Universität Bonn. Physikalisches Institut

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1 Universität onn Physikalisches Institut Measurement of the Flavour Composition of Di Events in Proton-Proton Collisions at s = 7 ev with the ALAS Detector at the LHC Marc Lehmacher CERN-HESIS-213-6/6/213 his dissertation presents a measurement of the flavour composition of di events produced in proton-proton collisions at a center-of-mass energy s = 7 ev. he data is reconstructed with the ALAS detector at the LHC and the full data sample of 21 is used. hree types of flavours, bottom, charm and light, are distinguished and thus six possible flavour combinations are identified in the di events. Kinematic variables, based on the properties of displaced decay vertices and optimised for flavour identification, are employed in an event-based likelihood fit. Multidimensional templates derived from Monte Carlo are used to measure the fractions of the six di flavour states as functions of the leading transverse momentum in the range 4 GeV to GeV and rapidity y < 2.1. he fit results agree with the predictions of leading- and next-to-leading-order calculations, with the exception of the di fraction composed of a bottom and a light flavour, which is underestimated by all models at large transverse momenta. In addition, the difference between bottom production rates in leading and subleading s is measured and found to be consistent with the next-to-leadingorder predictions. he ability to identify s containing two b-hadrons is demonstrated and used to identify a deficiency in the predictions of leading order Monte Carlo for the contribution of these s to di production. Physikalisches Institut der Universität onn Nussallee 12 D-31 onn ONN-IR June 213 ISSN

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3 Measurement of the Flavour Composition of Di Events in Proton-Proton Collisions at s = 7 ev with the ALAS Detector at the LHC Dissertation zur Erlangung des Doktorgrades (Dr. rer. nat.) der Mathematisch-Naturwissenschaftlichen Fakultät der Rheinischen Friedrich-Wilhelms-Universität onn von Marc Lehmacher aus Siegburg onn,

4 Dieser Forschungsbericht wurde als Dissertation von der Mathematisch-Naturwissenschaftlichen Fakultät der Universität onn angenommen und ist auf dem Hochschulschriftenserver der UL onn elektronisch publiziert. 1. Gutachter: Prof. Dr. Norbert Wermes 2. Gutachter: Prof. Dr. Ian rock ag der Promotion: Erscheinungsjahr: 213

5 Summary: his dissertation presents a measurement of the flavour composition of di events produced in proton-proton collisions at a center-of-mass energy s = 7 ev. he data is reconstructed with the ALAS detector at the LHC and the full data sample of 21 is used. hree types of flavours, bottom, charm and light, are distinguished and thus six possible flavour combinations are identified in the di events. Kinematic variables, based on the properties of displaced decay vertices and optimised for flavour identification, are employed in an event-based likelihood fit. Multidimensional templates derived from Monte Carlo are used to measure the fractions of the six di flavour states as functions of the leading transverse momentum in the range 4 GeV to GeV and rapidity y < 2.1. he fit results agree with the predictions of leading- and next-to-leading-order calculations, with the exception of the di fraction composed of a bottom and a light flavour. his fraction is underestimated by all models at large transverse momenta. In addition, the difference between bottom production rates in leading and subleading s is measured and found to be consistent with the next-to-leading-order predictions. he ability to identify s containing two b-hadrons is demonstrated and used to identify a deficiency in the predictions of leading order Monte Carlo for the contribution of these s to di production. Finally, the fake vertex reconstruction probability in light s is measured to be in agreement with predictions, thereby demonstrating the excellent performance of the ALAS detector simulation. iii

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7 Contents 1 Introduction 1 2 Experiment Large Hadron Collider ALAS detector Coordinate system and variables Inner Detector Calorimeter Muon detector rigger Di production 3.1 Quantum Chromodynamics Proton-proton scattering at the LHC Hard-scattering and the QCD factorisation theorem Parton shower Hadronisation Hadrons with heavy flavour Di events Event and selection Reconstruction and selection of s and tracks Jet reconstruction Jet selection rack reconstruction rack selection Secondary vertex reconstruction in s Secondary vertex reconstruction efficiencies rigger selection Di event selection Monte Carlo simulation 41.1 Monte Carlo samples v

8 .2 ruth-particle s Jet flavour labeling Detector simulation Jet p reweighting heoretical predictions Heavy quark production in hadronic collisions Heavy flavour in inclusive production Heavy flavour in di events Differences in heavy flavour rates in leading and subleading s Flavour composition analysis Analysis variables Analysis templates emplate construction emplate features uning of templates on data Simulation instabilities Analysis method Di system Di flavour asymmetry Fitting model emplate fit Validation of fitting approach Measurement results Data fit results Monte Carlo vertex reconstruction efficiencies Data-Monte Carlo comparison Flavour fractions Additional parameters Unfolding Systematic uncertainties Reweighting of the p and y distributions Pile-up Jet energy scale ottom and charm vertex reconstruction efficiencies emplate shapes Charm flavour asymmetry Admixture of s with two charm hadrons rack impact parameter smearing Unfolding procedure Combined systematic uncertainties Discussion of results vi

