has been found to underestimate the data, at least for events with heavy flavour. Fig shows the number of SPD tracklets with η < 1 found in data and from an analysis on a sample of minimum-bias events generated with PYTHIA using Perugia0 tune, at reconstructed level. The number of tracklets was evaluated for events with at least a D 0 candidate passing the selection, i.e. the events used to build the D 0 -hadron correlation distributions. To produce the Monte Carlo tracklet distributions, the Monte Carlo truth of the D 0 candidates was not checked. This allowed to include in the evaluation of the number of tracklets also events with background candidates, producing an event sample similar to the one used for the data analysis. The comparison denotes a shift of the Monte Carlo distributions toward lower tracklet multiplicities with respect to those from data, visible also by comparing the mean values of the distributions. Since the number of tracklets is strongly correlated to the event track multiplicity, this discrepancy could explain the underestimation of the measured 183

186 CHAPTER 4. D-hadron correlation analysis per-trigger yield obtained in the comparison of Fig In this view, in the near future further comparisons between data results and expectations from other event generators (e.g. Herwig) will be performed. Comparing the near side peak of data and Monte Carlo distributions, the values of the peak yield and width obtained by PYTHIA seem to slightly underestimate data results, even if compatibility within the uncertainties is found between data and Monte Carlo. Anyway, due to the level of the uncertainties, no firm conclusions can be drawn on this comparison. For the away side peak, instead, the statistical fluctuations present on data results, mainly induced by the background subtraction, do not allow any comparison with Monte Carlo simulation results. Figure 4.38: Distributions of the number of tracklets found in events with at least a selected D 0, on data (top row) and Monte Carlo LHC10f6a (MB, PYTHIA Perugia0) sample (bottom row), for the three D 0 p T ranges in which the correlation analysis was performed. The mean value of the distributions is also shown in the labels. 4.9 Outlook and perspectives for p-pb and Pb-Pb analyses The feasibility of the D-hadron correlation analysis was studied also in data samples of p-pb collisions at s NN = 5.02 TeV and Pb-Pb collisions at s NN = 2.76 TeV. In both cases the analysis was executed with the same strategy as in pp, but using different selection criteria for D mesons and associated tracks. Since the main goal was to verify whether a significant result could be obtained with the collected statistics and performance of the ALICE detectors, the analysis was stopped after the Event Mixing correction and the background subtraction. No efficiency correction, feed-down subtraction and secondary contamination removal were applied to the distributions. 184

187 CHAPTER 4. D-hadron correlation analysis The p-pb analysis was performed on minimum-bias events, collected in two periods of data taking (LHC13b and LHC13c data samples). Figure 4.39 shows the azimuthal distributions of correlations between D 0 trigger particles and charged tracks, for the 8 < p T (D 0 ) < 16 GeV/c range and associated track p T thresholds of 0.3 and 1 GeV/c. No normalization to the number of trigger particles is applied to the results. A fit function composed of two Gaussians and a constant term is superimposed on data to guide the eye. The near side and away side peaks are clearly visible on top of the pedestal level. In Fig a distribution from the D + analysis in p-pb events is shown, for the 5 < p T (D + ) < 8 GeV/c and an associated track p T threshold of 0.5 GeV/c. The same fit function is superimposed to the results. In this p T range it is more difficult to observe the two correlation peaks, especially on the away side. In any case, from these preliminary checks the p-pb analysis appears to be promising for both mesons. It is hence worth to continue performing the analysis, which is currently proceeding through the evaluation of all the corrections. Figure 4.39: D 0 -hadron azimuthal correlation distributions for p-pb collisions at s NN = 5.02 TeV. Results are shown for the 8 < p T (D 0 ) < 16 GeV/c range, with associated track p T thresholds of 0.3 GeV/c (left) and 1 GeV/c (right). Analysis procedure includes only background subtraction and event mixing correction. Normalization to the number of D 0 trigger particles is not applied to the results. A fit function composed of a double Gaussian and a constant term is shown to guide the eye. The D 0 -hadron correlation analysis was also tried on Pb-Pb events at s NN = 2.76 TeV, collected during the 2011 data taking. Only the events in the 0-10% centrality class (about events) were selected for the correlation evaluation. In the resulting azimuthal correlation distributions it was not possible to obtain clear near side and away side peaks. Their height, indeed, is expected to be much smaller than the baseline level obtained in such collisions. In addition, due to the small S/B values of the signal peaks, the statistical fluctuations induced by the background correlation subtraction completely overwhelm the physical structures of the correlation distributions. Furthermore, it was also estimated that the analysis on Pb-Pb collisions will not be feasible even with the statistics collected during the 185

