Ricerca del decadimento. nell esperimento LHCb al CERN

Transcription

1 Facoltà di Scienze Matematiche, Fisiche e Naturali Ricerca del decadimento X(3872) J/ψω nell esperimento LHCb al CERN Tesi di Laurea Magistrale in Fisica CERN-THESIS /09/2014 Candidato: Lorenzo Capriotti Matricola: Relatore: Roberta Santacesaria Correlatore: Antonio Augusto Alves Jr. Anno Accademico 2013/2014

2 -You tried to predict movements in the yen by drawing on patterns from nature. Yes, of course. The mathematical properties of tree rings, sunflower seeds, the limbs of galactic spirals. [...] The way signals from a pulsar in deepest space follow classical number sequences, which in turn can describe the fluctuations of a given stock or currency. You showed me this. How market cycles can be interchangeable with the time cycles of grasshopper breeding, wheat harvesting. You made this form of analysis horribly and sadistically precise. But you forgot something along the way. - What? - The importance of the lopsided, the thing that s skewed a little. You were looking for balance, beautiful balance, equal parts, equal sides. But you should have been tracking the yen in its tics and quirks. The little quirk. The misshape. The misweave. That s where the answer was. Don DeLillo, Cosmopolis (2003)

3 Contents 1 Introduction 7 2 Exotic charmonia: theoretical and experimental status Exotic quarkonia in the charm sector X(3872) Experimental status Theoretical models The J/ψω decay channel The LHCb experiment at CERN Large Hadron Collider LHCb detector Vertex Locator (VELO) Ring-Imaging Cherenkov Detectors (RICH) Tracking System Magnet ECAL and HCAL Muon system Trigger Analysis tools Stripping and reconstruction Monte Carlo simulations Data Analysis Data samples Event selection Stripping cuts Decay reconstruction Preselection cuts Monte Carlo sample Multivariate analysis Input variables and training phase B + mass fit

4 4.4.3 Application phase of MVA Background subtraction: splot technique Application of splot technique J/ψω mass spectrum Resonances contribution Hypotheses for the excess of events at 5350 MeV/c Efficiency corrections J/ψω mass resolution Results Summary Appendices 77 A The splot technique 78 A.1 Preliminary step: total correlation A.2 The splot formalism

5 List of Figures 2.1 Charmonium spectrum Peak observed by Belle (2003) Result of the X(3872) particle angular analysis from CDF Determination of X(3872) quantum numbers: BaBar analysis of X(3872) J/ψω on the left, LHCb analysis of X(3872) J/ψρ on the right Distribution of the test statistics t for the simulated experiments with 2 + and 1 ++ at LHCb Simulation of the prompt production cross section as a function of the relative centre of mass momentum of the system D 0 0 D (the allowed phase space region is highlighted) Spectrum of [cq][ c q] states according to the tetraquark model Corrected M(J/ψω) distribution for B + (top) and B 0 (bottom) decays The CERN accelerator complex Polar angles of the b- and b-hadrons calculated with PYTHIA LHCb detector, lateral view (non-bending plane) VELO system configuration and VELO sensors RICH detectors layout Inner Tracker layout Trigger Tracker layout Tracking system layout LHCb magnet, perspective view Calorimeters segmentation: ECAL on the left, HCAL on the right Resolved π 0 reconstruction efficiency for the channel B 0 π + π π Muon system configuration B mass spectrum after the application of preselection cuts Dalitz plot for K + ω squared mass vs J/ψω squared mass, generator level (MC) B + mass spectrum (MC), before and after fixing the π 0 mass. 38 4

6 4.4 π 0 mass spectrum (MC) B + mass vs π 0 mass (MC) ω mass (MC) Dalitz plot for K + ω squared mass vs J/ψω squared mass, after the reconstruction and preselection phases (MC) Input variables, with signal and background distributions Correlation matrices for signal and background samples MVA methods performance (ROC curve) PLE method response B + mass spectrum, after the cut on r L B + mass spectrum, before and after the cut on r L B + mass fit, without the bump contribution, for r L > B + mass fit, with the bump contribution, for r L > Statistical significance (blue), signal efficiency (magenta) and background rejection (black) as a function of rl cut (left axis for the significance and right axis for the rest) B + mass fit for two different values of cut on r L, where the different bump contribution within the signal interval is clearly visible Fit on B + mass for both the selection criteria, with fit results ω invariant mass distribution after the r L cut ω invariant mass signal distribution (background subtracted) π 0 mass signal distribution (background subtracted) J/ψω mass, MVA_LL > J/ψω mass, MVA_LL > M(ω) cut J/ψππ and Kπ invariant mass, MVA_LL > J/ψππ and Kπ invariant mass (background subtracted), MVA_LL > J/ψω mass without Ψ(2S) and K (892) contributions, MVA_LL > J/ψω mass without Ψ(2S) and K (892) contributions, MVA_LL > M(ω) cut M(J/ψω) vs M(Kω), MVA_LL > M(J/ψω) vs M(Kω), MVA_LL > M(ω) cut M(J/ψω), MVA_LL > 0.65, after cut on M(Kω) M(J/ψω), MVA_LL > M(ω) cut, after cut on M(Kω) B + mass vs (J/ψKππ) mass B + mass vs (K J/ψ) mass B + mass vs (J/ψππ) mass B + mass vs (K π) mass B + mass vs (K ω) mass Effect of the cut flow on the J/ψω mass distribution (black histogram before the application of the cuts, red histogram after) 64 5

7 4.38 Effect of the cut flow on the J/ψω mass distribution (black histogram before the application of the cuts, red histogram after) Efficiency of every step as a function of M(J/ψω). Asymmetric errors are computed according to the Agresti-Coull formula [49] Total efficiency distributions for both MVA cut values Fit on the linear component of the total efficiency for both MVA cut values Fit on the M(Kω) cut efficiency for both MVA cut values Total efficiency distributions, data from MC and functional form M(J/ψω), MVA_LL > 0.65, efficiency corrected M(J/ψω), MVA_LL > M(ω) cut, efficiency corrected δm for M reco (J/ψω) [4100, 4150] MeV/c J/ψω mass resolution J/ψω mass, threshold region Corrected J/ψω mass with the new MC normalization, MVA_LL > Corrected J/ψω mass with the new MC normalization, MVA_LL > M(ω) cut

8 Chapter 1 Introduction In this thesis, a search for the decay X(3872) J/ψω within the decay channel B + K + (J/ψ µ + µ )(ω π + π (π 0 γγ)) is shown. The analysis is performed on data collected by the LHCb experiment at the Large Hadron Collider at CERN during 2011 and Improving the knowledge of this decay channel could help in better understanding the nature of the exotic X(3872). This channel has been studied by the BABAR experiment at the SLAC National Accelerator Laboratory in Menlo Park, California (USA), resulting in a limit on the branching fraction: BR(X(3872) J/ψω) > 1.9%. This thesis is structured as follows: in Chapter 2, an introduction on exotic quarkonia is presented, focusing on the X(3872) since its first evidence at the Belle experiment in A report on the theoretical and experimental status follows, along with the importance of the specific decay that has been the object of this analysis. in Chapter 3, a description of the LHCb detector is given, from the physics reasons behind the choice of its geometry to the technical specifications of every subdetector. The trigger and the offline analysis tools are briefly described. in Chapter 4, a detailed and stepwise exposition of the analysis workflow is presented: the processes of event reconstruction, the event selection, the statistical background subtraction and the analysis of heavy resonances contributions are described. The last part of the chapter covers the computation of the efficiency correction function and the J/ψω mass resolution. in Chapter 5, the results of this analysis are shown, along with a short summary and the forecast for LHC Run-II. 7

9 Chapter 2 Exotic charmonia: theoretical and experimental status Since the proliferation of discoveries of new strongly interacting subatomic particles, an urge arose to create a model for the purpose of categorizing the observed states and eventually predicting new ones. Fermi and Yang, in 1949, thought of describing all the resonances as proton-neutron bound states, and Sakata [1] extended the model in 1956 in order to include the strange particles. Although these models gave wrong predictions regarding the baryons, and were therefore unable to explain the totality of hadrons, they were the starting point for Gell-Mann and Zweig who, independently, began to develop what we know today as the Constituent Quark Model [2]. CQM was born in 1961 and it s based on the SU(3) formalism: the fundamental representation is composed by three elementary particles (up quark, down quark and strange quark) and the antifundamental representation by their antiparticles. Mesons and baryons are described as a tensor product of these representations. Using the Kronecker decomposition, they can be expressed as follows: Mesons: 3 3 = 1 8 Baryons: = (2.1) or, in other words, a meson is a [q q] bound state and a baryon is a [qqq] bound state, where q = (u, d, s). Among the generators of the SU(3) algebra, the so called Gell-Mann matrices, only two commute between them, and they are related to isospin I and hypercharge Y : these two quantities can label each particle in each meson and baryon multiplet. With this model, Gell-Mann and Ne eman were able to predict, in 1962, a new particle which would have completed the baryons decuplet, the Ω, and it was discovered two years later at Brookhaven National Laboratory [3]. CQM remains a valid effective theory for classifying hadrons, even after the introduction of heavy quarks (c, b, t). However, recently discovered states seem not to fit into the conventional 8