9 9 Summary and conclusion 19 Appendix 1 A Dependence of templates on rapidity 1 emplates for leading and subleading s 119 C Dependence of templates on heavy flavour production processes 123 D Results of the analysis validation 1 E Data-Monte Carlo comparison of fit results 133 F Summary of measured flavour fractions 141 ibliography 143 Acknowledgements 148 vii

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11 CHAPER 1 Introduction Particle physics deals with the fundamental buildings blocks of matter and their interactions with each other. he underlying quantum field theoretical framework is called the Standard Model of particle physics (SM) [1 4] and has been designed to encompass and describe all known phenomena of the microcosm. Although already established as a theory in the 6s and 7s of the 2th century, it still successfully holds up to any experimental test carried out in the years since then. Phenomena discovered in the meantime that were not originally built into the theory, as for example the fact that neutrinos are massive, can be integrated into the SM. Over the years, one by one the particles predicted by the SM were discovered at various experiments, some of them recently such as the top quark in 199 [ 7] and the tau neutrino in 21 [8]. With the advent of the Large Hadron Collider (LHC) the success story of the SM seems to be unbroken as the final missing and long-searched-for constituent, the higgs boson, might have been found already early in the endeavour in 212 [9, 1]. Recent measurements at the LHC are in agreement with SM predictions within the statistical and systematic uncertainties and no conclusive evidence is seen that might compromise confidence in the SM. One of the two large general-purpose detectors situated at the LHC is the ALAS experiment (A oroidal LHC ApparatuS) [11]. his detector was specifically designed to enable access to the complete field of possible physics measurements in high energetic proton-proton collisions as they happen at the LHC. On a fundamental level such proton-proton collisions are decribed by Quantum Chromodynamics (QCD), the theory of the strong interactions. Many relevant physics measurements are based on scattering of protons with high momentum transfer, socalled hard scattering, where according to perturbative QCD the scattering is traced back to high energetic interactions between the partonic constituents of the protons, i.e. the quarks and gluons (Figure 1.1). In this hard subprocess new quarks and gluons but also leptons are produced with large momentum transverse to the proton beam direction. he quarks and gluons involved radiate further gluons, which additionally can split up into quark-antiquark pairs, leading to the formation of a particle shower and finally to a many-particle final state. After this showering process quarks and gluons form hadrons, which emerge inside the detector as dense s of particles. Such produced particles can decay further in various ways inside the 1

12 1 Introduction detector, so that in many cases the decay products are measured and conclusions about the original particles from the hard subprocess can only be drawn indirectly. A a b Figure 1.1: Schematic representation of a generic hard scattering process. wo protons, A and, enter the diagram from the left. oth of them provide a parton, a and b, respectively. Each parton enters the hard scattering process represented by the circle in the middle. New particles are produced by the hard scattering in the middle while the proton remnants leave the picture at the top and bottom. A precise understanding of the associated phenomena of proton scattering and production is crucial for all physics measurements at ALAS. Monte Carlo simulations are indispensable at various stages of the physics analyses at ALAS and the other experiments at the LHC. hey are employed to simulate the physical processes taking place in proton-proton collisions as well as the detector response. hese simulations are constantly updated and adjusted to accommodate all improvements in theoretical and experimental knowledge. So any new insight into the underlying processes of QCD and production at the LHC can give important feedback to the model builders who then in turn improve the Monte Carlo simulations. Understanding the underlying QCD processes is vital to study SM and eyond-sm physics at the LHC, like for example Higgs studies or searches for Supersymmetry. Of particular interest for an understanding of the underlying QCD dynamics is the production of s containing heavy flavour hadrons, i.e. bottom and charm hadrons, which are likely to have originated from bottom or charm quarks. hese quarks have masses above the QCD scale, which means that the total production cross section of the corresponding s as well as the distribution of the heavy flavour hadrons should be relatively independent of any low energy hadronisation effects and therefore mainly depend on effects that are calculable perturbatively. hus, by measuring the production features of such s one can get a handle on the details of the underlying dynamics. In the following, three types of flavours are distinguished: light, b- and c-s. he flavour is defined by the flavour of the heaviest hadron in the. A light originates from fragmentation of a light flavour quark (up u, down d and strange s) or gluon and does not contain any bottom or charm hadrons. A b- contains at least one bottom 2

