Analysis of the first data from ATLAS experiment at LHC

Transcription

1 Czech Technical University in Prague Faculty of Nuclear Sciences and Physical Engineering Department of Physics RESEARCH WORK Analysis of the first data from ATLAS experiment at LHC Bc. Jakub Cúth 2011 Supervisor: prom. fyz. Václav Vrba, CSc.

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3 Work tittle: Department: Author: Branch of study: Kind of project: Supervisor: Abstract: Keywords: Analysis of the first data from ATLAS experiment at LHC Department of Physics FNSPE CTU in Prague Bc. Jakub Cúth Nuclear Engineering Masters s degree research work prom. fyz. Václav Vrba, CSc. The work is denoted to the analysis of the first data from the LHC collider registered by the ALTAS apparatus. In this report is particularly studied production of J/ψ which can be produced directly in the vertex of colliding protons or as a result of the B-hadron decay. The measurement of the pseudo-proper time of J/ψ appeared an efficient tool to separate these two processes. The report has been worked-out within the Prague B-physics group. ATLAS, B-physics, J/ψ, pseudo-proper time IV

4 Název práce: Katedra: Autor: Obor: Druh práce: Vedouci práce: Abstrakt: Klíčová slova: Analýza prvních dat z experimentu ATLAS na LHC Katedra Fyziky na FJFI ČVUT v Praze Bc. Jakub Cúth Jaderné inženýrství Výzkumný ůkol prom. fyz. Václav Vrba, CSc. Práce obsahuje stručný přehled současné částicové fyziky se záklandím matematickým aparátem pravděpodobnosti a statistiky. Samostatná kapitola se pak věnuje experimentu ALTAS na urychlovači LHC. Upořádání jeho detektorů, jeho trigger systém a zpracování dat. V poslední kapitole se nachází samotná analýza, která byla uskutečněna ve spolupráci s Pražskou B-physics skupinou. Jedná se o studii inkluzivních rozpadů B-mezonů na J/ψ ve tří-mionových srážkách. ATLAS, fyzika B-hadronů, J/ψ, vlastní čas. V

5 Prohlášení Prohlašuji, že jsem svůj výzkumný úkol vypracoval samostatně a použil jsem pouze podklady uvedené v přiloženém seznamu. Nemám závažný důvod proti užití tohoto díla ve smyslu 60 Zákona č. 121/2000 Sb., o právu autorkém, o právech souvisejících s právem autorským a o změně některých zákonů (autorský zákon). Declaration Here I declare that I wrote my research work independently and exclusively with the use of cited bibliography. I agree with the usage of this thesis in accordance with the Act 121/2000 (Copyright Act). V Praze dne Bc. Jakub Cúth VI

6 Acknowledgement First of all, I would like to thank my supervisor Václav Vrba, for an opportunity to work on the ATLAS experiment, for introducing me to CERN and particle physics and for leading this work. My big thanks belongs to Michal Marčišovský and Martin Zeman for their help with data analysis and for comments and corrections of this work. The last but not least, I wish to express gratitude also to other colleagues of the Prague ATLAS group, who helped me or supported me with advice. VII

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8 Contents Content IX Introduction 1 1 Basic physical and mathematical concepts in particle physics Standard Model of particles and fields Elementary particles Quantum Chronodynamics and Electroweak theory Beyond the Standard Model Mathematical aparatus Probability Statistics Error estimation The ATLAS experiment at the LHC CERN and the LHC A Toroidal LHC Aparatus Detector system ATLAS trigger Software framework of ATLAS Athena Root Pseudo-proper time of J/ψ candidates in three-muon events Fitting Conclusions 19 Bibliography 21 IX