10 mesons and baryons model: in particular, their internal structure might be different from [q q] and [qqq]. Actually, other combinations are in principle allowed: multiquarks (such as tetraquark or pentaquark), mesonic molecules, and, given the non Abelian nature of Quantum Chromodynamics (QCD), even gluons can contribute explicitly to this structures with hybrid states, glueballs, and others. Since none of these states have been observed for a long time after the theories were first published (around mid-1960s), it was chosen to label every non [q q] or [qqq] state as exotic state. 2.1 Exotic quarkonia in the charm sector Different exotic meson candidates exist. In the light quark sector, for example, the f 0 (980) and the a 0 (980) are considered to be strong candidates for K K molecules. It is very difficult, however, to disentangle these states from the very dense background of non exotic states, as it would require enormous data sample and a very refined data analysis. The charmonium sector ([c c] states), instead, provides a cleaner environment, given by the large difference between heavy quark masses (unlike the light quark sector), and can profit from a wide range of detailed studies on the excited charmonium spectrum. Figure 2.1: Charmonium spectrum In Figure 2.1 the charmonium spectrum is shown [4], where the solid lines are 9

11 CQM predictions, the shaded lines are the observed conventional charmonium states, and the red dots are the exotic candidates placed in the most probable spin assignment column. Various D D mass thresholds are also shown. The charmonium states shown in Figure 2.1 are described as a charm-anticharm pair bound by a short distance force dominated by a single gluon exchange, plus a linearly increasing confining potential. The energy levels are then computed by solving a non-relativistic Schrödinger equation with that potential, while the splitting within multiplets is caused by a spin-dependent correction of order (v/c) 2. This QCD-based phenomenological description has been particularly efficient in describing the observed charmonium states until 2003, when the Belle Collaboration observed for the first time a narrow peak in the J/ψπ + π invariant mass spectrum at 3872 MeV/c 2 [5]. Since the observation of the X(3872) by the Belle Collaboration, various other neutral exotic charmonium states have been observed by different collaborations, all of them decaying into a charmonium state (mostly J/ψ) or a D D pair. Hints of three charged structures were also observed by Belle: Z(4430), Z 1 (4050), Z 2 (4250), between 2007 and 2008 [6, 7]. These mesons are particularly interesting since, being charged, their minimal quark content is necessarily exotic: c cdū. The Z(4430) resonance has been recently confirmed by the LHCb Collaboration, demonstrating its tetraquark nature [8]. Another charged exotic state, called Z c + (3900), was recently observed by the BESIII Collaboration [9]. 2.2 X(3872) Experimental status The X(3872) was first seen in 2003 by the Belle Collaboration at KEK, in Japan, as a narrow peak in the J/ψπ + π invariant mass distribution in the decay B + K + π + π J/ψ. It is shown in Figure 2.2. After the Belle announcement, it was observed also by the CDF [10] and D0 [11] Collaborations at the Fermilab Tevatron in Chicago, and was confirmed also by the BaBar Collaboration at the SLAC National Accelerator Laboratory in California [12]. Both BaBar and Belle observed the decay X(3872) γj/ψ, which indicates that the X(3872) has positive charge conjugation, C = +1 [13, 14]. This suggested that the dipion system from the decay X(3872) J/ψπ + π comes from a ρ meson. This idea was indeed confirmed by CDF, with the implication that the X(3872) cannot be an excited charmonium state because that decay would violate isospin conservation [15]. 10

12 Figure 2.2: Peak observed by Belle (2003) Figure 2.3: Result of the X(3872) particle angular analysis from CDF Moreover, BaBar observed evidence for the decay X(3872) J/ψω at a rate comparable to that of J/ψππ [16]: BR(X(3872) J/ψω) BR(X(3872) J/ψππ) = 0.8 ± 0.3 (2.2) suggesting that X(3872) could be a mixture of I = 0 and I = 1 states. An angular analysis of the final state particles, performed by CDF in the channel X(3872) J/ψπ + π ruled out all the J P C assignments except for 1 ++ and 2 +, as can be seen in Table 2.3 [17]. 11

13 The BaBar analysis of the decay X(3872) J/ψω favoured the J P C = 2 + hypothesis with a confidence level of CL = 68% over the 1 ++ hypothesis, without ruling it out (CL = 7%). The LHCb Collaboration, however, determined in 2013 that the quantum numbers of X(3872) are 1 ++, with 8.2σ rejection of the 2 + hypothesis from the channel X(3872) J/ψππ [18]. The BaBar and LHCb analysis can be observed in Figure 2.4, while in Figure 2.5 the LHCb result is shown. (a) BaBar 3π mass distribution (b) LHCb X(3872) helicity angle distribution Figure 2.4: Determination of X(3872) quantum numbers: BaBar analysis of X(3872) J/ψω on the left, LHCb analysis of X(3872) J/ψρ on the right Figure 2.5: Distribution of the test statistics t for the simulated experiments with 2 + and 1 ++ at LHCb 12

14 2.2.2 Theoretical models Several models have been proposed to explain the nature of X(3872) [19, 20]. The more plausible are: Excited charmonium state: the observed decay in J/ψ implies that the X(3872) must contain a c c pair. The c c state with J P C = 1 ++ is the χ c1 (with spectroscopic term symbol 2 3 P 1 ) and has not been observed yet. The predicted mass is M(χ c1) = 3950 MeV/c 2. However, the decay X(3872) J/ψρ violates isospin conservation in the hypothesis of a pure charmonium state. Mesonic molecule [21]: the X(3872) mass is very close to the sum of the masses of the D 0 and D 0 mesons. This led to the speculation that the X(3872) could be a D 0 D 0 loosely bound state, with very small binding energy (E MeV), which implies a molecule radius of about R (2M D E 0 ) 1 2 = 8 fm. Such a large radius allows the molecule constituents to decay autonomously and, since the D 0 D 0 molecule wavefunction is expected to contain an admixture of J/ψρ and J/ψω, it could explain the isospin violation. However, the small binding energy allows a small range of relative centre of mass momentum for the molecule to be formed in hadronic colliders. A simulation has been performed [22], in which the integrated prompt production cross section is shown as a function of the relative momentum of the centre of mass: in the phase space region that would allow the formation of a D 0 D 0 molecule with a binding energy of E 0, the upper bound on the cross section is found to be σprompt th = nb, about 40 times smaller than the lower bound on the CDF experimental cross section (σprompt CDF = 3.1 nb). This result is shown in Figure 2.6. Figure 2.6: Simulation of the prompt production cross section as a function of the relative centre of mass momentum of the system D 0 D 0 (the allowed phase space region is highlighted) 13

15 Tetraquark model [23]: this model considers 4 quark states of the form [cq][ c q]. Due to the X(3872) mass, q = u, d. The two neutral flavour eigenstates are: X u = [cu][ cū] X d = [cd][ c d] while the neutral mass eigenstates are described by a mixing angle: [ ] [ ] [ ] Xlow cos θ sin θ Xu = sin θ cos θ X high with a mass difference of M = (7 ± 2)/ cos(2θ) MeV/c. The mixing angle can be determined by the ratio of 3π to 2π decay rates and it s found to be θ 20 from Belle data. Summarizing, the tetraquark model predicts a neutral exotic partner for the X(3872) with a mass difference of M = 8±3 MeV, along with other partners according to the spin-spin interactions between diquarks (which can be scalar or vector). Moreover, only one of the two mass eigenstates (X low and X high ) is supposed to be produced in B + decays, while the other is supposed to be produced in B 0 decays. This means that the X(3872) seen in B + decays and the one seen in B 0 decays are different states with mass difference M. Belle determined a mass difference between the X(3872) produced in charged versus neutral B decays of M = 0.9 ± 0.9 MeV, which is consistent with zero. Furthermore, no other state in the [cq][ c q] spectrum has been observed. X d Figure 2.7: Spectrum of [cq][ c q] states according to the tetraquark model 14