188 CHAPTER 4. D-hadron correlation analysis Figure 4.40: D + -hadron azimuthal correlation distributions for p-pb collisions at s NN = 5.02 TeV. Results are shown for the 5 < p T (D + ) < 8 GeV/c range, with an associated track p T threshold of 0.5 GeV/c. Analysis includes only background subtraction and event mixing correction. Normalization to the number of D + trigger particles is not applied to the results. A fit function composed of a double Gaussian and a constant term is shown to guide the eye. Run2 data taking, when an increase of statistics by a factor up to 10 with respect to that currently available is expected for central collisions. Studies on the feasibility of the analysis in peripheral collisions will also be performed in the near future. It was also verified the possibility of running the Pb-Pb analysis after the ALICE upgrade, which will take place during the LS2 ( ). Major improvements are planned for many ALICE detectors. In particular, the improvement of the tracking and vertexing performance of the ITS detector will allow us to significantly reduce the combinatorial background in the invariant mass distributions. This, in turn, should reduce the statistical error introduced by the background subtraction in the ϕ correlation distributions, which is the limiting factor of the present Pb-Pb analysis. The expected large increase of collected events will be crucial as well to reduce the influence of statistical fluctuations on the ϕ correlation distributions. Figure 4.41 shows, in red, the estimates for S/B (left panel) and statistical significance (right panel) of the D 0 meson Gaussian peaks in the invariant mass distributions as a function of the D 0 p T, obtained with the upgraded ITS by analyzing the expected statistics of Pb-Pb collisions at s NN = 5.5 TeV. These values are compared to those achievable with the current detector in the Pb-Pb analysis at the same energy [185]. Both sets refer to the events inside the 0-10% centrality class. As anticipated, a striking increase by a factor 5-10 is obtained on average for the S/B values, while the statistical significance per event (Sign./ N ev ) is more than doubled, with an additional increase that will occur due to the increment of the statistics collected in the runs after the upgrade. Quantitative estimates of the impact of the improved D 0 reconstruction on the 186

189 CHAPTER 4. D-hadron correlation analysis Figure 4.41: Comparison of S/B ratio (left) and statistical significance normalized to the size of the event sample (right) for the D 0 invariant mass peaks expected with the current and the upgraded ITS as a function of the D 0 p T, in Pb-Pb collisions at s = 5.5 TeV. D 0 mesons are reconstructed from the Kπ decay channel. correlation analysis were performed as well. In left panel of Fig the D 0 -hadron azimuthal correlation distribution expected using the upgraded ITS is shown for the 8 < p T (D 0 ) < 16 GeV/c range and an associated track p T threshold of 0.3 GeV/c, for Pb-Pb collisions in the 0-10% centrality class ( events, about 500 times the statistics currently available for the 0-10% centrality class). The starting point for building the distribution was the correlation pattern simulated by PYTHIA in pp collisions at s = 7 TeV (the only predictions currently available), with a shifted baseline to account for the different multiplicity of the Pb-Pb events. The distribution is shown normalized to the number of D 0 trigger particles, after the subtraction of the pedestal and with the default fit function superimposed. Both peaks are clearly visible, while the statistical fluctuations have negligible influence on the results. On the right panel, the expected relative statistical uncertainty is shown for the values of the near side peak yield, for the three p T ranges and different associated p T thresholds. With the upgraded detector the uncertainties are expected to be very small, especially for p T > 5 GeV/c. Thus, it should be possible to obtain solid results also in Pb-Pb, allowing a comparison with pp and p-pb collision systems. As a reference, the relative statistical uncertainty for the near side peak yield in pp collisions, from the results shown above using the D 0 trigger only, are 22.5%, 20.8% and 17.5% for the 3 < p T (D 0 ) < 5 GeV/c, 5 < p T (D 0 ) < 8 GeV/c and 8 < p T (D 0 ) < 16 GeV/c intervals, respectively. The better performance obtained with the ALICE upgrade, however, will help to improve the measurements also in the pp collision system, allowing to reduce the statistical uncertainties of the pp reference as well. 187

190 CHAPTER 4. D-hadron correlation analysis Figure 4.42: Left: estimates for the D 0 -hadron azimuthal correlation distribution in Pb- Pb collisions from a Monte Carlo simulation with the upgraded ITS, for the 8 < p T (D 0 ) < 16 GeV/c range, with an associated track p T threshold of 0.3 GeV/c. Events are selected in the centrality range 0-10%. The distribution is shown after the subtraction of the pedestal. The default fit function is superimposed to the data distribution, together with the extracted values for yields and widths of the near and away side peaks. Right: estimates for the statistical uncertainty on the near side yield, from the Pb-Pb analysis on the expected statistics after the ALICE upgrade. Estimates are shown for the three D 0 p T ranges as a function of the p T threshold used for the pp and p-pb analyses. 188