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10 Introduction This research work is was performed on data from the first year of data taking at the ATLAS experiment on the LHC collider at s= 7 TeV. It is a part of work performed by the Prague B-physics working group at the ATLAS experiment. Particular task of this work is the study of pseudo-proper time of J/ψ coming from decays of B-mesons. On grounds of pseudo-proper time selection the purity of non-prompt J/ψ is investigated. The candidates from di-muon channel have been selected on the basis of their quality. The procedure is described in this report. Study of this pseudo-proper time allows identification of J/ψ candidates coming from decays of heavier bottom hadrons and direct production. This analysis is useful as a support study for other analyses B-mesons and J/ψ. 1

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12 Chapter 1 Basic physical and mathematical concepts in particle physics 1.1 Standard Model of particles and fields Search for the constituents of matter caused development of new kind of physics a quantum physics. It appeared as a neccessity to deal with effects at small distance scales. On the distances of m wave character of the particles play significant role in their description. Nowadays widely-used model in the particle physics is relativistic quantum field theory. It combines the Einstein s special theory of relativity with many-particle system description and the quantum physics. It employs a mechanism of gauge invariance and it s effect of emergence of new fields which correspond to forces Elementary particles Standard Model is based on a set of elementary particles and the same number of antiparticles. They are divided into groups according to their spin into fermions (half-integer spin) and bosons (integer spin). There are four types of elementary bosons, which are carriers of three forces. Photon γ is a mediating boson of the electromagnetic force, gluons g ( Nc 2 1 = 8 types ) are strong force mediators and W ± and Z 0 -bosons mediate the weak force. Figure 1.1: Table of Standard Model particles. There are two groups of elementary fermions: Data from [1]. quarks and leptons. Quarks have six flavours and three colors. Quarks cannot be observed as a free particles, however, together with gluons they are constituents of hadrons. Hadrons are particles consisting of three quarks, then they are referred to as baryons. The case of an quark anti-quark pair is called meson. Hadrons are colorless, i.e. there the resulting color combination is white which can be accomplished by three quarks of all three colors or anti-colors or a doublet carrying a color and an anti-color charge. 3

13 1.1. Standard Model of particles and fields Lepton group contains electrons, muons, tauons and their corresponding neutrinos. In Standard Model neutrinos are massless, neutral, weak-only interacting and left-handed and were predicted as explanation of violation of momentum conservation. The leptons are the only elemental fermions, which can be observed as free particles. Therefore are goo for precise measurements at specified energies. Only lepton, which we can collide with adequate luminosity is electron, however there already are concepts of muon colliders. The Standard Model fermions occur in three generations. Practically all baryonic matter in the Universe is built from first-generation quarks u and d, which make up nucleons (protons and neutrons). Nucleons together with electrons create atoms from which the observable world is built Quantum Chronodynamics and Electroweak theory Popular way how to solve a problem in physics, is looking for symmetries. Every symmetry of the system decrease the number of variables and hereby simplify the solution. Symmetries in physics are expressed as conservation laws, and are connected to groups of transformations. Therefore development of mathematical theory of groups has remarkable position in particle physics. Now we will follow particle interactions as are described in [1]. The Standard Model is theory based on SU(3) (SU(2) U(1)) symmetry, where SU(3) corresponds to a Quantum Chronodynamics and SU(2) U(1) corresponds to an Electroweak model. Strong interaction of quarks and gluons is described by Quantum Chronodynamics (QCD). It is SU(3) gauge theory of color intermediation. In (eq. 1.1) is the QCD Lagrangian, where ψ q,a are quark-field spinors for quark q, mass m q and color-index a. L = q ψ q,a ( iγ µ µ δ ab g s γ µ t C ab AC µ ) ψq,b 1 4 F A µνf A µν (1.1) The γ µ are the Dirac γ-matrices, the A C µ corresponds to the gluon fields, with C running through all kinds of quarks. The t C ab are 3 3 matrices generators of the SU(3) group. The g s is the QCD coupling constant and F A µν is field tensor F A µν = µ A A ν + ν A A µ g s f ABC A B µ A C ν [ t A, t B] = if ABC t C, (1.2) where f ABC are the SU(3) structure constants. 4