16 Other models have been suggested (cusp close to M(D 0 D 0 ) threshold, dynamically generated resonance, hybrid c cg resonance) but they present numerous gaps with experimental data and are regarded as very unlikely models with respect to the aforementioned ones The J/ψω decay channel As previously specified, the decay channel X(3872) J/ψω was first seen by BaBar in 2010, both in B + and B 0 decays in X(3872)K + and X(3872)K 0, respectively. The number of observed signal events is 21.1 ± 7.0 for B + decay and 5.6±3.0 for B 0 decay, leading to a combined signal consisting of 34.0±6.6 events. The probability to be an upward background fluctuation is , corresponding to a significance of 4.0σ for a normal distribution. In figure 2.8, the efficiency corrected M(J/ψω) distribution is shown for charged (top) and neutral (bottom) B decays, along with the result of the fit. A second peak, at about 3920 MeV/c 2, can be observed and corresponds to the decay Y(3940) J/ψω: the Y(3940) meson, subsequently called X(3915), has been an exotic candidate until 2012, when BaBar measured its quantum numbers and identified it with the excited charmonium state χ c0 (2P) [24]. Figure 2.8: Corrected M(J/ψω) distribution for B + (top) and B 0 (bottom) decays It must be noticed that the decay X(3872) J/ψω is subthreshold, since M(X(3872)) < M(J/ψ) + M(ω). The mass difference is 9 MeV/c 2, and this 15

17 implies that only a low mass ω contributes to this decay. The BaBar analysis result for the charged B decay channel is: BR(X(3872) J/ψω) BR(B + X(3872)K + ) = (6 ± 2 ± 1) 10 6 which, using the PDG limit of BR(B + X(3872)K + ) [43]: gives the following limit: BR(B + X(3872)K + ) < (2.3) BR(X(3872) J/ψω) > As shown in Section 2.2.1, BaBar used this decay channel to measure the X(3872) quantum numbers. The assignment J P C = 2 + is found to be favoured by the data. LHCb, two years later, measured J P C = 1 ++ in the J/ψππ channel with a 8σ significance. As already stated, the final states J/ψρ and J/ψω have different isospin (respectively, I = 1 and I = 0). The ratio (2.2) implies a mixture of states with different isospin: it is possible, then, that the particle decaying in J/ψρ may be different from the particle decaying in J/ψω. A measurement of this channel is therefore required, in order to search for the isospin partner predicted by the tetraquark model, to obtain a better measurement on the branching ratio and possibly to repeat the angular analysis already performed on the J/ψππ channel, to verify whether the two aforementioned decays come from the same exotic state or not. 16

18 Chapter 3 The LHCb experiment at CERN LHCb is, along with ATLAS, CMS and ALICE, one of the main experiments at CERN (Conseil Européen pour la Recherche Nucléaire), in Geneva. The purpose of the experiment is to analyse data from proton-proton collisions inside the LHC accelerator (Large Hadron Collider), focusing on the decays of heavy mesons (composed by charm and bottom quarks), to explore the difference between matter and antimatter and to search for rare decays and rare particles. LHCb is located at the Intersection Point 8 (IP8), one of the four points along the LHC circumference where protons collide; from 1989 to 2000, IP8 was the location of the DELPHI experiment. 3.1 Large Hadron Collider The particle accelerator LHC [25] is situated inside a 26.7 km circumference tunnel (built from 1983 to 1988 and formerly used for LEP - Large Electron Positron collider) at a depth of about 100 m underground, between Switzerland and France, near the city of Geneva. It s the most powerful particle accelerator ever built, operating at a centre of mass energy of 7 TeV from 2010 to 2011, 8 TeV during 2012 and 13 TeV from 2015, when the machine will be restarted after an almost two years period of stop (Long Shutdown 1). The accelerator complex at CERN, shown in Figure 3.1, made by 4 smaller accelerators, injects the proton flux into the LHC pipes after a stepwise preliminary acceleration up to 450 GeV. LHC is composed of two rings (beam pipes) where the proton bunches travel in opposite directions in ultra-high vacuum. The acceleration is given by a system of superconducting magnets placed alongside the rings, with an operating temperature of C (1.9 K). The protons are then forced to collide in four points (IP1 - ATLAS, IP2 - ALICE, IP5 - CMS, IP8 - LHCb) with a crossing rate of 40 MHz, that is 25 ns between two consecutive collisions. 17

19 The nominal peak luminosity is L = cm 2 s 1 ; the LHCb experiment was designed to work at about 1/50 of such luminosity, to avoid misreconstruction of secondary vertices, even if during operation this experiment has proved to be able to run at luminosity as high as cm 2 s 1. Figure 3.1: The CERN accelerator complex 3.2 LHCb detector The LHCb detector is a single-arm spectrometer with an angular acceptance from 10 mrad to 300 mrad in the bending plane and to 250 mrad in the non-bending plane [26, 27]. Its geometry is very different from the barrel plus endcaps design which characterizes the other large detectors at CERN, and it is due to the fact that at high energy the b-hadrons (and b-hadrons) are produced mainly in the forward region. In Figure 3.2 the distribution of the polar angles of b- and b-hadrons is shown: they are mainly produced at very small angles with respect to the beam direction and in the same hemisphere. The LHCb detector is composed by several subdetectors: from the nearest with respect to the interaction point (vertex locator) to the furthest (muon detector). Each subdetector has a unique design and is optimized to measure 18

20 a different physical quantity. In Figure 3.3 the geometry of the detector and the position of each subdetector are shown. b θ 1 θ 2 z b LHCb MC s = 7 TeV 0 π/4 [rad] θ 2 π/2 3π/4 π/4 π/2 3π/4 π π θ 1 [rad] 0 Figure 3.2: Polar angles of the b- and b-hadrons calculated with PYTHIA Figure 3.3: LHCb detector, lateral view (non-bending plane) 19

21 3.2.1 Vertex Locator (VELO) The first subdetector, starting from the interaction point, is the Vertex Locator (VELO) [28]. Displaced secondary vertices are a distinctive feature of b-hadron decays, and a precise measurement of track coordinates close to the interaction point is a fundamental requirement for the LHCb experiment. The VELO system consists in 25 silicon stations placed along the beam direction, each one composed by one left module and one right module. Each module is composed by two measuring sensors: a radial one (R sensor) and an angular one (Φ sensor). The azimuthal coverage is about 182 for each sensor, giving a small overlap between the right and left modules in order to simplify the relative alignment and guarantee a full azimuthal acceptance. The VELO system configuration and a schematic view of the sensors are shown in Figure 3.4. The VELO system is able to measure tracks in the full LHCb angular acceptance; in addition to that, the backwards hemisphere is also partly covered (in order to enhance the resolution on the primary vertex) and the two most upstream modules are used as a pile-up veto counter for the L0 trigger. The errors on the primary vertex arises mainly from the number of tracks produced in a pp-collision. For an average event, the resolution in the z-direction is 42 µm and 10 µm perpendicular to the beam. The resolution on the decay length ranges from 220 µm to 370 µm, depending on the decay channel. Figure 3.4: VELO system configuration and VELO sensors Ring-Imaging Cherenkov Detectors (RICH) Hadron identification in LHCb is achieved with a high performance Ring-Imaging Cherenkov system, composed by two detectors aiming at different momentum ranges [29]. RICH1, located upstream of the magnet, identifies low momentum particles (from 1 GeV/c up to about 60 GeV/c) combining silica aerogel and C 4 F 10 gas radiators with a polar angle acceptance 20

22 from 25 to 300 mrad. RICH2, located downstream of the magnet and the tracking stations, has a more limited angular acceptance (from 15 to 120 mrad in the horizontal plane and from 15 to 100 mrad in the vertical plane); it covers the high momentum range, from about 15 GeV/c up to about 100 GeV/c, using a CF 4 radiator. Both RICH1 and RICH2 layouts are shown in Figure 3.5. Cherenkov light is focused onto the photon detector planes using tilted spherical mirrors and secondary plane mirrors, in order to reflect the image out of the spectrometer acceptance. The baseline photon detectors are multianode photomultiplier tubes (MaPMT). The anodes are arranged in an 8 8 array of pixels, each 2 mm 2 mm, separated by 0.3 mm gaps. (a) RICH1 (b) RICH2 Figure 3.5: RICH detectors layout Tracking System The tracking system, consisting of 4 stations (TT, T1, T2, T3) between the vertex detector and the calorimeters, provides efficient reconstruction and precise momentum measurement of charged tracks, track directions for ring reconstruction in the RICH and information for the higher level trigger [30, 31]. Each tracking station (except for TT) is composed by an Inner Tracker (IT), located in an elliptical shaped region around the beam pipe, and an Outer Tracker (OT) which covers most of the acceptance. In the region covered by the IT the particle flux is about 20 times bigger than the flux in the OT region, so IT requires a finer granularity and a different technology to handle a greater flux. The first station, the Trigger Tracker (TT) is located between RICH1 and the 21