13 hadron, whereas a c- only contains charm and lighter hadrons. Inclusive b- and bottom-antibottom (b b) production have been studied in hadronic collisions by several experiments in the past [12 16], see also a review [17] and references therein, as well as the historical account in [18]. CMS published cross-sections for inclusive bottom production [19], b b decaying to muons [2] and bottom hadron production [21], as well as b b angular correlations [22]. he b b cross-section was also measured by LHCb [23]. ALAS published a measurement of the inclusive b- and b b cross-section in proton-proton collisions [24]. In this case explicit b- identification (b-tagging) was used. However, the b b final state constitutes only a part of the total heavy flavour quark production in events with two s, so-called di events, and the inclusive bottom cross-section contains a significant contribution from multi- states. Charm or light final states are not explicitly reconstructed in any of these analyses. A measurement of the full flavour composition of di events on the other hand can provide more detailed information about the different QCD processes involving heavy quarks. Several mechanisms contribute to heavy flavour quark production. One important mechanism that is calculable perturbatively is the creation of quark-antiquark pairs in the hard interaction (Figure 1.2a). Another production process is the so-called heavy flavour quark excitation, where a single heavy flavour quark from the sea quarks of one of the protons scatters against another parton from the other proton (Figure 1.2b). In contrast to this, heavy flavour quarks can also be produced in the showering process by gluon splitting into two heavy flavour quarks, which depends on non-perturbative effects (Figure 1.2c). In inclusive heavy flavour cross sections the different mechanisms for prompt heavy flavour quark production in the hard interaction as mentioned above remain indistinguishable. hus a comparison with theoretical calculations is difficult there. In contrast to this, a more exclusive study of the production of di events containing heavy flavour s allows the different prompt heavy flavour quark creation processes to be separated. For example, the dominant QCD production mechanisms are different for pairs of bottom flavour s and pairs consisting of one bottom and one light. g Q Q Q g q Q Q g g Q g g via gg Q Q via gq gq (a) Heavy flavour pair creation (b) Heavy flavour excitation (c) Gluon splitting q Figure 1.2: Examples for different production processes of heavy flavour in proton-proton collisions, (a): heavy flavour quark pair creation Q Q via the strong interaction through gluon fusion gg Q Q, (b): production of a single heavy flavour quark Q, so-called heavy flavour quark excitation, via the strong interaction through the scattering of a heavy flavour quark from the proton sea on a gluon gq gq, (c): production of heavy flavour quarks via gluon splitting in the final state (light quarks are denoted q). A more detailed definition and explanation of these processes can be found in Chapter 6. 3

14 1 Introduction he di system (Figure 1.3) can be decomposed into six flavour states based on the contributing flavours. hree of the di states are the symmetric bottom+bottom, charm+charm and light+light pairs. he three other combinations are the flavour-asymmetric bottom+light, charm+light and bottom+charm pairs. In the following, these six di flavour states will be denoted, CC, UU, U, CU and C, where U stands for light, C for charm and for bottom. In contrast to the mentioned measurements such a decomposition of the di system allows a simultaneous measurement of all six di flavour states, including those with charm. his approach provides more detailed information about the contributing QCD processes and challenges the theoretical description of the underlying dynamics as employed in QCD Monte Carlo simulations. Di Event Jet 1 (e.g. ) Proton eam Proton eam Jet 2 (e.g. C) Figure 1.3: Simple sketch of a di event where two high-momentum and back-to-back s are produced in proton-proton collisions. oth s can have one of the three possible flavours, i.e. bottom, charm C or light U. his dissertation describes the first measurement of the flavour composition of di events produced in proton-proton collisions using the ALAS detector, thereby demonstrating the excellent separation of charm and bottom flavoured s in the detector. In particular C, CC and CU di production is studied for the first time at the LHC. he measurement uses the full data sample collected by ALAS in 21. he results of the analysis have been published in []. he analysis procedure exploits reconstructed decay vertices of long-lived hadrons inside s. Since kinematic properties of such displaced secondary vertices depend on the flavour, a measurement of the individual contributions of each flavour to the overall di production can be made by employing a fit using templates of kinematic variables constructed from such vertices. No explicit b-tagging is used, i.e. no flavours are assigned to individual s. he flavour composition is derived from an event-based unbinned extended maximum likelihood fit of multidimensional templates to the full data sample. he templates are constructed from distributions of kinematic variables for the different flavour hypotheses on the basis of Monte Carlo simulation. he kinematic variables themselves are optimised for flavour identification. In order to arrive at an analysis method that is stable and applicable over the whole 4

15 aimed-at kinematic range, these variables are additionally chosen according to wether they are insensitive to kinematics, i.e. transverse momentum p and rapidity y. Di events are selected by looking for event signatures with two high p s that pass certain quality criteria and are directed into opposite directions, i.e. have a back-to-back topology. hese s are required to be fully contained within the ALAS Inner Detector acceptance region in rapidity, such that track and vertex reconstruction inside s are not affected by the Inner Detector acceptance. In addition the measurement is made in bins of leading p. ased on the entirety of such selected events the di flavour fractions are measured as functions of the leading transverse momentum. his dissertation is organized as follows. First, the experimental setup is described in Chapter 2. A brief overview of the underlying theoretical framework of di production at the LHC is given in Chapter 3. hen Chapter 4 describes the reconstruction algorithms of the main analysis objects, like s, tracks and vertices, as well as the event and selection procedure. Chapter summarizes the Monte Carlo simulation and flavour labeling. In Chapter 6 the theoretical predictions for the flavour composition of di events are discussed. A detailed account of the analysis method is presented in Chapter 7, which includes a description of the analysis variables and the template construction. In Chapter 8 the measurement results of the analysis are presented and systematic uncertainties are discussed in detail. he document is closed by a summary and conclusion in Chapter 9.