14 CHAPTER 1. Basic physical and mathematical concepts in particle physics The SU(2) U(1) is theory which unify the electromagnetic and weak interaction. The Electroweak Lagrangian after spontaneous symmetry breaking is L F = ( ψ i i / m i gm ) ih ψ i 2M i W g 2 Ψ i γ µ (1 γ 5 )(T + W µ + + T Wµ )Ψ i 2 i e q i ψi γ µ ψ i A µ i g ψ i γ µ ( gv i g 2 cos θ Aγ i 5) ψ i Z µ, (1.3) W i where the ψ i and Ψ i resp. are left-handed and right-handed resp. fermion fields of i th fermion generation with mass m i and charge q i in units of e. The g and g resp. are gauge coupling constants of SU(2) and U(1) group resp. with gauge bosons triplet W i µ, i = 1, 2, 3 and B µ respectively. Weinberg mixing angle is defined as θ W tan 1 (g /g) and positron electric charge is e = g sin θ W. The A B cos θ W + W 3 sin θ W is massless photon field, the W ± ( W 1 iw 2) / 2 and the Z B sin θ W + W 3 cos θ W are massive weak field bosons. The T ± are weak isospin raising and lowering operators, and the g i V t 3L(i) 2q i sin 2 θ W and the g i A t 3L(i) are vector and axial-vector couplings, where t el is weak isospin of fermion. The H is physical neutral Higgs scalar. The Higgs mechanism and spontaneous symmetry breaking are theories of origin of the particle masses. However, existence of Higgs boson and its mass are subjects of current particle physics research. Answer to these questions will determine the understanding of the world around us Beyond the Standard Model Nonetheless, the Standard Model is well working and elaborated theory, it is obvious, that it does not explain all observed processes in particle physics. Consequently, there are additional theories waiting for their confirmation. Deep scrutiny of this theories is out of the scope of this research work, therefore, we will make a slight introduction into some of them [2]. Super symmetry or SUSY postulates, that every known particle have super-symmetric partner. If the particle is boson (fermion) its SUSY-particle is fermion (boson). It assumes, that mass of super-particles will be at order of m W, m Z. The most usable scheme is minimal super-symmetric standard model (MSSM), where is expected not one Higgs particle, but two dublets of Higgs bosons (H1,2 0, H± ) [2]. After success of unification of electromagnetic and weak interactions, there is tendency to add strong force and create one super-interaction. The idea is to combine SU(2) SU(1) electroweak symmetry with SU(3) colour symmetry into one SU(5) at energy high above electroweak scale (Georgi Glashow model). 5

15 1.2. Mathematical aparatus The theory, which adds gravitation into this unification process is called theory of everything (TOE) [2]. In the String theory particles are not 0-dimensional objects, but 1-dimensional strings. The string can vibrate, and this is translates into properties that are observable (charge, spin, flavour... ). Additional dimensions (except space and time) are needed for fully functionality of this theory. The Super-string theory, which goes from string theory, connects strings with super-symmetry. It is expected, that length order of the string is at Planck scale. The Plank length is l P = M P c = m, where M P is Planck mass M P = c/g N = GeV (G N Newton s gravitation constant). The idea is, that string creates closed loop and different mode of oscillation represents different particle [2]. 1.2 Mathematical aparatus Now we will introduce probability and statistics inspired by [3, 1]. There are many ways, how to define probability.for our purpose is best frequency interpretation. Let x is one possible outcome of an observation, then probability is defined as frequency of observation of this value in many repetitions of experiment Probability Let x be continuous variable, then function P(x, θ) complying these rules (eq. 1.4), (eq. 1.5) is probability density function (referred as p.d.f.), where θ are parameters of the function. P(x, θ) 0, x, where defined, (1.4) P(x, θ)dx = 1, x, where defined. (1.5) Probability density function P(x, θ) in point x defined in this way presents probability of observation variable in range (x; x + dx). Now we defined some p.d.f. without normalization, which will be used for further analysis. Definitions are adopted from [1, 4]. G(x; µ, σ) = e (x µ)2 2σ (1.6) c+i L(x; µ, σ) = 1 x µ s ln s+ e σ s ds (1.7) 2πi c i { e x τ 1 if x < µ B(x; τ 1, τ 2 ) = e x (1.8) τ 2 else For more simple notation we will used square brackets in p.d.f product as normalization, [ ] P 1 (x; θ 1 ) P 2 (y; θ 2 ) y = P 1(x; θ 1 )P 2 (y; θ 2 ). (1.9) P2 (y; θ 2 )dy 6