23 magnet. Due to its reduced dimensions it contains only IT modules. The other stations are located between the magnet and RICH2. The silicon tracker system (composed by TT and IT) uses about silicon microstrips detectors with a strip pitch of 198 µm for the IT and 183 µm for the TT. To improve track reconstruction, the detectors are composed by four layers arranged in an x-u-v-x geometry, in which the strips are vertical in the first and in the last layer, whereas the other two (u,v) layers are rotated by stereo angles of ±5 C, providing the sensitivity in the vertical direction. In Figure 3.6 the IT (around the beam pipe) is shown, and in Figure 3.7 the TT is shown. The Outer Tracker is composed by an array of straw tubes modules. Each module consists of two panels and two sidewalls, which form a mechanically stable and gas-tight box, and contains up to 256 straw tubes, with an inner diameter of 4.9 mm, filled with a mixture of argon (70%) and carbon dioxide (30%) gas, which guarantees a fast drift time and a sufficient drift-coordinate resolution (200 µm). Like the silicon tracker, also OT modules are composed by four layers arranged in x-u-v-x geometry. The whole tracking system layout is shown in Figure 3.8. Figure 3.6: Inner Tracker layout 22

24 Figure 3.7: Trigger Tracker layout Figure 3.8: Tracking system layout 23

25 3.2.4 Magnet The LHCb experiment utilizes a dipole warm magnet to bend the tracks of charged particles in order to measure their momentum with a good resolution [32]. The magnet consists of two trapezoidal coils bent at 45 C on the two transverse sides and placed mirror-symmetrically. The bending power, given by the integrated magnetic field, is 4 Tm, enough to measure momenta of charged particles up to 200 GeV/c within 0.5% uncertainty. A perspective view of the LHCb magnet is given in Figure 3.9. Figure 3.9: LHCb magnet, perspective view ECAL and HCAL The LHCb calorimeter system [33] is utilized for the identification of high transverse energy hadrons, electrons and photons candidates. It measures their energy and position and selects candidates for the Level-0 trigger. The structure consists of a single-layer preshower detector (PS), made by 14 mm thick lead plates and 10 mm square scintillators, followed by an electromagnetic calorimeter (ECAL) and a hadronic calorimeter (HCAL). A scintillator pad detector (SPD) is located before the PS. The ECAL submodule is constructed from 70 layers, consisting of 2 mm thick lead plates and 4 mm thick polystyrene-based scintillator plates. The length corresponds to 25 X 0. The electromagnetic calorimeter is designed to give adequate granularity and energy resolution for π 0 reconstruction: for P t < 2 GeV/c neutral pions are mainly reconstructed combining two separate clusters in the ECAL (resolved π 0 ), while for greater transverse momenta the two photons form a single cluster (merged π 0 ). The resolved π 0 efficiency (defined as the number of resolved neutral pions identified in a mass window of ±30 MeV/c 2 over the number of resolved and merged π 0 in acceptance) for the channel B 0 π + π π 0 is found to be between 40-48% for P t < 2 GeV/c 24

26 and drops linearly for greater transverse momenta, reaching 5% for P t = 6 GeV/c, as can be observed in Figure 3.11 [34]. The HCAL consists of 16 mm thin iron plates inter spaced with 4 mm thick scintillating tiles arranged parallel to the beam pipe. The length corresponds to 5.6 λ I. Figure 3.10 shows the segmentation of the sections of both ECAL and HCAL. Figure 3.10: Calorimeters segmentation: ECAL on the left, HCAL on the right. Figure 3.11: Resolved π 0 reconstruction efficiency for the channel B 0 π + π π 0 25

27 3.2.6 Muon system The muon system for the LHCb experiment [35] consists of five tracking stations placed along the beam axis, the first (M1) in front of the calorimeters and the other four, inter spaced with three iron filters, downstream the calorimeters. The configuration of the stations is shown in Figure The muon stations are equipped with Multi Wire Proportional Chambers (MWPCs) except for the inner region of M1, equipped with Gas Electron Multiplier (GEM) chambers, more appropriate for the greater particle flux. The efficiency for each chamber is required to be high enough to achieve a 95% trigger efficiency on the trigger algorithm, which requires a quintuple coincidence in a time window smaller than 25 ns. The inner and outer angular acceptances of the muon system are 20 (16) mrad and 306 (258) mrad in the bending (non-bending) plane, similar to that of the tracking system. This provides a geometrical acceptance of about 20% for muons from b decays relative to the full solid angle. Each station is subdivided in four regions with dimensions and logical pad size which scales a factor of two from one region to the next one. Since the muons energy decreases with the distance from the beam axis, the multiple scattering effect in the absorber increases in the same direction, limiting the spatial resolution of the detector, therefore the granularity of the detector varies accordingly. Figure 3.12: Muon system configuration 26

28 3.2.7 Trigger The LHCb experiment was designed to operate at a nominal average luminosity of cm 2 s 1, about 1/50 of the nominal peak luminosity of LHC: this implies a smaller number of interaction per bunch crossing and a better vertex reconstruction, a fundamental requirement for B-physics. The rate of useful p-p interaction is 10 MHz, and needs to be reduced at about 2 khz in order to be stored and analysed offline: in order to achieve that, two trigger selections are used [36]. The Level-0 trigger (L0) is embedded in the electronics and reduces the event rate at 1 MHz combining informations from VELO, ECAL, HCAL, PS, SPD and the muon system. The High Level Trigger (HLT) is software-based and reduces the event rate at 2 khz, with full event reconstruction based on particle identification, tracks measurement, vertex reconstruction and impact parameter measurement. 3.3 Analysis tools Stripping and reconstruction Data selected by the trigger (both L0 and HLT) are stored and analysed offline by a first set of algorithms to provide a pre-categorization of candidates according to each specific analysis need. This procedure combines all informations from all subdetectors, identifies particles and associates them with tracks, vertices (built from the crossing point of two or more tracks) and energy deposits. At this stage, events are flagged according to the category they belong to, checking the presence of particular features: for example, the DiMuon stream includes all the events with at least a couple of high transverse momentum muons, with opposite charges. This procedure is called Stripping. Each of these streams contains several StrippingLines, a loose selection (with standard requirements) of typical decays, which allows to search for a particular decay channel in a subset of the whole data. An example: it s pointless to search for the decay B + K + ω(j/ψ µ + µ ) in events that don t contain at least a couple of muons with opposite charge, from the same vertex and with an invariant mass not very far from the J/ψ nominal mass. A standard set of minimal cuts is therefore defined for each StrippingLine. All the LHCb software operates within the Gaudi framework [37]. The group of C++ LHCb libraries used to reconstruct tracks, to apply calibrations and finally provide well identified and momentum measured particles is called Brunel [38]. The software tool used to reconstruct the relevant physical processes, i.e. typically full b or c decay chains, is called DaVinci [39]. DaVinci is also used for the complete event reconstruction and the selection peculiar to the specific analysis under development. 27

29 3.3.2 Monte Carlo simulations Simulated datasets can be generated with the Monte Carlo (MC) method to extract certain parameters useful for the analysis, to have a prior knowledge of the trend of interesting physical quantities and to train the tools that are later used on data. MC data can be obtained with the simulation application Gauss [40]. It generates a physical process of interest through the PYTHIA [41] generator package, which takes into account the physics inherent the p-p interaction and all the known theoretical models in order to simulate correctly the collision, the hadronization process and the consequent B decays of interest. The detector response is then simulated with the Geant4 [42] package, taking into account a detailed description of the detector geometry and the response of each subdetector. 28

30 Chapter 4 Data Analysis In this chapter detailed descriptions of the B + K + ωj/ψ decay channel reconstruction and selection are shown. The analysis strategy consists of the following sequential processing steps, taking as input data selected by the DiMuonJpsi2MuMuDetached stripping line, described in detail in Section 4.2.1: First of all, a reconstruction of the decay chain is performed, combining all reconstructed particles in order to list all the possible signal candidates for each event with specific requirements. Cuts in this phase are very loose. This first step is required to extract all the possible candidates of interest in the whole stripped dataset, and it is described in Section Once the events are reconstructed, a preselection is performed in order to remove a large fraction of obvious sources of background, according to LHCb fiducial cuts, which are known to be highly efficient on signal events and assure a significant background suppression. The preselection phase is described in Section The preselected events are then processed through Multivariate Analysis algorithms (MVA), which optimally combine signal-background discriminating information and allow to perform a final selection in order to enhance the signal to background ratio. This process is described in Section 4.4. The obtained B + K + (J/ψ µ + µ )(ω π + π π 0 ) mass spectrum is now analyzed. In order to eliminate the residual background, it is fitted with a Probability Density Function (PDF) that takes into account the signal and the background contribution, in order to obtain the functional form for each component. With these as input, the splot technique is applied: it consists of a statistical background subtraction through computation of proper weights. In this way, signal and background 29