191 Conclusions The measurement of angular correlations between D 0 mesons (trigger particles) and unidentified charged particles (associated particles) in proton-proton collisions is the main result of this thesis. The analysis was performed using the ALICE detector at the LHC. The tools and the analysis framework needed to perform the correlation analysis were developed for this study and were also applied to other collision systems (p-pb and Pb-Pb). From the 2010 pp statistics, composed of about events, it was possible to obtain results for azimuthal correlation distributions in three different D 0 transverse momentum ranges, 3 < p T (D 0 ) < 5 GeV/c, 5 < p T (D 0 ) < 8 GeV/c and 8 < p T (D 0 ) < 16 GeV/c, and for three values of the associated track p T threshold, 0.3, 0.5 and 1 GeV/c. The present statistics did not allow us to evaluate two dimensional ( ϕ, η) correlation distributions. The measurements with the lowest associated track p T threshold, 0.3 GeV/c, showed a good agreement with an analogue analysis performed using D + mesons as trigger particles in the 5 < p T (D 0 ) < 8 GeV/c and 8 < p T (D 0 ) < 16 GeV/c intervals, while in the 3 < p T (D 0 ) < 5 GeV/c range the D + analysis is not yet completed. In the two p T intervals where both D 0 and D + results are available (and compatible), the weighted average of the correlation distributions was evaluated. This allowed us to reduce the influence of statistical and systematic uncertainties. Both D 0 results and D meson averages were approved by the ALICE Collaboration as Preliminary results. As further complementary results, the weighted averages of D 0 and D + azimuthal correlation distributions were computed for the three D meson p T ranges also using higher values of the associated track p T thresholds, i.e. 0.5 and 1 GeV/c. A comparison of the azimuthal correlation distributions to expectations from the PYTHIA event generator was performed. Different tunes of PYTHIA parameters were considered for this study. The comparison showed a substantial agreement within the uncertainties between data and the model. By fitting the data using a proper function, it was possible to extract some physical quantities, like the baseline height of the D-hadron azimuthal correlation distributions, the yield and the width of the near side peaks. The dependence of these quantities on the D meson p T was evaluated. The values of the physical quantities extracted from the fit to the distributions can be used as benchmarks for the comparison with future p-pb and Pb-Pb measurements. With the available statis- 189

192 Conclusions tics and the current performance of the ALICE detectors, the statistical fluctuations on the correlation results and, as a consequence, the uncertainties on the physical observables extracted by fitting the distributions do not allow us to put constraints on the theoretical models describing the charm quark production and fragmentation. However, major improvements on this points are expected already from the analysis on the statistics collected in the next data taking, starting in An overview of the status of the analysis in p-pb collisions at s NN = 5.02 TeV has been presented, showing that solid results can be achieved for this collision system. Final results for this analysis are expected in the upcoming months. Finally, it was demonstrated that the correlation analysis is instead not feasible on the Pb-Pb data sample currently available. Anyway, it was verified that, after the upgrade of the ALICE detectors, the improvements in the performance on the D 0 meson reconstruction, as well as the larger statistics, will allow us to obtain results for Pb-Pb collisions as well. This will enable a comparison of the ϕ correlation distributions from all the three collision systems, allowing us to quantify the effects of the QGP on the fragmentation and hadronization of the charm quarks. 190

193 Appendix A - ALICE offline analysis framework This appendix will briefly describe the basic tools for data analysis and offline computing available in the ALICE experiment. It will present a short review of the ROOT analysis framework [186, 187], of its customization and extension for ALICE experiment AliRoot [188] and of the AliEn interface [189, 190], which allows us to redistribute the analysis load on a delocalized computer network based on Grid technology. ROOT analysis framework The ROOT framework provides a series of tools which allow one to analyze huge amounts of data in a very efficient way, enabling to perform a vast series of operations. It is mainly employed in particle physics (e.g. at CERN, DESY, GSI, Fermilab): in this context it is very useful in handling the overwhelming quantity of data obtained from particle collisions and it allows generation of particle interactions, simulation of detectors, event reconstruction and data analysis in general. Also other science fields have recently adopted the ROOT framework, like biology, economics, astronomy and more. ROOT was firstly developed in the context of the NA49 experiment at CERN. NA49 generated a huge amount of data, about 10 Terabytes per run. This rate provided the best environment to develop and test the next generation data analysis software. In 2002 ROOT became an official project within the Physics Department at CERN and could gradually be extended in many directions to become the cornerstone of most High Energy Physics software systems (and not only) nowadays. ROOT is completely written in C++ language and it also includes a C++ interpreter (CINT). The CINT interpreter covers about 90% of C++ instructions and allows the user to execute small macros or scripts inside the ROOT framework, without having to compile the code and to link the needed libraries before the execution. Most importantly, ROOT is an object oriented framework, with high modularity, which makes it highly versatile, powerful and capable of dealing with very different tasks. It allows the usage of a rich variety of mathematical and statistical instruments for data analysis, like multi-dimensional histograms, common mathematic functions, random number generators, multi-parameter fitters, minimization algo- 191