16 CHAPTER 1. Basic physical and mathematical concepts in particle physics Statistics Statistic generally concerns with parameter estimation. Estimation is usually done by method of maximum likelihood. If measurements x i are statistically independent and P(x; θ) is joint p.d.f. for x i then the likelihood function is Actually, this is only about minimalization of likelihood function, which could be done numerically. L(θ) = N P(x i ; θ). (1.10) Theory says that parameter estimation is done by solving likelihood equation i=1 ln L θ i = 0, i = 1,, n. (1.11) Another way is method of least squares. If measurement y i have Gaussian distributed error, and theoretical prediction, that mean value follow function F (x i ; θ) and we have known variance σi 2. Then minimum of (eq. 1.12) defines least square estimator. N χ 2 (y i F (x i ; θ)) 2 (θ) = 2 ln L(θ) + const. = All these things are implemented in RooFit package. i=1 σ 2 i (1.12) Error estimation Let y(x 1,, x n ) be function of n variables x 1,, x n and σ i is error of measurement of variable x i. Then error σ y of function y will be computed by definition in (eq. 1.13). σ y = n ( ) y 2 σi 2 (1.13) x i i=1 7

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18 Chapter 2 The ATLAS experiment at the LHC The Large Hadron Collider hosts four large experiments, this analysis was performed on the data collected on the ATLAS experiment. 2.1 CERN and the LHC The CERN, from French Conseil Européen pour la Recherche Nucléaire, is the European Organization for Nuclear Research. It was founded in 1954 as one of Europe s first joint ventures. Today it is one of the world s largest and most respected centres for scientific research and has 20 member states [6]. The LHC with 27 km in circumference is the largest synchrotron in the world and it was build in the former LEP tunnel 100 m underground at CERN [7]. There are numerous experiments exploring microworld at CERN. Most of them are using Figure 2.1: Complex of CERN accelerators. Picture from [5]. rich complex of particle accelerators available (fig. 2.1) in modes of colliders or fixed target experiments. At the top of the complex there is a flagship of CERN the LHC. The LHC is a synchrotron accelerating bunches of protons (or lead ions) up to the energy of 14 TeV. It is a FODO lattice of magnets to keep particles on stable trajectories. Particles are accelerated by means of RF cavities. There are six experiments residing on the LHC ring. The ALICE experiment studies properties of dense hot matter in lead ion collisions. The LHCb searches for CP-violation in systems of B-mesons. CMS and ATLAS are general purpose collider detectors built for purpose of finding new physics. The other two smaller experiments, TOTEM and LHCf are focused for total proton-proton cross section measurements and forward physics resp., 2.2 A Toroidal LHC Aparatus The ATLAS is the largest experiment at the LHC and its brief description is provided. The z-axis of the detector is defined in the beam-line direction and transversal plane xy is orthogonal to it. 9

19 2.2. A Toroidal LHC Aparatus Detector system The experiment is composed of three main subdetectors. Track and vertex reconstruction is provided by the inner detector (ID) located at the center of ATLAS. The middle section contains the calorimetry systems for measurement of energy carried by particles. The outermost part is the muon spectrometer (MS). Figure 2.2: Principle of particle identification. Dashed lines mean no signal in detector. Neutrinos are identified as missing transversal energy or momentum. Order of subdetectors on the ATLAS (same as on fig. 2.2) provide the identification of particles. Tracks of particles are bended in magnetic field. Orientation of the track bending give information about charge of particle, and degree of bending corresponds to momentum. The Inner Detector has three sub-detectors. The Pixel Detector (Pixel) with 80 millions of pixels, the Semiconductor Microstrip Tracker (SCT) with 60 m 2 of active area and 6 millions of strips, and the Transition Radiation Tracker (TRT). The trajectories of charged particles are bend in the transversal plane by a 2 T field of solenoidal magnet. The precision of measurement of the track parameters is 14 µm and 115 µm for d 0 and z 0 resp. [8]. The Calorimeter is made of two detectors. A Liquid Argon Calorimeter (LAr), which works at temperature 183 C is an electromagnetic calorimeter. The second is a Tile Calorimeter (TileCal) with of plastic scintillator tiles and works as hadron calorimeter. 10