31 distributions for J/ψω mass, which is the variable of interest for this analysis, are obtained separately. The B + mass fit and the application of the splot technique are described, respectively, in Section and Section 4.5. To correct the obtained J/ψω mass spectrum for the effect of the analysis cuts, a Monte Carlo sample is generated and analysed with the same set of cuts as real data. From this sample, the efficiency curve as a function of M(J/ψω) is obtained and applied to real data. The same MC sample is also used to train the aforementioned MVA. The efficiency correction computation is detailed in Section Data samples In this analysis the full data sample is used, corresponding to an integrated luminosity of about 1 fb 1 (2011) + 2 fb 1 (2012) of p-p collision data, recorded with the LHCb detector at a centre of mass energy of 7 TeV for 2011 data and 8 TeV for 2012 data. A fully simulated Monte Carlo data sample is produced, consisting of 2 million events for the 2011 data taking conditions and 4 million events for the 2012 data taking conditions. A Phase Space (PHSP) model is applied to the simulation, in order to obtain a uniform phase space coverage for the efficiencies study. The complete decay chain is: B + K + (J/ψ µ + µ )(ω π + π (π 0 γγ)) (4.1) and the complex conjugate. Detailed informations about the MC dataset will be given in section Event selection Stripping cuts The StrippingLine used is the so called StrippingFullDSTDiMuonJpsi2MuMu DetachedLine, which attempts to select J/ψ µ + µ candidates, coming from a B decay and thus forming a vertex detached from the primary vertex, combining two muon tracks with opposite charge and moderate transverse momentum. Some standard cuts are applied. First of all, in order to obtain a good muon track, a cut on the track χ 2 /N dof is applied, where N dof is the number of degree of freedom of the track fit. The particle identification algorithm must assert that the selected track is indeed associated to a muon: this implies a cut on the difference of the logarithm of the likelihood fit of the muon hypothesis 30

32 with respect to the pion hypothesis (Delta Log-Likelihood, DLL µ π ). The two muon tracks need to originate from the same vertex, and this is obtained with a cut on the J/ψ Decay Vertex (DV) χ 2 /N dof. Since the B + travels for a measurable distance before decaying, the J/ψ is required to be detached from the Primary Vertex (PV): a cut on the Decay Lenght Significance (DLS) is applied, which is defined as the distance between the reconstructed µ + µ vertex and the PV, divided by its error. When multiple PVs are present in a single p-p collision, only the best PV (in terms of reconstruction quality) is considered for this computation. Finally, it is required to the invariant mass of the two muons not to be outside a 200 MeV/c 2 mass window centred at the J/ψ nominal mass (from the Particle Data Group [43]). A summary of the stripping cuts is provided in Tab 4.1. Candidate Variable Cut Pt >550 MeV/c µ DLL µπ >0.0 Track χ 2 /N dof <5.0 DV χ 2 /N dof <20 J/ψ DLS >3.0 M(µµ) [ , ] MeV/c 2 Table 4.1: Stripping line selection cuts Decay reconstruction Each J/ψ candidate in the stripped dataset is combined with two pions with opposite charge, a neutral pion and a charged kaon. Reconstructed pions (both charged and neutrals), kaons and muons are extracted from the LHCb StandardParticles repository: it contains particle candidates reconstructed with standard loose cuts. The standard algorithms used in the reconstruction are, in particular, StdLoosePions, StdLooseKaons, StdLooseMuons, StdLooseResolvedPi0: In StdLoosePions, StdLooseKaons and StdLooseMuons a cut on the transverse momentum of reconstructed particle is applied (P t > 200 MeV/c), along with a cut on the χ 2 of the fit on the charged track Impact Parameter (IP) in order to remove a significant fraction of background composed by prompt particles (χ 2 (IP ) > 4.0). Notice that the stripping cut on muons P t is higher. 31

33 In StdLooseResolvedPi0 a photon pair with P t (γ) > 200 MeV/c and M(γγ) [85, 185] MeV/c 2 is combined to form a π 0. Each photon pair is required to be resolved, i.e. to form two separated clusters in ECAL (the distance between two impact points must be greater than one cell size). An additional cut is imposed on the track fit χ 2 of pions to improve their reconstruction. They are then combined to reconstruct an ω: a cut on their invariant mass is applied (M(π + π π 0 ) [390, 1000] MeV/c 2 ) along with a cut on the χ 2 of the vertex fit. The mass window is large enough to include also the decay B + J/ψK + (η π + π π 0 ). The stripping selection of J/ψ candidates is improved with a tighter cut on the mass (it s also asymmetric, to account for the radiative tail) and a cut on the transverse momentum. To reconstruct a B + candidate, J/ψ, ω and K + candidates are combined, requiring to have an invariant mass in a 1000 MeV/c 2 window centred in the B + nominal mass and to form a vertex with a good χ 2. In addition to J/ψ detachment and K-π non-zero IP requirements, a further restriction is directly applied on each B + : candidates with measured lifetime less than 0.20 ps are discarded, in order to reduce the large combinatorial background from particles produced in primary p-p interactions. Finally, a cut on B + transverse momentum is applied. A summary of the reconstruction cuts is provided in Tab 4.2. During this phase, the J/ψ mass is constrained to its nominal value for the events that pass the reconstruction cuts: since the J/ψ decaying in two muons has a very low misidentification rate, its width can be removed, thus improving the B + mass resolution. 32

34 Candidate Variable Cut B + J/ψ ω Pt > 1.5 GeV/c DV χ 2 /N dof < 15.0 τ > 0.20 ps M(KωJ/ψ) M B MB P DG < 500 MeV/c 2 P t > 1.5 GeV/c 2 DV χ 2 /N dof < 20 M(µµ) [3040, 3140] MeV/c 2 P t > 1.0 GeV/c 2 DV χ 2 /N dof < 20 M(π + π π 0 ) [390, 1000] MeV/c 2 π ± IP χ 2 /N dof > 4.0 P t > 200 MeV/c 2 Track χ 2 /N dof < 4.0 K + P t > 200 MeV/c 2 IP χ 2 /N dof > 4.0 π 0 P t > 200 MeV/c 2 M(γγ) [85, 185] MeV/c 2 γ P t > 200 MeV/c 2 Table 4.2: Reconstruction cuts. The last 4 rows include the StandardParticles cuts Preselection cuts After the reconstruction algorithm, a cut based selection is performed in order to obtain a significant background rejection retaining a large fraction of signal. The cuts are LHCb fiducial cuts, known to be highly efficient on signal events, and they are reported in Table 3.3. In most cases they are simply a hardening of the reconstruction cuts, but other variables are also considered. 33

35 Candidate Variable Cut B + DV χ 2 /N dof < 9.0 Pt > 2.0 GeV/c J/ψ ω µ ± π ± K + τ P t > 0.25 ps > 2.0 GeV/c DV χ 2 /N dof < 20 M(µµ) [3040, 3140] MeV/c 2 P t > 2.0 GeV/c DV χ 2 /N dof < 10 M(π + π π 0 ) [390, 1000] MeV/c 2 P t > 1.0 GeV/c IP χ 2 /N dof > 9.0 Track χ 2 /N dof < 4.0 DLL µπ > 0.0 P t > 200 MeV/c IP χ 2 /N dof > 9.0 Track χ 2 /N dof < 4.0 DLL Kπ < 0.0 P t > 200 MeV/c IP χ 2 /N dof > 9.0 Track χ 2 /N dof < 4.0 DLL Kπ > 0.0 π 0 M(π 0 ) [85, 185] MeV/c 2 P t > 200 MeV/c CL > 0.01 All tracks Track Ghost Prob. < 0.4 Table 4.3: Preselection cuts DDL Kπ is the Delta Log-Likelihood of the kaon hypothesis with respect to the pion hypothesis: it s a variable provided by the LHCb identification system, it s positive for a well reconstructed pion and negative for a well reconstructed 34