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17 CHAPER 2 Experiment he ALAS detector is one of four large experiments at the Large Hadron Collider, which is located at the European Organization for Nuclear Research (CERN) at the French-Swiss border close to Geneva. 2.1 Large Hadron Collider A schematic plan of the LHC [26] site is shown in Figure 2.1. he LHC is a proton-proton collider 1 with a design center-of-mass energy of s = 14 ev 2. he circular LHC tunnel has a circumference of about 27 km and is located on average about 1 m underground. wo counter rotating proton beams are operated in separate, adjacent vacuum tubes. At four points around the collider large experiments are situated, where the two beams are crossed and the protons from each beam are brought to collide. he protons are pre-accelerated in a series of linear and circular accelerators until they have gained an energy of 4 GeV, at which point they are injected into the LHC ring. Here they are then accelerated to their final energy. he LHC runs with pulsed beams of proton bunches with up to 1 11 protons per bunch. At design luminosity the bunches have a spacing of ns corresponding to a distance of 7 m. Each bunch has a length of a few centimeters and its width is squeezed to about 16 µm transverse to the beam direction at the collision points. he proton beams are guided around the LHC by a superconducting magnet system, which is embedded into a cryogenic system where the temperature is kept at 1.9 K with the help of superfluid liquid helium. Dipole magnets keep the protons on their orbit, whereas quadrupole and higher multipole magnets are used to focus the beam in space and energy. Also the accelerating radio frequency cavities are operated in a superconducting state at 4. K. Eight of these cavities are connected consecutively for each beam and are installed in one long straight section. 1 Alternatively, the LHC can also be filled with heavy ions instead of protons. 2 s = (P 1 + P 2 ) 2 is the square of the center-of-mass energy of the colliding particles with four-momenta P 1 and P 2, i.e. in this case s is just the sum of the individual proton energies s = E 1 + E 2 = 7 ev + 7 ev. 7

18 2 Experiment Figure 2.1: he Large Hadron Collider (LHC) with the major experiments including the general-purpose detectors ALAS and CMS, taken from Construction of the LHC and the experiments was finished in 28 and beams were circulated for the first time in September of that year. First collisions at the injection energy of s = 9 GeV took place on 23th November 29. On 3 March 21 a physics run at a higher energy of s = 7 ev was started, which continued for a large part of the rest of that year. he luminosity3 during this run reached a peak value of cm s. After further data periods in 211 the energy was increased to s = 8 ev later in 212 and the luminosity reached peak values of cm 2 s 1. his analysis is done using the full data run of 21 with a center of mass energy of s = 7 ev, i.e. 3. ev per beam, and an integrated luminosity of 39 pb 1. At the LHC design luminosity of 134 cm 2 s 1 the average number of so-called minimumbias events4 is roughly 23 per bunch crossing. Any collision happening at the LHC therefore contains a superposition of particles coming from several events. Events that contain one hard scattering will therefore trigger the detector, but are overlaid with additional, typically low energetic particles, so-called pile-up, which cannot be separated from the originally interesting 3 he luminosity L describes the intensity of the colliding beams, i.e. the number of particles that can interact per unit area per second, and is normally given in units of cm 2 s 1. It is related to the number R of interactions per second N via N = σl, where σ is the cross section. he luminosity integrated over time L dt is a helpful quantity to express the size of a data R sample, as for a given process with cross section σ the number of measured events in a given time is N = σ L dt. For convenience, the integrated luminosity is given in units of inverse cross section, i.e. barn 1 =b 1. 4 Minimum bias events are all events that pass the minimal trigger requirements of ALAS. 8

19 2.2 ALAS detector event. Depending on luminosity, this pile-up poses a serious background to many measurements and has to be taken into account in the analysis. he average number of interactions created in a bunch crossing scales linearly with luminosity. So even in the low luminosity conditions of the LHC run in 21 at s = 7 ev an average number of pile-up events of up to roughly 3 arose. 2.2 ALAS detector he ALAS detector was designed to allow the study of a wide range of physics processes occurring at LHC energies. From the inside to the outside it consists of an inner tracking detector (ID), an electromagnetic calorimeter, a hadron calorimeter and a muon spectrometer. In addition a trigger system was installed that suppresses uninteresting events to keep the data volume manageable. For this analysis the tracking devices, the calorimeters and the trigger system are of particular importance. he most important aspects of the ALAS detector relevant for this thesis are summarized in the following, a detailed description of the ALAS detector can be found in [11]. he layout of the ALAS detector is illustrated in Figure 2.2. With a diameter of m, a length of 44 m and a weight of 7 t the ALAS detector is the largest experiment at the LHC Coordinate system and variables As typical for many high energy physics detectors, the ALAS detector has cylindrical symmetry, see Figure 2.2. A right-handed coordinate system is used with its origin at the nominal proton interaction point in the centre of ALAS. he z-axis is directed along the beam line, the x-axis points from ALAS to the centre of the LHC ring and the y-axis is oriented upwards. In the transverse plane the usual cylindrical coordinates (r, φ) are used, i.e. radial distance from the beam pipe r and azimuthal angle φ. As it is common at hadron colliders the pseudorapidity η is used as a measure of the polar angle θ with η = ln tan(θ/2). In the limit of massless objects or very high energies the pseudorapidity becomes equal to the rapidity y = 1/2 ln[(e + p z )/(E p z )], with the longitudinal momentum component p z. he latter is additive under longitudinal Lorentz boosts along the beam direction and thus y is invariant under such transformations. Furthermore the statistical distribution of particles produced in hadron collisions dn/dy is flat in y for purely kinematic production of particles, i.e. without taking into account any production dynamics. he simpler pseudorapidity serves as a helpful approximation of the rapidity, its steep rise at small angular distances from the beam line corresponding to the increasingly dense particle environment in this region. An object s momentum p is fixed by its φ and η coordinates as well as the transverse momentum component p = p 2 x + p 2 y. Similarly, also other transverse variables are assigned in the x y plane, like e.g. transverse energy E. he distance in the rapidity-azimuthal space is defined as R = φ 2 + y 2. R can alternatively be defined using η instead of y. If not specified otherwise, the first definition using the rapidity y is used in the following. 9