20 CHAPTER 2. The ATLAS experiment at the LHC The outermost part of the ATLAS is the Muon Spectrometer. It is a toroidal magnet system, which bends muon tracks in the beam-line direction in order to measure momentum. There are four types of muon chambers. The Thin Gap Chambers (TGC) and Resistive Plate Chambers (RPC) act as a muon trigger units in ATLAS. A Monitored Drift Tubes (MDT) and Cathode Strip Chambers (CSC) precisely measure momenta of muons ATLAS trigger The ATLAS has about 100 million of electronic readout channels. The number of channels imply event size of 1.5 MB with zero suppresion, therefore the ATLAS must have a sophisticated three level trigger system. First level (LVL1) is hardware based (FPGA and ASIC) and reduce signal rate to 100 khz. Level two (LVL2) and Event Filter (EF) are joined to form a High Level Trigger (HLT). It is as a software which runs on large computing farms. Final event rate is O(100)Hz. 2.3 Software framework of ATLAS Athena Athena was derived from Gaudi LHCb framework and arch over all software for data processing. It is mainly written in C++, but some components are in Fortran with C++ wrapper. For configuration and interaction are processes controlled by python scripts called job-options. A Raw Data files (RAW) from the trigger are the first step of analysis. Next is an Event Summary Data file (ESD), containing all information for physics and detector study. After derivation of the data for physical analysis purposes an Analysis Object Data file (AOD) is created. This is the last product of global production. Every working group have own selection algorithms to store only necessary information and save to a n-tuple file. The n-tuples are ROOT files containing one ore more trees. Usually the n-tuples are small files ( MB) and we can work with them locally. Our n-tuples are processed by ROOT TSelector class, which can be executed parallel and thus streamline the analysis Root The n-tuples are ROOT files containing one ore more trees. Usually the n-tuples are small files ( MB) and we can work with them locally. Our n-tuples are processed by ROOT TSelector class, which can be executed parallel and thus streamline the analysis. As output is a ROOT file with histograms and fits. Simple histogram fitting could be done by ROOT built-in functions. Nevertheless RooFit package is advanced utility optimized for fitting, even though the work with it is more challenging. 11