36 kaon, and a proper cut reduces the probability of K π misidentification. A ghost track is defined as a pseudo-random combination of hits, and it s characterized by having a low probability of χ 2 from the track fit and missing hits. A ghost track therefore is not associated to any real track and it s merely a result of hit combination mistakes. A specialized algorithm determines a probability for each track to be a ghost. The Confidence Level (CL) cut assures a good quality particle ID of the photons. The variable ranges from 0 to 1 and is computed from information about the cluster size, the shower shape and the energy deposit. CL on π 0 is the product of the two photons CLs. The cut on ω mass has not been touched, in order to be able to see also the η contribution. The signal efficiency of the preselection cuts set, computed from the fully reconstructed Monte Carlo dataset, is found to be 37.0%. In Figure 4.1 the (K + J/ψω) mass spectrum, after the application of the preselection cuts, is shown. A peak is visible in correspondence of the B + nominal mass: in order to enhance the signal to background ratio, i.e. to remove a significant fraction of the background maintaining a high number of signal events, the dataset will be processed through a multivariate analysis, as will be shown in Section 4.4 Figure 4.1: B mass spectrum after the application of preselection cuts 4.3 Monte Carlo sample A Monte Carlo dataset is necessary in order to obtain simulated information about different aspects of the analysis, such as signal efficiency of the selection 35

37 procedure, signal distribution for different variables and so on. The sample used in this analysis is composed by 6 million events (2 million for 2011 and 4 million for 2012 data taking conditions). As already stated in section 4.1, the decay (4.1) has been generated following the PHSP (PHase SPace) model, according to which each B + particle decays in a three body state (J/ψK + ω) without any intermediate resonance. As an example of the flat shape of the phase space model, the Dalitz plot for the J/ψω and K + ω systems invariant squared masses is shown in Figure 4.2. A generator level dataset has been used to produce this plot, thus before any analysis cut. Figure 4.2: Dalitz plot for K + ω squared mass vs J/ψω squared mass, generator level (MC) A set of acceptance and kinematic cuts is applied at generator level to produce only events that can be triggered and reconstructed by the reconstruction software, before submitting the simulated dataset to the full Geant4 detector simulation. These cuts avoid waste of computational resources to simulate tracks which do not have any chance to be reconstructed, because they are either outside the LHCb geometrical acceptance or below the minimum momentum threshold required for efficient reconstruction. In Tab. 4.4 and Tab. 4.5 a summary of the acceptance and kinematic cuts is provided: y = log [ tan( θ)] is the pseudorapidity, while θ is the polar angle. 2 The generated sample is then submitted to the same reconstruction chain as real data, and for each reconstructed event also true generated quantities 36

38 Candidate Variable Cut J/ψ y (1.8, 4.5) µ, π ±, K + θ (0.005, 0.400) rad γ P x P z < P y P z < P z > 0 MeV/c Table 4.4: Acceptance cuts at generator level Candidate Variable Cut J/ψ P t > 1000 MeV/c π ±, K + P t > 150 MeV/c µ P t P > 500 MeV/c > 6000 MeV/c γ P t > 150 MeV/c B + τ > ns Table 4.5: Kinematic cuts at generator level are available for efficiency studies. Like in real data, also in the MC dataset the J/ψ mass is constrained to its nominal value during the reconstruction procedure. The following plots are generated from the MC sample after the reconstruction and preselection cuts. In Figure 4.3 the B + mass spectrum in shown, in black: an asymmetric tail is visible on the right side of the spectrum. This can be partly explained by the tail for high masses on the π 0 mass distribution that can be observed in Figure 4.4, while the correlation plot is shown in Figure 4.5. The tail on π 0 mass distribution is due to the highly energetic neutral pions decaying in two photons with a very small angle, which may release part of their energy in the same calorimeter cells. The high mass tail is an indication that the correction to take into account this superposition is not 37

39 properly done. This is a known problem and a new set of algorithms and variables are being developed to overcome it. Note that this behaviour in the π 0 mass distribution is observable in real data, as will be seen in Figure In order to reduce this effect, a new variable for the B + mass is defined as follows: M(B + ) π 0 fixed = M(B + ) M(π 0 ) + M P DG (π 0 ) (4.2) where M(π 0 ) P DG is the nominal π 0 mass taken from PDG. The B + mass distribution after the neutral pion mass fixing is shown, in red, in Figure 4.3, where the distribution looks narrower and more symmetric. By fitting the B + mass spectrum with a Gaussian function, it can be measured that the width of the B + mass peak improves from σ MC = 31.4 MeV/c 2 to σ MC = 23.5 MeV/c 2 when the fixing procedure in applied. In Figure 4.6 the three pions invariant mass spectrum is shown, and, as expected, the same tail on the right side of the distribution can be observed. Figure 4.7 shows the Dalitz plot for (K + ω) invariant squared mass vs (J/ψω) invariant squared mass. Since all these plots are generated from a simulated dataset that has been submitted to the reconstruction and preselection chain, as described in Sections and 4.2.3, the typical flat shape of the phase space model, see Figure 4.2, cannot be observed any more. Figure 4.3: B + mass spectrum (MC), before and after fixing the π 0 mass 38

40 Figure 4.4: π 0 mass spectrum (MC) Figure 4.5: B + mass vs π 0 mass (MC) 39

41 Figure 4.6: ω mass (MC) Figure 4.7: Dalitz plot for K + ω squared mass vs J/ψω squared mass, after the reconstruction and preselection phases (MC) 40

42 4.4 Multivariate analysis After the reconstruction and the cut based selection, the dataset is ready to be processed through multivariate classification methods: they are algorithms which combine information from a set of input variables in order to separate the signal from the background components. These techniques need to be trained on samples of signal events and background events. For the signal, MC events are used, while for the background real data in B + mass sidebands ( M M P DG B > ±150 MeV/c 2 ) are taken. This preliminary training phase + determines the mapping function that will later classify events in real data. The classification is based on an output variable, computed for each event, in which signal and background distributions must be well separated. The chosen method is the Projective Likelihood Estimator (PLE): the method of maximum likelihood consists of building a model out of probability density functions (PDF) that reproduces the input discriminating variables for signal and background. For each event, the likelihood for being of signal type is computed as a product of all signal PDFs evaluated at the measured variable value, and conveniently normalized. Since a factorization of PDFs will take place, this method is only valid with the assumption of uncorrelated (or loosely correlated) variables. For an event i, a Likelihood ratio r L (i) is defined as: r L (i) = L S (i) L S (i) + L B (i) (4.3) where: L S (i) = L B (i) = N var k=1 N var k=1 p k S(x k (i)) (4.4) p k B(x k (i)) (4.5) where p k S and pk B are the signal and background PDFs for the kth input variable x k, and N var is the number of input variables. Each PDF is normalized as: p k S,B(x k )dx k = 1 (4.6) for k [1, N var ]. Since the analytic form of the PDFs is generally unknown, this method empirically approximates the PDF shapes from the training data, building a model for each variable as a result of an interpolation of polynomial spline functions of second degree to the signal and background distribution histograms. Then, for each event, r L (i) is computed at the measured variable value. 41

43 It can be shown that in absence of model inaccuracies, i.e. if the input variables present no correlations and the PDFs are built correctly from the interpolations, the Likelihood ratio provides the best signal from background separation. This, along with the computational speed of both the training and the application phases, are the reasons of the choice of this method. The selection is accomplished using the Toolkit for Multivariate Data Analysis (TMVA) [44], provided by the ROOT framework [45] Input variables and training phase The choice of the input variables for a multivariate analysis must be dictated by two main conditions: it is compulsory to find a set of uncorrelated variables (the more they are correlated, the worse the performances will be) which can guarantee a good discrimination between signal and background distributions. The variables chosen for this analysis are the following (all the logarithms are taken to smooth the distributions): log(min P V [χ 2 IP (B+ )]): the logarithm of the minimum reduced χ 2 of the B + Impact Parameter with respect to all Primary Vertices in an event. A signal B + is expected to come from a PV, and so the IP (i.e. the perpendicular distance between the B + reconstructed momentum vector and the PV) should be close to zero, with a good χ 2. The signal distribution for this variable presents indeed a peak at zero, far below the background distribution peak. log(min P V [χ 2 IP (K+ ), χ 2 IP (π+ ), χ 2 IP (π )]): the logarithm of the minimum IP reduced χ 2 with respect to all PVs and with respect to all charged hadrons in the final state. Since K and π must come from a detached vertex, their IP χ 2 is peaked at a far greater value than zero, while the background is composed mainly of prompt particles with low IP χ 2. min[cos(θ xy J/ψ,K ), cos(θxy J/ψ,π + ), cos(θ xy J/ψ,π )]: the minimum of the cosine of the angle between the J/ψ momentum and the momentum of one of the hadrons in the final state, in the transverse (xy) plane. Particles decaying from a B are supposed to have a smaller angle between their transverse momenta with respect to prompt particles, since the latter lack of a transverse component from the pp interaction. Vertex χ 2 /N dof (B + ): the reduced χ 2 of the decay vertex fit of the B +. This variable has a signal peak at 1, corresponding to good reconstructed vertices from the charged tracks of muons, pions and the kaon. P t (π 0 ): the π 0 transverse momentum. Background π 0 s are characterized by low P t, while signal ones present a peak at over 1 GeV/c and a longer distribution tail towards high transverse momenta. 42