194 Appendix A - ALICE offline analysis framework rithms and more. It also includes a graphic interface which grants the user a quick and easy interaction with the framework. The backbone of ROOT architecture is based on about 1200 classes organized in a hierarchical tree structure, arranged in 60 libraries and divided in 19 categories (modules), which group them on the basis of their main usage (e.g. physics, matrix, minimization, histogram categories). Most of the classes (with some notable exceptions) inherit common methods from a common base class (TObject), and then differentiate by adopting specific members and methods. The ROOT framework can be widely extended by adding user classes and libraries that become effectively part of the system. These libraries are loaded dynamically and the included classes share the same services of native ROOT classes (including object browsing, I/O, dictionary and so on). For this peculiarity, ROOT was particularly suitable to be the ground of the ALICE offline analysis framework. ALICE offline framework: AliRoot AliRoot is the extension of the ROOT framework to the ALICE experiment. It completes the set of ROOT native classes with personalized libraries, which describe the structure and the geometry of the detector and of all its subsystems and their response to the passage of the tracks, allowing track reconstruction, quality assurance checks and data analysis. The general structure of the AliRoot package is shown in Fig. 4.43, where it is possible to see its modular architecture. The whole system is built on ROOT framework, while its core is the STEER module, which contains steering, run management, interface classes and base classes for simulation and reconstruction and allows managing all the other modules. These can be organized in several categories, like the event generators (in EVGEN) as HIJING, PYTHIA, ISAJET; the transport codes (in Virtual MC) as GEANT3, GEANT4, FLUKA; the single detectors, which are granted a specific module each; the analysis code. Finally, AliRoot allows the usage of the AliEn interface, for delocalized analysis, which will be discussed in the next paragraph. Modularity is one of the most important features of AliRoot, since it allows the user to add, exclude or substitute parts of the system without having to adapt the rest and without altering the AliRoot structure. Another essential feature is re-usability, which grants the maximum amount of backward compatibility while evolving the system and lets the user run his code in all the versions of the system without major changes. The way in which data analysis is handled grants the highest flexibility too. Output from event reconstruction both for real and simulated data is formatted in a peculiar format, the Event Summary Data (ESD). This format contains a tree (esdtree), structured in various branches, each of them including information about a specific element of the analysed events, i.e. primary vertices, reconstructed tracks, secondary vertices. This structure is the same independently from the data taking 192

195 Appendix A - ALICE offline analysis framework conditions, detector configuration and other possible variables. In order to speed up and facilitate the execution of specific analyses, which involve only a part of the event (e.g. D 0 meson reconstruction), ESD output are transformed in Analysis Object Data (AOD). AODs have the same tree structure as ESDs, but they contain only the general information on the event, needed to perform most of the data analyses, while all the other data are discarded, increasing the efficiency and the computing performance of the analyses. Figure 4.43: Basic structure of the AliRoot architecture. The Grid and AliEn interface From the LHC restart in 2010, ALICE accumulated about 8 PB of raw data. This quantity grows to about 20 PB if considering also reconstruction, Monte Carlo simulations and analysis results. In order to elaborate this massive amount of data, expected to grow by 5 additional PB per year of data taking, a CPU power of about 18 MSI2k is required. Since it is not possible to concentrate in a single place all the needed computing resources for storing and analysing this data volume, they are delocalized in many computing centres all over the world, distributed in a network arranged following the MONARC Tier model. Computing and data storage centres are thus organized in a tree hierarchy, in different levels (tiers) according to their capabilities. The core of the network is the CERN itself (Tier-0), where all raw data are stored and online analyses are performed. Backups of all data are stored also in various Tier-1, the bigger computing centres, where offline reconstructions take place. Next level is composed of many smaller centres (Tier-2); they do not store raw data but they contribute significantly to the requested computing power, being used for main data analyses and 193