20 2 Experiment Figure 2.2: Side view of the ALAS detector and its main components [11] Inner Detector he innermost detector, the tracker, is divided into three parts: the silicon pixel detector, the closest layer being situated at. cm from the beam axis, the semiconductor tracker (SC) and the transition radiation tracker (R), with the outermost layer lying at 1.7 m from the beam axis, see Figure 2.3. hese offer full coverage in the azimuthal angle φ and a coverage in pseudorapidity of η < 2., with the exemption of the R, which only reaches up to η = 2.. he ID s main purpose is the reconstruction of the trajectories of charged particles coming from the point of interaction. It is fully contained inside a solenoid magnetic field of 2, which bends the charged particle tracks and thereby allows a momentum measurement of each track on the basis of the track s curvature. he ID was specially designed to handle the dense track environment of proton collisions at the LHC and measure track properties precisely. In particular the ID s good momentum resolution as well as high reconstruction efficiency are essential for many measurements, as is the precise reconstruction of the primary interaction vertex (PV) where the hard proton collision took place. For this analysis also the reconstruction of displaced decay vertices, so-called secondary vertices (SV), is a key ingredient. Pixel dectector he pixel detector is composed of three layers of silicon pixel modules in the barrel and three end-cap discs at both sides. Overall, there are 1744 identical pixel modules, each of them provided with pixels with a size of 4 µm 2. In sum, these amount to more than 1

21 2.2 ALAS detector Figure 2.3: Side view of the ALAS Inner Detector (ID) consisting of pixel detector, semiconductor tracker (SC) and transition radiation tracker (R) [11]. 8 million readout channels in the pixel detector alone. he pixel detector covers the complete azimuthal angle φ and the polar angle up to η = 2.. SC he pixel detector is surrounded by layers of silicon microstrip detectors, four concentric barrels and nine end-cap discs on each side, which make up the 912 sensors of the SC detector. In the end-caps the sensors contain radial strips of constant azimuth. In the barrel region four rectangular, single-sided microstrip sensors are combined into one module. wo sensors are daisy-chained together on each side of the module, where the backside pair is placed at a small stereo offset angle to provide two-dimensional position information. hus, in the barrel region, the SC is able to provide four space points in addition to the three precision measurements per track provided by the pixel detector. Angular coverage is the same as for the pixel detector. R he R consists of more than 3 gas-filled straw tubes with a diameter of 4 mm each that work as proportional drift tubes. In the barrel region they are aligned in parallel to the beam axis and most of them have a length of 144 cm, whereas they are 37 cm long and radially aligned in wheels in the end-caps. he barrel tubes are divided into two parts around η = to reduce occupancy. he R delivers on average 36 space points per track originating from the PV. Additionally, the R is employed for electron identification by making use of radiator material placed in between the straw tubes that causes electrons to emit transition radiation, which is detected by the xenon-based gas mixture in the straw tubes. In contrast to the two 11