44 Figure 4.8 shows all the input variables for signal and background distributions. In Figure 4.9 the correlation matrices for signal and background events are shown: they are negligible for the signal sample and minor for the background sample, so that the uncorrelated variables hypothesis can reasonably be considered satisfied. The variables are nevertheless linearly decorrelated before the beginning of the training, diagonalizing the correlation matrix and creating another set of variable with no real physical meaning, but with the same per event method response. The performance of the MVA, computed on a MC sample independent with respect to the one used for the training phase, is represented, in Figure 4.10, by the Receiver Operating Characteristic (ROC) curve, where the background rejection (1 - background efficiency) is plotted as a function of signal efficiency, for three different MVA methods (Fisher discriminants, Boosted Decision Tree and Likelihood). Since the performance are very similar, the Likelihood method was chosen because, as already stated, it can be shown that, in the hypothesis of uncorrelated variables, this method provides optimal signal to background separation. In Figure 4.11 the Likelihood Ratio distribution for both signal and background is shown. Figure 4.8: distributions Input variables, with signal and background 43

45 (a) Signal sample (b) Background sample Figure 4.9: Correlation matrices for signal and background samples Figure 4.10: MVA methods performance (ROC curve) 44

46 Figure 4.11: PLE method response B + mass fit As an example of how MVA works, in Figure 4.12 the B + mass spectrum is shown, corresponding to a cut on r L > 0.65, which is one of the cuts that will be used later in the analysis. The comparison of this figure with Figure 4.1 shows the remarkable discriminating power of this technique: the two distributions are directly compared in Figure In principle the cut value for r L could be determined by choosing a point on the ROC curve of Figure 4.10; however, since real data may not be well reproduced by MC events, we prefer to choose the optimal cut value by estimating the number of signal and background events entirely on real data. This is achieved by fitting the B + mass distribution, in order to extract the number of signal and background events as a function of the cut on r L. The unbinned, extended likelihood fit is performed with the RooFit Toolkit for Data Modeling [46]. The total PDF of the fit was firstly chosen to be a sum of a double gaussian for the signal and an exponential function for the combinatorial background. The result is shown in Figure As clearly visible, the fit does not describe well the B + mass peak as it seems that a component at around 5350 MeV/c 2 (about 70 MeV/c 2 higher than the B + nominal mass) prevents the fit from following closely the B mass lineshape. Different hypothesis have been tested to explain this excess of events, listed and described in section 4.8, without reaching any definitive conclusion. It was decided to include it in the fit, to interpret it as a background component and to describe it with another gaussian function. 45

47 Figure 4.12: B + mass spectrum, after the cut on r L Figure 4.13: B + mass spectrum, before and after the cut on r L The total PDF, therefore, is defined as: p T OT (x) = C 0 [N sig p sig (x) + N bkg p bkg (x)] = C 0 [N sig (C S 1 G S 1 (x) + C S 2 G S 2 (x)) + N bkg (C B 1 G B (x) + C B 2 E B (x))] (4.7) where: G S i (x) = G B (x) = σ S i 1 e (x M ) B+ 2π 2 2(σ S i )2 (4.8) (x M 1 bump ) 2 σ B 2π e 2(σ B ) 2 (4.9) E B (x) = e τx (4.10) 46

48 where σ S,B i are the widths of the gaussians, M B + is the mean value of both the signal gaussians which has been fixed to the B + nominal mass, M bump is the mean value of the background excess at arount 5350 MeV/c 2, τ is the slope of the exponential function, C S,B 1, C S,B 2 are the relative yields of the signal or background components, C 0 is a suitable normalization constant and N sig and N bkg are the signal and background yields for the whole fit. In Figure 4.15 the fit using the total PDF (4.7) is shown. Adding the bump contribution to the PDF improves the width of the peak (defined as the symmetric interval around the B + nominal mass which contains 95.5% of the signal) from 26.3 MeV/c 2 to 23.2 MeV/c 2 and the reduced χ 2 from 1.25 to Notice that, as told in section 4.3, the B width from MC is σ MC = 23.5 MeV/c 2. Figure 4.14: B + mass fit, without the bump contribution, for r L > 0.65 Figure 4.15: B + mass fit, with the bump contribution, for r L >

49 4.4.3 Application phase of MVA The optimal cut on r L is chosen through the observation of the signal efficiency and background rejection distributions as a function of r L. These are obtained from the estimated number of signal and background events as follows: ɛ sig = N sig(r L > r cut L ) N sig(r L > 0) (4.11) R bkg = 1 ɛ bkg = 1 N bkg(r L > r cut L ) N bkg(r L > 0) (4.12) Where N sig and N bkg are the numbers of signal and background events in a symmetric interval which contains 95.5% of the signal PDF integral centred in the B + nominal mass, in a subset of the events given by the condition r L > rl cut. The condition r L > 0 means that no cuts on r L have been applied, since the range of this variable goes from 0 to 1. Therefore, to compute ɛ sig and R bkg as in (4.11) and (4.12), the following relations between N sig,bkg and N sig,bkg have been used: N sig = N sig N bkg = N bkg MB + +ρ M B + ρ MB + +ρ M B + ρ p sig (x)dx (4.13) p bkg (x)dx (4.14) where the interval [M B + ρ, M B + + ρ], which can be computed numerically, is such that: MB + +ρ p sig (x)dx = (4.15) M B + ρ Equations (4.13), (4.14) and (4.15) rely on the fact that p sig and p bkg are normalized to 1 in the whole mass range. In Figure 4.16 the plots for the signal efficiency (magenta histogram) and the background rejection (blue histogram) are shown, along with the statistical significance distribution (black histogram), defined as: S(r cut L ) = N sig(r L > r cut L N sig(r L > r cut L ) ) + N bkg(r L > rl cut) (4.16) The green dotted line indicates the point of maximum statistical significance, found at MVA_LL = rl cut = 0.9. The significance is referred here to the B+ signal peak, but we are interested in a presumably small subset of such signal containing the intermediate X(3872) resonance. Therefore, since the number of signal candidates is very low here, a decision was made to go on with the analysis by trying two looser alternative selection criteria: 48

50 Apply a relatively hard cut on the MVA, rl cut = 0.65, with a signal efficiency of 60% and a background rejection of 86% (red line on the right, Figure 4.16). Apply a looser cut, r cut L = 0.15, with a signal efficiency of 73% and a background rejection of 68% (red line on the left, Figure 4.16). In order to recover background rejection, an additional cut, around the ω mass, is applied on the three pions invariant mass, M(ω) [700, 850] MeV/c 2. Notice that, being X(3872) J/ψω a subthreshold decay, only an ω with low mass contributes. Figure 4.16: Statistical significance (blue), signal efficiency (magenta) and background rejection (black) as a function of (left axis for the significance and right axis for the rest) r cut L As can be clearly seen, the signal and significance distributions in Figure 4.16 present structures which, even if not significant within errors, indicate some systematic effect in the evaluation of the signal and the background components. These fluctuations are due to the fact that, for different cut values of the Likelihood ratio rl cut, the mean and the width of the gaussian component of the total PDF describing the excess at 5350 MeV/c 2 vary in an irregular way. This means that, according to the model we used for the fits, the number of events belonging to the excess contribution found within the interval (4.15) can be significantly different between one fit and another. For example, for MVA_LL > 0.08, i.e. the third bin in Figure 4.16, 240 events due to the excess contribution are found within the signal interval, while in the next step, for MVA_LL > 0.12, this number decreases to 80. This reduction implies an increase of signal events, observable in the signal 49

51 efficiency distribution, and therefore an increase of the significance. In Figure 4.17, the two aforementioned fits are shown, where the different gaussian contribution of the bump in the signal interval is clearly visible. The vertical red lines are the lower and upper limit of the signal interval centred in the B + nominal mass. The effect of this behaviour could, however, be taken into account when evaluating the systematic error. (a) B + mass fit, MVA_LL > 0.08 (b) B + mass fit, MVA_LL > 0.12 Figure 4.17: B + mass fit for two different values of cut on r L, where the different bump contribution within the signal interval is clearly visible 50

