Measurement of QCD Jet Background in the Identification of Tau Leptons with Multijet Events with the ATLAS Detector at the LHC.

Transcription

1 Measurement of QCD Jet Background in the Identification of Tau Leptons with Multijet Events with the ATLAS Detector at the LHC. Bachelor-Arbeit zur Erlangung des Hochschulgrades Bachelor of Science im Bachelor-Studiengang Physik vorgelegt von Marc Iltzsche geboren am in Freital Institut für Kern- und Teilchenphysik Fachrichtung Physik Fakultät Mathematik und Naturwissenschaften Technische Universität Dresden 2012

2 Eingereicht am 21. Mai Gutachter: Jun.-Prof. Dr. Arno Straessner 2. Gutachter: Prof. Dr. Michael Kobel

3 iii Summary Abstract The aim of this bachelor thesis is the study of the misidentification rate for different tau identification methods. The influence of the origin of the QCD background jets on the misidentification rate is also discussed. Therefore, di-jet and tri-jet events are selected. The quality of the tau identification is discussed depending on the transverse momentum and the pseudorapidity of tau candidates as well as depending on the number of reconstructed vertices per event. Furthermore, the influence of an additional trigger matching for the selected tau candidates is examined. This is motivated by the application of tau identification in analysis, like the search of Standard Model Higgs bosons. Abstract Ziel dieser Bacherlorarbeit ist die Untersuchung der Missidentifikationsrate für verschiedene Tau-Nachweisalgorithmen. Dabei werden 2-Jet und 3-Jet Ereignisse als QCD-Untergrund verwendet. Die Güte der Tau-Identifikation wird in Abhängigkeit vom Transversalimpuls und der Pseudorapidität der Tau-Kandidaten, sowie der Anzahl an rekonstruierten Vertices in einem Ereignis diskutiert. Der Einfluss von quark- und gluon- induzierten Jets auf die Missidentifikationsrate ist ebenfalls Gegenstand der Arbeit. Mit Hinblick auf spätere Analysen wird die Veränderung der Identifikationsgüte durch zusätzliche Auswahlbedingungen für die Tau-Kandidaten untersucht.

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5 Contents List of Figures vii List of Tables xii 1 Introduction Physics motivation LHC and ATLAS-Detector Structure of the ATLAS detector Inner detector Calorimeters Muon spectrometer Magnet system The Tau Lepton Data and Monte Carlo samples Reconstruction and Identification Reconstruction Identification Eventselection General quality criteria Conditions for reconstructed jets and events Multijet selection Di-jet selection Tri-jet selection Monte Carlo specific selections Additional probe trigger matching Mis-identification rate Analysis Distributions of identification variables for data, QCD background and Z ττsignal

6 vi Contents Di-jet analysis Comparison between identification variables after di-jet and tri-jet selection Distributions of identification variables for data and quark and gluon initiated jets Di-jet analysis Tri-jet analysis Fake rates Dijet analysis Tri-jet analysis Comparison between the fake rates after di-jet and tri-jet selection Influence of performing probe trigger matching Fake rate depending on the transverse momentum Fake rate depending on the pseudorapidity Fake rate depending on the number of reconstructed vertices Influence of quark and gluon initiated jets on the mis-identification rate Conclusion 37 6 Outlook 38 7 Appendix Definition of used identification variables LLH scores after di-jet and tri-jet selection Comparison of LLH variables between data, QCD background and Z τ τ signal Comparison of LLH variables between data, quark and gluon initiated tau candidates Fake rates for data and MC simulated background Bibliography 61

7 List of Figures 1.1 Schematic overview of the ATLAS detector [7] Feynman diagram of hadronic τ decay LLH score distributions for 1-prong and 3-prong tau candidates after applying the di-jet selection for data, QCD background and Z ττ decay signal Di-jet production at LHC Distribution of the transverse momentum, p T, for 1-prong tau candidates after applying the di-jet selection Tri-jet production at LHC Distribution of the transverse momentum, p T, for 1-prong tau candidates after applying the tri-jet selection Distribution for LLH variable Ntrack iso for 1-prong tau candidates after applying the di-jet selection for data, QCD background and Z ττ decay signal Distribution for LLH variable f core for 1-prong and 3-prong tau candidates after applying the di-jet selection for data, QCD background and Z ττ decay signal Distribution of LLH variable f core for 1-prong tau candidates after applying the di-jet and tri-jet selection for data, QCD background and Z ττ decay signal Distribution of LLH variable R track for 1-prong tau candidates after applying the di-jet and tri-jet selection for data, QCD background and Z ττ decay signal Distribution of LLH variable R cal for 1-prong tau candidates after applying the di-jet selection for data, quark initiated jets and gluon initiated jets Distribution of LLH variable f core for 1-prong tau candidates after applying the tri-jet selection for data, quark initiated jets and gluon initiated jets Mis-identification rate of the LLH-based identification method after di-jet selection for 1-prong tau candidates for data and MC simulated background in dependence of p T for the loose and tight working point Mis-identification rate of the BDT- and LLH-based identification method for 1- prong and 3-prong tau candidates after di-jet selection for data and MC simulated background in dependence of p T for the loose and tight working point