22 2 Experiment semiconductor detectors the R has a coverage in pseudorapidity of η < 2.. Furthermore only R φ information can be provided by the R. ID resolution he intrinsic accuracies of the pixel detector are 1 µm in the R-φ plane and 1 µm in the z direction [27]. he SC detector has intrinsic accuracies per module of 17 µm in the R-φ plane and 8 µm in the z direction. he R has an intrinsic accuracy of 13 µm per straw in the R-φ plane. Despite the low intrinsic resolution of the R the overall precision of the ID is nonetheless significantly improved by combining measurements from all three sub-detectors due to the large number of space points and longer measured track length from the R Calorimeter he energy of particles and s are measured in several types of sampling calorimeters, which lie around the Inner Detector and the solenoid magnet. Overall, these different types of calorimeters cover a range in pseudorapidity of η < 4.9. he inner part is an electromagnetic calorimeter with a fine granularity optimized to measure electromagnetic showers coming from electrons and photons, which covers a pseudorapidity range of η < 3.2. his is encompassed by the various parts of the hadron calorimeter with their coarser granularity suited for hadronic showers and reconstruction covering the same overall range in pseudorapidity. A forward calorimeter completes the coverage over 3.1 < η < 4.9 close to the beam line. Electromagnetic calorimeter he electromagnetic calorimeter (EM) is split up into a barrel ( η < 1.47) and two end-cap components (1.37 < η < 3.2). eing a sampling calorimeter it consists of alternating layers of active material (liquid Argon) and absorber material (lead) with a characteristic accordionshaped kapton electrode structure. his particular setup allows to place the read-out electronics at the outer rim of the calorimeter, thereby avoiding any azimuthal cracks and making the calorimeter fully symmetric in φ. o correct for energy losses in the inner parts of the detector a pre-sampler calorimeter, also using the liquid argon technology, is placed before the main EM calorimeter. Hadron calorimeter he hadron calorimeters are made of scintillator tiles (as active material) and steel (as absorber) in the central region ( η < 1.7) and of liquid argon and copper/tungsten in the end-caps (1. < η < 3.2). he tile calorimeter is further subdivided into a barrel part ( η < 1.), which encloses the barrel part of the EM calorimeter, and two extended barrel compartments (.8 < η < 1.7). he hadron end-cap calorimeter (HEC) is made up of two independent wheels at each side being situated directly outside of the end-caps of the EM calorimeter, compare Figure

23 2.2 ALAS detector Muon detector All particles but muons and neutrinos are stopped inside the calorimeters. Since neutrinos cannot be detected directly at ALAS, any charged standard model particles arriving in the outermost detector parts have to be muons. he muon spectrometer is located outside of the calorimeters and comprises three layers of muon chambers of different technologies, three cylindrical layers in the barrel region and three layers perpendicular to the the beam in the end-cap regions. It uses a toroidal magnetic field with a bending power of up to 7. m to deflect muon tracks. he magnetic field is provided by a large superconducting air-core toroid magnet in the barrel region ( η < 1.4) that gives ALAS its characteristic appearance. his is completed by two smaller magnets inserted into both ends of the barrel toroid providing magnetic bending up to η < 2.7. Different technologies have been chosen for the muon chambers. For the momentum measurement monitored drift tubes are used over a large part of the η-range. hese are complemented by more robust cathode strip chambers in the regions with large particle rates 2. < η < 2.7. Precise tracking information is hence provided for η < 2.7. In addition, specific muon chambers are installed as trigger system in η < 2.4. hese are resistive plate chambers in the barrel region and thin gap chambers in the end-caps rigger As described above, at design luminosity of 1 34 cm 2 s 1 one expects 23 inelastic protonproton collisions per bunch crossing. aking into account that the bunch spacing can be as small as ns one arrives at an event rate of nearly 1 GHz. Already the bunch crossing rate of about 4 MHz is far beyond any reasonable rate that could be handled by any read-out and storage system. For this reason, a trigger system is implemented to select interesting hard scattering events online and discard any irrelevant event at as early a stage as possible. he ALAS trigger system consists of three consecutive levels: Level 1 (L1), Level 2 (L2) and Event Filter (EF). he L1 trigger is hardware-based and uses coarse detector information to identify regions of interest, whereas the L2 trigger is based on fast online data reconstruction algorithms. Finally, the EF trigger uses offline data reconstruction algorithms. Only events passing all three trigger levels are written to the longtime storage and are therefore available for offline analysis. he final output event rate is roughly 2 Hz with an average event size of about 1 2 M. Among other things, the L1 trigger searches for high transverse-momentum leptons, s and large total transverse energy. In this analysis single- triggers are used, which make use of calorimeter information with reduced granularity [27, 28]. he L1 calorimeter trigger uses calorimeter energy deposits to identify various types of objects with high transverse energy as well as energy sums of interest. For this the calorimeters are subdivided into trigger towers of size.2.2 in η φ without keeping the EM and hadron calorimeters separate. Regions of interest with high energy deposition are made out on the η, φ grid with a sliding window algorithm. Depending on the respective level 1 trigger the energy deposit is required to exceed a certain threshold in E in order that an event be kept for further processing. In case an event passes the threshold the acquired information is passed on to the L2 trigger, where the decision is refined using the full detector granularity and precision in the found region of 13

24 2 Experiment interest. Finally the EF trigger runs the full offline reconstruction algorithms using the precision of the complete detector, thus assembling the full event. 14