52 In Figure 4.18 the fit on B + mass is shown, along with the single components of the total PDF, for both the selection criteria. Figure 4.18: Fit on B + mass for both the selection criteria, with fit results 4.5 Background subtraction: splot technique The splot technique [47] is a statistical tool dedicated to the analysis of a data sample consisting in several sources of events, that are only signal and background events for the purpose of this analysis, merged into a single sample. Combining information from a set of variables for which the distributions for signal and background events are known (discriminating variables), this technique allows to compute, for each event, a particular weight corresponding to the likeliness that the event belongs to each of the sources. By weighting the events with these, so called, sweights, one can obtain the spectra of another set of variables, called control variables, for signal and background components separately. For this analysis, we use the B + mass spectrum as the only discriminating variable. See Appendix A for a more detailed description of the splot formalism. 51

53 4.5.1 Application of splot technique Giving as input to the splot technique the B + mass fit models shown in Figure 4.18, it is possible to plot any desired control variable distribution (in our case, J/ψω mass, π 0 mass, ω mass and so on) of the signal or the background by weighting each event with the corresponding weight, W sig or W bkg, respectively. All the variables are considered after the MVA based selection, as explained in section The computation of the sweights is performed with the RooStats framework for advanced statistical analysis [48], built on the RooFit toolkit. Figure 4.19: ω invariant mass distribution after the r L cut Figure 4.20: ω invariant mass signal distribution (background subtracted) 52

54 In Figure 4.19 the ω mass distribution after the MVA selection only is shown, for MVA_LL > 0.65, while in Figure 4.20 the background subtracted distribution of the same variable is shown. The η and ω peaks are clearly visible, respectively, at 547 MeV/c 2 and 782 MeV/c 2. Let s note that, by performing a simple fit on the π + π π 0 mass spectrum, including two gaussian functions for the two peaks and an exponential for the background, we estimate: N η = 43 ± 7 (4.17) N ω = 969 ± 35 (4.18) with which we can derive the product branching fraction ratio: BR(B + K + J/ψη) BR(η π + π π 0 ) BR(B + K + J/ψω) BR(ω π + π π 0 ) N η N ω = ± (4.19) which is consistent with the PDG value: BR(B + K + J/ψη) BR(η π + π π 0 ) BR(B + K + J/ψω) BR(ω π + π π 0 ) = (4.20) Of course this estimate implies the efficiency to be constant in the whole spectrum, which for sure is not a justifiable assumption. In Figure 4.21 the π 0 mass signal distribution is shown, for MVA_LL > Figure 4.21: π 0 mass signal distribution (background subtracted) The asymmetry can be partly due to the imperfect model with which the B mass is fitted, since it can influence the computation of sweights. Furthermore, as already told in Section 4.3 and observed in MC data, see Figure 4.4, the π 0 mass distribution exhibits a tail for high masses due to the imperfect treatment of superposition of clusters of the two photons in the calorimeter. 53

55 4.6 J/ψω mass spectrum In Figure 4.22 and Figure 4.23 the (J/ψω) invariant mass signal distribution is shown, for both MVA selections. The red histogram is the Monte Carlo phase space distribution after the application of the same reconstruction, preselection and MVA cuts as real data, and it is normalized to the integral of the data in the whole J/ψω mass spectrum. The Monte Carlo distribution does not describe well the data, since a huge excess of events is present at about 4600 MeV/c 2. Notice that a similar behaviour was already observed by BaBar[16]. To investigate the reasons behind this excess, a search for intermediate resonances contributions has been performed, as can be seen in the next section. Figure 4.22: J/ψω mass, MVA_LL > 0.65 Figure 4.23: J/ψω mass, MVA_LL > M(ω) cut 54

56 4.7 Resonances contribution Given the discrepancy between the data distribution and the phase space Monte Carlo in the J/ψω invariant mass distribution, a possible contribution due to intermediate resonances was searched for. The presence of resonant states in the decay can indeed reflect into peaking structures also in the J/ψω mass spectrum. The most obvious resonances, Ψ(2S) and K (892), can be observed clearly in the dataset before background subtraction, as shown in Figure Figure 4.24: J/ψππ and Kπ invariant mass, MVA_LL > 0.65 Figure 4.25: J/ψππ and Kπ invariant mass (background subtracted), MVA_LL > 0.65 In Figure 4.25 the same distributions, after the background subtraction, are shown. The Ψ(2S) and K (892) peaks are not completely removed but the number of events cannot justify the excess observed in the J/ψω mass spectrum. Nevertheless, a cut is applied on both J/ψππ and Kπ invariant mass to remove the residual peaks, excluding the following ranges: 3670 < M(J/ψππ) < 3700 MeV/c 2, 880 < M(Kπ) < 910 MeV/c 2. The resulting J/ψω mass spectra are shown in Figure 4.26 and

57 Figure 4.26: J/ψω mass without Ψ(2S) and K (892) contributions, MVA_LL > 0.65 Figure 4.27: J/ψω mass without Ψ(2S) and K (892) contributions, MVA_LL > M(ω) cut An interesting structure can be observed when plotting (Kω) invariant mass versus (J/ψω) invariant mass after the background subtraction. It is shown in Figure 4.28 and Figure 4.29, emphasised by a black circle, at around M(Kω) 1400 MeV/c 2. The most probable hypothesis is that the structure comes from the decay B + K + 1 (1270)J/ψ, with K + 1 (1270) K + ω. The product of branching fractions is: BR(B + K + 1 (1270)J/ψ) BR(K + 1 (1270) Kω) (4.21) 56

58 and it is more than three times bigger than our searched signal: BR(B + X(3872)K + ) BR(X(3872) J/ψω) (4.22) and one order of magnitude smaller than B + K + J/ψω branching ratio: BR(B + K + J/ψω) (4.23) Figure 4.28: M(J/ψω) vs M(Kω), MVA_LL > 0.65 Figure 4.29: M(J/ψω) vs M(Kω), MVA_LL > M(ω) cut In order to try to reduce the K + 1 (1270) contribution, a cut on (Kω) invariant mass M(Kω) > 1700 MeV/c 2 has been applied, corresponding to the red 57

59 horizontal line observable in Figure 4.28 and Figure The agreement between data and phase space Monte Carlo improves significantly after this cut, as shown in Figure 4.30 and Figure Notice that the same cuts on J/ψππ, Kπ and Kω invariant masses have been applied also in the Monte Carlo sample. With these cuts, an excess of events can be observed in the X(3872) region, particularly with MVA_LL > 0.15 and M(ω) cut. Figure 4.30: M(J/ψω), MVA_LL > 0.65, after cut on M(Kω) Figure 4.31: M(J/ψω), MVA_LL > M(ω) cut, after cut on M(Kω) 58

60 4.8 Hypotheses for the excess of events at 5350 MeV/c 2 Before to proceed with the analysis flow, a description is given in this section of the tests done on data to try to find and interpretation of the background component at arount 5350 MeV/c 2 in the B + mass spectrum. The first hypothesis tested assumes that the excess could be caused by a B decay with relatively high branching ratio which, due to misreconstruction or to random association with one or more particles, can be classified as signal. The channel we analysed is B + J/ψK + π + π, with a branching fraction which is about 2.5 times bigger than BR(B + K + J/ψω). If this was the origin of the excess, the underlying hypothesis would be that a random π 0, wrongly associated with the B + vertex, could produce an accumulation of events in the excess region. In Figure 4.32 the B + mass spectrum versus the J/ψKππ invariant mass spectrum is shown. The B + J/ψKππ peak is clearly visible in the latter spectrum, but the contribution of this decay channel to our spectrum is clearly located at high B + masses, i.e. for M(B + ) J/ψKω > 5450 MeV/c 2. Nonetheless, this contribution has been removed before performing the fit on the B + mass distribution described in Section Figure 4.32: B + mass vs (J/ψKππ) mass Other tests were made to check whether inclusive decays containing known resonances can be invoked as an explanation for the excess. The B + mass has been plotted as a function of (K J/ψ), (J/ψππ), (Kπ) and (Kω) systems 59

61 invariant masses, shown, respectevely, in Figures 4.33, 4.34, 4.35 and The first spectrum presents no clear structures, as expected since there are no known resonances with this final state. In the others, the contributions of, respectively, Ψ(2S), K (892) and K 1(1270) can be observed, as already stated in Section 4.7. However, no clear correlation is found between these three resonances and the bump at 5350 MeV/c 2. Figure 4.33: B + mass vs (K J/ψ) mass Figure 4.34: B + mass vs (J/ψππ) mass 60