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22 Chapter 3 Pseudo-proper time of J/ψ candidates in three-muon events Our analysis concerns in the proton-proton collisions with production of B-hadrons decaying into muons in the final state. The B-hadron as name suggests containins b-quark (or anti-quark) and lighter quarks (see chapter 1). The scope of our analysis is study of production mechanisms of b-quark pairs. This is done by studying azimuthal angle α correlation between J/ψ produced in the dacay of one B-hadron and muon coming from the semileptonic decay of another B hadron. J/ψ decays into two muons in about 6% of all cases, and since the muons are easily identified and measured with good precision, it makes a good decay channel. We identify J/ψ in the di-muon channel by it s invariant mass. The analysis presented in this chapter is devoted to the measurement of J/ψ pseudo-proper lifetime. It is performed for three-muon events, where two muons are coming from the J/ψ decay. B-hadrons typically fly O(100) µm from the primary vertex before decaying and thus are easily identifiable. To separate J/ψ candidates coming from primary vertex and those from B-hadron decays a discriminating variable pseudo-proper lifetime is used. On the next figure a di-muon invariant mass is shown. J/ψ peak dominates the plot at invariant mass 3096 MeV. Several light resonances are easily identifiable at lower invariant masses such as ω (782 MeV) and φ (1020 MeV). Besides J/ψ another charmonium excited state, Ψ(2S) resides at 3686 MeV. At about 9 GeV we see bottomonium states, Y. J/ψs are selected by applying 200 MeV wide window on the di-muon invariant mass. This selection is powerful enough to select signal from background. Irreducible background on the plot below the J/ψ peak is dominated mainly by calculating invariant mass of muons, which did not come from a common vertex and fake muons. 3.1 Fitting For angular analysis we will need J/ψ signal as pure as possible. Besides muon reconstruction quality cuts (require combined muons, i.e. have both MS and ID tracks) we need to separate J/ψ coming from decays of B-hadrons (indirect) from directly produced J/ψ background. This is achieved by measuring the decay vertex of J/ψ. Vertex resolution in the z-axis (see definition in 2.2) due to the detector geometry is not sufficient so we will use measurements in the transversal plane only. The pseudo-proper time τ is defined as lifetime in transversal plane and it is Lorentz invariant. In (eq. 3.1) is mathematical definition, where L xy is distance of J/ψ vertex from the primary vertex in the transversal plane, m J/ψ is J/ψ invariant mass, p T is transversal momentum of J/ψ candidate and c is the speed of light in vacuum. 13

23 3.1. Fitting Figure 3.1: Schematic image of the typical process J/ψ + µ. Table 3.1: Pseudo-proper time model parameter values before and after fit. parameter start max min fitted error µ σ τ = L xym J/ψ p T c We will use t as computed pseudo-proper time and t err as its error (calculated by (eq. 1.13). First of all, we try to fit error of pseudo-proper time. Concerning the model of error of pseudoproper time distribution, the Landau distribution seems to fit it well. τ error = L(t err ; µ, σ) (defined in (eq. 1.8)), where µ and σ parameters of Landau distribution. The results after fit by Migrad and Hesse algorithms from MINUIT package (RooMinuit wrapper used) are in table 3.1. As we can see (fig. 3.3), the error model fits sufficiently and we can use it for next analysis. Result of this fit is only informative and shows us only the agreement of our model with data. Now we will divide analysis of pseudo-proper time to several parts. We will distinguish between signal (denoted as sig) and background (bkg) according to di-muon invariant mass. Next is prompt (pt) and non-prompt (npt) dividing. On figure 3.2 is highlighted J/ψ mass peak Pseudo-proper time was fitted by model function τ model, which consists of signal and background model functions (eq. 3.2), where c bkg (0; 1) is real (3.1) 14

24 CHAPTER 3. Pseudo-proper time of J/ψ candidates in three-muon events Figure 3.2: Invariant di-muon mass of di-muon candidate. Selected region is an example of mass window for J/ψ selection constant. τ model = (1 c bkg )τ sig + f B τ bkg (3.2) The signal model function (eq. 3.4) consists of prompt τ (pt) sig and non-prompt τ (npt) sig component mixed by coefficient c (npt) sig (0; 1). As prompt signal model function was chosen Gaussian. Originally it is Dirac δ-function, but due to the detector and reconstruction smearing is convoluted by Gaussian. Dirac convolved by Gaussian is simple Gaussian. Non-prompt J/ψ obey exponential decay law. Therefore, τ (npt) sig Gaussian (again due to smearing). is exponential convoluted by Both functions τ (pt) (npt) sig and τ sig are multiplied by τ (sig) (error), which was fitted by Landau distribution. The square brackets in p.d.f. product symbolize normalization, as defined in (eq. 1.9). τ sig = (1 c (npt) sig )τ (pt) sig + c(npt) sig τ (npt) sig (3.3) [ ] τ (pt) sig = τ error (sig) G sig (t; µ (sig) τ, t err.σ τ (sig) ) t (3.4) [ ] τ (npt) sig = τ error (sig) (sig) t/τ e decay G sig (t; µ (sig) τ, t err.σ τ (sig) ) t (3.5) τ (sig) error = L(t err ; µ (sig) err, σ err (sig) ) (3.6) The background model (eq. 3.8) is similar to signal model. It consists of prompt and nonprompt model functions. The prompt model is simple Gaussian (smearing factor), normalized and multiplied by error. However, non-prompt is sum of two models normalized according to t. First, τ (npt) (npt) bkg(1) is convolution of decay exponential and smearing Gaussian. Second, τ bkg(1) is bifurcated 15