25 CHAPER 3 Di production he theory of the strong interaction, Quantum Chromodynamics (QCD), is fundamental for the calculation of physics processes as they happen at the LHC. his is in particular true for this analysis, where the flavour composition of di events is studied in proton-proton collisions. his chapter summarizes some of the fundamental concepts of QCD relevant for LHC physics in general and di production in particular. Section 3.1 gives a short summary of some of the basic principles underlying QCD. Section 3.2 lists the physics processes behind proton collisions. Section 3.3 introduces the formalism of hard-scattering and the factorisation theorem of QCD. hen, parton shower and hadronisation are explained in Section 3.4 and Section 3., respectively. he properties and decay of hadrons with heavy flavours is summarized in Section 3.6. Finally, the concept of di events is introduced in Section 3.7. his overview is based to some extend on the in-depth reviews in [29, 3]. 3.1 Quantum Chromodynamics he strong coupling constant and perturbative QCD Quantum Chromodynamics is the theory of the strong interaction, which is one of the three fundamental forces within the SM. It governs the interactions between quarks and gluons and is responsible for binding them into mesons and baryons, generically called hadrons. In addition to this, the long range part of the strong interaction causes protons and neutrons to form atomic nuclei. In analogy to the charge of the electromagnetic interaction the hard interaction couples to the colour charge of quarks and gluons. A fundamental property of QCD is called confinement and is the reason that quarks and gluons do not exist as free particles but only appear inside colourless bound states. An important quantity of QCD is the so-called strong coupling constant α S (Q 2 ), which specifies the strength of the interaction and depends on the energy scale Q 2. α S and thus the strength of the strong interaction increases when going to

26 3 Di production lower energy scales. At high energies and small α 1 S, QCD processes can be calculated in a perturbative approach, where the production cross section for a process is expanded in a power series in α S. In practice, this series is truncated at some order n in α S, i.e. O(α n S ), so that one arrives at approximate results. he required quantum field theoretical calculations can be done at the leading order (LO) and typically also at the next-to-leading order (NLO) in the expansion, but usually become very complex already at this stage. In energy regimes with small Q 2, α S (Q 2 ) becomes so large that at some point perturbation theory is no longer applicable. At the LHC, processes are typically subdivided into the two categories soft and hard. Hard means that the process takes place at a high energy or with large momentum transfer and thus can be calculated precisely in perturbative QCD (see also the following sections). Soft processes are dominated by non-perturbative QCD effects and are therefore often less well understood. Due to these properties the coupling constant α S (Q 2 ) is also referred to as the running coupling constant of QCD. Perturbative QCD only determines how α S (Q 2 ) varies with the scale, the absolute value has to be obtained from experiment at some reference scale. Often, the socalled QCD scale Λ is chosen as reference point, which represents the scale at which α S would diverge, if extrapolated outside the perturbative regime. Depending on the precise definition Λ takes values in the order of a few 1 MeV [29]. QCD perturbation theory breaks down for scales below Q 1 GeV i.e. scales on the order of the lighter quark masses. Feynman diagrams One approach for the perturbative calculation of QCD processes is based on a set of mathematical tools called Feynman rules, which are derived from the Lagrangian of QCD. Conceptually these are very convenient since the mathematical calculation for any process can be translated into an equivalent diagrammatic representation with so-called Feynman diagrams. Here, any Feynman diagram corresponds to one particular transition amplitude for a given initial state of particles to evolve into a particular final state of particles via the exchange of one or several virtual intermediate particles. hese intermediate particles are not on their mass shell, i.e. their energies and momenta do not have to obey the classical four momentum mass relation m 2 = E 2 p 2, where m is the rest mass. Here, the virtuality of a particle is defined as the amount by which the particle is off its mass shell. Figure 3.1a depicts a basic example. wo quarks enter on the left and annihilate into a virtual gluon, which splits up into two quarks. More generally, any number and type of intermediate particle can occur that is allowed by the Feynman rules. he order in perturbation theory to which any such diagram contributes is determined by the number of vertices, as each vertex contributes a factor of α S to the amplitude, see Figure 3.1a. he lowest order calculation is defined by the diagrams with the smallest number of vertices contributing to the process. In this respect Figure 3.1a would be a leading order diagram for quark pair creation while Figure 3.1b and 3.1c contribute to higher orders. Higher order diagrams can typically be derived from the lowest order by adding additional gluons or quarks in the diagram according to the Feynman rules, either as real emissions (see Figure 3.1b) or virtual loops (see Figure 3.1c). o calculate the cross section for any pro- 1 In quantum physics, high energy scales can be equivalently considered as short distance scales. Similarly, low energies correspond to long distance scales. his is also the reason why particle colliders are build with increasingly higher energies in order to probe matter at smallest distances. 16

27 3.1 Quantum Chromodynamics cess with given initial and final state at a fixed order in perturbation theory, one first needs to compile all contributing Feynman diagrams. he sum of all diagrams, i.e. of the individual transition amplitudes, gives the transition amplitude of this particular process, which is also called matrix element. he absolute squared amplitude corresponds to the transition probability for this process. Finally, to arrive at the cross section one has to integrate these results over the appropriate phase space region. At the LHC protons and not standalone quarks are accelerated and brought to collision. his has consequences, which are explained in the next sections. q q q q q q α α α α α α α α α q q q q q q (a) (b) (c) Figure 3.1: (a) lowest order diagram of order O(α 2 S ) for quark pair creation and two examples for higher order corrections (b) and (c). Renormalisation A priori, in many of the calculations of the Feynman diagrams inside the SM divergencies appear that seem to spoil perturbation theory. However, all of these divergencies can be rewritten via a regularisation procedure as additions to the physical observables of the theory, like masses and coupling constants. Since physical observables are finite one has to reconsider the definition of the corresponding quantities appearing in the original Feynman rules. he latter are considered as so-called bare masses and couplings, which do not correspond to the measurable quantities. It can be shown that a renormalisation of the physical quantities can remove all of these divergencies to all orders in perturbation theory, thus rendering physical quantities finite and the calculations meaningful. Here, the divergencies are ascribed to the bare quantities, which are not observable, and are subtracted from the results. For this reason, the SM is called a renormalisable theory. his procedure introduces a new scale µ R at which the subtraction is done. In effect, the renormalised strong coupling constant depends on the choice made for µ R. Formally, cross sections calculated to all orders in perturbation theory are independent of the specific choice of µ R. However, in practice the calculations are done up to a fixed order in perturbation theory and thus one has to choose a specific value for µ R. he sensitivity on this scale can be reduced by going to higher orders in the perturbative expansion. 17