8 viii List of Figures 4.9 Mis-identification rate of the BDT-based identification method for 3-prong tau candidates after di-jet selection for data and MC simulated background in dependence of p T for the medium and tight working point Mis-identification rate of the LLH-based and BDT-based identification method for 3-prong tau candidates after di-jet selection for data and MC simulated background in dependence of η for the medium working point Mis-identification rate of the LLH-based identification method for 1-prong tau candidates after di-jet selection for data and MC simulated background in dependence of n vtx for the loose working point Mis-identification rate of the BDT-based identification method for 1-prong and 3- prong tau candidates after di-jet selection for data and MC simulated background in dependence of n vtx for the medium working point Mis-identification rate of the LLH-based identification method for 1-prong tau candidates after tri-jet selection for data and MC simulated background in dependence of p T for the loose working point Mis-identification rate of the LLH-based and BDT-based identification method for 3-prong tau candidates after tri-jet selection for data and MC simulated background in dependence of p T for the medium working point Mis-identification rate of the LLH-based and BDT-based identification method for 3-prong tau candidates after tri-jet selection for data and MC simulated background in dependence of η for the medium working point Mis-identification rate of the LLH-based identification method for 1-prong and 3- prong tau candidates after tri-jet selection for data and MC simulated background in dependence of n vtx for the medium working point Mis-identification rate of the BDT-based identification method for 1-prong and 3- prong tau candidates after tri-jet selection for data and MC simulated background in dependence of n vtx for the medium working point Mis-identification rate of the LLH-based identification method for 1-prong and 3- prong tau candidates after di-jet and tri-jet selection for data in dependence of p T for the medium working point Mis-identification rate of the LLH-based identification method for 1-prong and 3- prong tau candidates after di-jet and tri-jet selection for data in dependence of η for the medium working point Mis-identification rate of the LLH-based identification method for 1-prong and 3- prong tau candidates after di-jet and tri-jet selection for data in dependence of n vtx for the tight working point

9 List of Figures ix 4.21 Mis-identification rate of the LLH-based identification method for 3-prong tau candidates after di-jet and tri-jet selection for data in dependence of p T for the medium working point with and without applied probe tau trigger matching Mis-identification rate of the BDT-based identification method for 3-prong tau candidates after di-jet and tri-jet selection for data in dependence of η for the medium working point with and without applied probe tau trigger matching Mis-identification rate of the LLH-based identification method for 1-prong tau candidates after di-jet and tri-jet selection for data in dependence of n vtx for the medium working point with and without applied probe tau trigger matching Mis-identification rate of the BDT-based identification method for 3-prong tau candidates after di-jet selection for QCD background, quark initiated jets and gluon initiated jets in dependence of p T for the loose and tight working point Quark and gluon fraction in the generated QCD background sample after di-jet selection with and without proceeded probe trigger matching Quark and gluon fraction in the generated QCD background sample after tri-jet selection with and without proceeded probe trigger matching Mis-identification rate of the BDT-based identification method for 3-prong tau candidates after di-jet selection for QCD background, quark initiated jets and gluon initiated jets in dependence of η for the loose and tight working point Mis-identification rate of the BDT-based identification method for 3-prong tau candidates after di-jet selection for QCD background, quark initiated jets and gluon initiated jets in dependence of n vtx for the loose and tight working point LLH score after di-jet and tri-jet selection for 1- and 3-prong tau candidates LLH-based identification variables f core, R track, R cal and f 2 lead cluster for 1-prong and 3-prong decays after di-jet selection without probe trigger matching for data, QCD background and Z ττ decay signal LLH-based identification variables Ntrack iso, m tracks, S flight T for 1-prong and 3-prong decays after di-jet selection without probe trigger matching for data, QCD background and Z ττ decay signal LLH-based identification variables f core, R track, R cal and f 2 lead cluster for 1-prong and 3-prong decays after tri-jet selection without probe trigger matching for data, QCD background and Z ττ decay signal LLH-based identification variables Ntrack iso, m tracks, S flight T for 1-prong and 3-prong decays after tri-jet selection without probe trigger matching for data, QCD background and Z ττ decay signal LLH-based identification variables f core, R track, R cal and f 2 lead cluster for 1-prong and 3-prong decays after tri-jet selection without probe trigger matching for tau candidates from data, quark initiated jets and gluon initiated jets