25 3.1. Fitting Figure 3.3: Error of pseudo-proper time of J/ψ candidate fitted by RooFit exponential distribution (defined in (eq. 1.8)). τ bkg = (1 c (npt) (pt) bkg )τ bkg + c(npt) bkg τ (npt) bkg (3.7) [ ] τ (pt) bkg = τ (bkg) (error) G(τ var ; µ (bkg) τ, t err.σ τ (bkg) ) t (3.8) [( ) ] τ (npt) bkg = τ (bkg) (error) 1 d (npt) bkg. τ (npt) bkg(1) + d(npt) bkg τ (npt) bkg(2) t (3.9) τ (npt) (bkg) t/τ bkg(1) = e decay G(τ var ; µ (bkg) τ, t err.σ (bkg) τ ) (3.10) τ (npt) bkg(2) = B(t; τ (1) bifur, τ (1) bifur ) (3.11) τ (bkg) error = L(t err ; µ (bkg) err, σ err (bkg) ) (3.12) Final goodness of fit is χ 2 = and all fitted parameters are written in table 3.2. From this table implies, that approximately one half of J/ψ is from B-hadron decay and other one is prompt (parameter c (npt) sig = ± 0.005). This is the main result of this report. 16

26 CHAPTER 3. Pseudo-proper time of J/ψ candidates in three-muon events Table 3.2: Parameters of fit: starting, maximal, minimal and final value and value after fit with error. parameter start max min fitted error c bkg c (npt) sig c (npt) bkg d (npt) bkg µ (sig) τ 0 const const const const σ (sig) τ τ (sig) decay µ (sig) err σ (sig) err µ (bkg) τ 0 const const const const σ (bkg) τ τ (bkg) decay τ (1) bifur τ (2) bifur µ (bkg) err σ (bkg) err

27 3.1. Fitting Figure 3.4: Pseudo-proper time of J/ψ candidate fitted by RooFit 18

28 Conclusions The ATLAS data from LHC irradiation runs 2010 proton-proton collisions have beed analysed in this research work. The standard ATLAS software framework were used in this analysis. Specific algorithms and code were developed by author in cooperation with the Prague B-physics group. The J/ψ from B-hadron decay was studied and from pseudo-proper lifetime measurement was concluded, that approximatelly one half of J/ψ are produced by B-hadrons (and the other half is prompt). It was found that pseudo-proper time significance S τ is a variable for efficient selection of nonprompt B-hadrons. It was found that non-prompt J/ψ candidate will have S τ > 2.5. S τ = t t err A future analysis will be focused on Monte Carlo simulation of three muon events from B-hadrons as well as measuring b-quark production mechanisms. Remaining issues are identification of fake muons and decays-in flight in particular. 19

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30 Bibliography [1] K. Nakamura et al. (Particle Data Group). The Review of Particle Physics. J. Phys, volume G 37: (2010). [2] D. H. Perinks. Introduction to High Energy Physics (Cambridge University Press, 2000), 4th edition. [3] G. Cowan. Statistical data analysis (Clarendon Press, 1998). [4] W. Verkerke and D. Kirkby. The RooFit Toolkit for Data Modeling. (2011). [5] CERN DSU - Communication Group. The accelerator complex. (2011). [6] CERN DSU - Communication Group. CERN in nutshell. (2008). [7] LHC Machine Outreach Team. LHC Machine Outreach. (2011). [8] ATLAS Collaboration. ATLAS Fact sheet. (2010). 21