28 3 Di production 3.2 Proton-proton scattering at the LHC According to QCD, protons are complicated bound states containing three valence quarks that are surrounded by a sea of virtual quarks and gluons. he valence quarks as well as these other quarks and gluons are collectively called partons. Relevant physics measurements at ALAS arise from proton collisions with large energy transfer, where the hard scattering takes place between the partonic constituents of the protons. his subprocess is calculable within perturbative QCD. New particles created in these collisions can be detected in ALAS if their transverse momenta are large enough. Since quarks and gluons are confined inside hadrons and do not exist as free particles, it is not possible to study these directly in the experiment. Only the bound states, i.e. the hadrons, can principally be detected experimentally. efore and after the hard scattering the involved partons radiate gluons, which can themselves emit further gluons or create quark-antiquark pairs, leading to many particles in the final state. echnically, this showering process, the so-called parton shower, is treated separately from the hard subprocess. After the showering process quarks and gluons form hadrons, which emerge inside the detector as dense s of particles. However, the hard subprocess of proton scattering is only part of the overall picture. Several aspects complicate proton scattering. For one, the hard scattering between partons inside the protons is overlaid by softer interactions between the two scattering protons. hese include multiple interactions of partons not taking part in the hard interaction. All of these softer processes contribute to the so-called underlying event. Furthermore, as seen in the chapter before, not single protons are being brought to collision at the LHC but bunches of up to 1 11 protons, which happens at design running conditions every ns. hus, one hard scattering of two protons is typically superimposed by over 2 soft scatterings between other protons from the same bunches. he latter collisions, however, are typically characterized by small momentum transfer as well as event vertices displaced from the main event vertex of the hard scattering. herefore, depending on the analysis, the interesting s from the hard scattering still stand out in the detector by their large energy deposits. Figure 3.2 demonstrates the overall complexity of proton scattering. From each side, left and right, a proton enters, distinguishable by the two big elliptical blobs ahead of the three horizontal arrows, which indicate the three valence quarks of each proton. Gluons (curly lines) and quarks (straight lines) inside these protons interact with each other after some initial state showering. he hard subprocess is depicted in the center by the circular blob. he underlying event is drawn as an elliptical blob somewhat below. Several particles are produced in the hard scattering (as well as the underlying event) that fly to the outside in the upper half circle (lower half circle in case of the underlying event), leading to a parton shower of gluons and quarks on the way. All produced quarks and gluons hadronise (small elliptical blobs) into various hadrons (small circular blobs), which eventually decay further into other hadrons or radiate photons etc. he complete chain of interactions is simulated by subsequent Monte Carlo programs: the calculation of the hard subprocess, the showering of coloured particles leaving the hard subprocess and the non-perturbative hadronisation leading to the outgoing hadrons. General-purpose Monte Carlo simulations model the complete sequence for selected processes, while dedicated Monte Carlo tools exist for other processes or specific steps in this 18

29 3.3 Hard-scattering and the QCD factorisation theorem chain. he following sections will detail the relevant steps. Decaying Hadron Hadronization Cluster Photon Hard Interaction Gluon Underlying Event Quark Proton Figure 3.2: Diagrammatic representation of a typical proton-proton scattering process, including a hard interaction and various subprocesses, extracted from [31] and provided with a legend. 3.3 Hard-scattering and the QCD factorisation theorem It is known from measurements of deep inelastic scattering of leptons and hadrons, that under specific circumstances the actual scattering occurs between the leptons and the point-like constituents of the hadrons. For the calculation of production cross sections for such processes parton distribution functions (pdfs) are introduced that quantify the distribution of partons inside a composite hadron. More precisely, pdfs correspond to the probability density functions of the fraction of momentum carried by the respective partonic constituents. he pdfs extracted from deep inelastic scattering can also be used to obtain hadronic cross sections at hadron colliders. In this case the hadronic cross section for a generic hard scattering of two hadrons A and can be obtained by weighting the subprocess cross section ˆσ ab X of the scattering of partons a and b with the pdfs f a/a (x a ) and f b/ (x b ) of each hadron σ A (P A, P ) = dx a dx b f a/a (x a ) f b/ (x b ) ˆσ(p a, p b ) ab X. (3.1) 19