10 x List of Figures 7.7 LLH-based identification variables Ntrack iso, m tracks, S flight T for 1-prong and 3-prong decays after tri-jet selection without probe trigger matching for tau candidates from data, quark initiated jets and gluon initiated jets LLH-based identification variables f core, R track, R cal and f 2 lead cluster for 1-prong and 3-prong decays after tri-jet selection without probe trigger matching for tau candidates from data, quark initiated jets and gluon initiated jets LLH-based identification variables Ntrack iso, m tracks, S flight T for 1-prong and 3-prong decays after tri-jet selection without probe trigger matching for tau candidates from data, quark initiated jets and gluon initiated jets Mis-identification rate of the LLH-based identification method after di-jet selection for data and MC simulated background in dependence of p T for all working points and 1-prong and 3-prong tau candidates Mis-identification rate of the LLH-based identification method after di-jet selection for data and MC simulated background in dependence of η for all working points and 1-prong and 3-prong tau candidates Mis-identification rate of the LLH-based identification method after di-jet selection for data and MC simulated background in dependence of n vtx for all working points and 1-prong and 3-prong tau candidates Mis-identification rate of the BDT-based identification method after di-jet selection for data and MC simulated background in dependence of p T for all working points and 1-prong and 3-prong tau candidates Mis-identification rate of the BDT-based identification method after di-jet selection for data and MC simulated background in dependence of η for all working points and 1-prong and 3-prong tau candidates Mis-identification rate of the BDT-based identification method after di-jet selection for data and MC simulated background in dependence of n vtx for all working points and 1-prong and 3-prong tau candidates Mis-identification rate of the LLH-based identification method after tri-jet selection for data and MC simulated background in dependence of p T for all working points and 1-prong and 3-prong tau candidates Mis-identification rate of the LLH-based identification method after tri-jet selection for data and MC simulated background in dependence of η for all working points and 1-prong and 3-prong tau candidates Mis-identification rate of the LLH-based identification method after tri-jet selection for data and MC simulated background in dependence of n vtx for all working points and 1-prong and 3-prong tau candidates

11 List of Figures xi 7.19 Mis-identification rate of the BDT-based identification method after tri-jet selection for data and MC simulated background in dependence of p T for all working points and 1-prong and 3-prong tau candidates Mis-identification rate of the BDT-based identification method after tri-jet selection for data and MC simulated background in dependence of η for all working points and 1-prong and 3-prong tau candidates Mis-identification rate of the BDT-based identification method after tri-jet selection for data and MC simulated background in dependence of n vtx for all working points and 1-prong and 3-prong tau candidates

12 List of Tables 1.1 Overview of hadronic τ decay modes Variables used in the Log-likelihood and BDT tau identification method [4] Object pre-selection conditions for jets, taus, muons and electrons Description of variables used in the Log-likelihood and BDT tau identification method 39

13 1 Introduction 1.1 Physics motivation Tau leptons play an important role in many physics analyses, e.g. the search for the Standard Model or supersymmetric Higgs decaying into two hadronically decaying tau leptons (H τ + had τ had ). Both, the leptonic and the hadronic tau decay provide a good possibility to investigate the electroweak symmetry, an important mechanism to understand the origin of particle masses. Hence, a detailed knowledge of the tau reconstruction and identification methods and their performance is crucial. 1.2 LHC and ATLAS-Detector The Large Hadron Collider (LHC) was built near Geneva (Switzerland) from April 1998 until August underground [6]. It is installed in a tunnel with a circumference of 27 km, lying 100 meters The LHC is designed for proton-proton- and heavy ion-collisions with a beam energy up to 7 TeV for p-p collision. This results in a nominal center-of-mass energy, s, of 14 TeV at a design luminosity of cm 2 s 1 [7]. Because of technical problems with the magnet system data are only taken for a center-of-mass energy of 7 TeV. For protonproton collisions, each beam consists of 2808 bunches. Each of them contains approximately protons under nominal operating conditions [7]. For each bunch crossing up to 20 collisions are expected [6]. The high amount of collisions in a very short time generates an enormous particle flux. Their signals can overlap, making it difficult to associate the detector signals to the particles. This effect is called pile-up. The ATLAS-detector is installed at one of the 4 beam crossing-points of the LHC. It is used for researches in different fields of particle physics, i.e. search for the SM Higgs boson and supersymmetric (SUSY) particles. With a weight of 7000 tonnes, a length of 46 meters and 25 meters in height, it is the detector with the largest volume installed at the LHC. A right handed coordinate system is used to describe the positions in the detector. The z-axis

14 2 1.3 Structure of the ATLAS detector is defined along the beam axis. The x-y plane is defined transversal to the z-axis, with the x-axis pointing to the centre of the ring. The azimuthal angle, φ, measures the angle with respect to the x-axis. The pseudo-rapidity, η, defined as: ( ( ) ) θ η = ln tan, 2 is used instead of the polar angle, θ. It is a measure of the angle between an object and the z-axis. A polar angle of θ = 90 corresponds to η = 0, an angle of θ = 0 corresponds to an infinite pseudo-rapidity. Assuming that the particles are massless, their energy is identical to their momentum. Hence in first order approximation η is equal to the rapidity y, which is additive under Lorentz boosts along the beam axis. The rapidity is defined as: (1.1) y = 1 2 ln E + p z E p z, (1.2) where E denotes the energy of the particle and p z, the absolute value of the z-component of the momentum. The distance between two points in the η φ plane is called R [4] R = ( η) 2 + ( φ) 2. (1.3) Further definitions are the transverse momentum p T = p sin θ and the transverse energy E T = E sin (θ), with p = p, the absolute value of the momentum. 1.3 Structure of the ATLAS detector The ATLAS detector consists of four main components which will be described in the following section [7]: Inner detector Electromagnetic/Hadronic calorimeter Muon spectrometer Magnet system The detector components are installed symmetric around the collision point of the beams along the z-axis. They consist of a barrel oriented along z-axis and two end-caps which are installed transversal to the z-axis, covering a range of η as large as possible (Figure 1.1).

15 1.3.1 Inner detector 3 Figure 1.1: Schematic overview of the ATLAS detector [7] Inner detector The inner detector consists of three different sub-detectors: the Silicon Pixel Detector, the Semi-Conductor Tracker (SCT) and the Transition Radiation Tracker (TRT). It is embedded in a 2 T solenoidal magnetic field to bend charged particles on a curved path. Based on the deflection, the sign of the electric charge can be determined. In combination, the three detectors measure the trajectory of a charged particle with high precision. This determines the interaction vertices, the particle momenta and the geometric conditions of the decay. In addition the TRT is used to distinguish pions from electrons. The Pixel detector and the SCT are covering a region of η < 2.5, while regions up to η 2.0 are covered by the TRT Calorimeters The purpose of the electromagnetic and hadronic calorimeters is the measurement of the energy of charged and neutral particles. They cover a range of η 4.9. The spatial resolution has to be high enough, to assign energy-deposits to single particles. The electromagnetic calorimeter consists of a lead-liquid argon (LAr) calorimeter, which covers a range of η 3.2 and the forward calorimeters (FCal) providing a pseudo rapidity coverage between 3.1 η 4.9. For hadronic calorimeters two different technologies are used. In the end caps a copper-lar calorimeter is used to cover the outer a region of η > 1.5. For η < 1.7 a scintillator-tile calorimeter is installed.

16 4 1.4 The Tau Lepton Muon spectrometer Because of their high mass (m = MeV [1]) muons do emit almost no bremsstrahlung. Muons are only interacting via the weak force, so they barely interact with the calorimeters and can traverse the whole detector system without causing showers. To detect the muons the muon spectrometer is installed. The muon spectrometer consists of a 4 chamber system: the Cathode Strip Chambers (CSC), the Monitored Drift Tubes (MDT), the Resistive Plate Chambers (RPC) and the Thin Gap Chambers (TGC). To measure the transverse momentum of the muon an internal magnetic field of 0.5 T 1 T is applied Magnet system The magnet system has to generate a stable and precise magnetic field up to 2 T in a volume of m 3. It consists of three sub-systems: one Barrel Toroid, two End-cap Toroids and one Solenoid. For the inner detector, the solenoid provides a 2 T axial magnetic field. The barrel toroid and the end-caps provide the magnet field for the muon spectrometer. 1.4 The Tau Lepton The tau lepton, τ, is the heaviest known lepton with a mass m = ( ± 0.16) MeV [1]. It was discovered by Martin L. Pearl in 1975 [8], its corresponding tau neutrino ν τ in the year 2000 [9]. The τ-lepton is the only lepton which can decay both leptonically and hadronically. It has a mean lifetime of (290.6 ± 1.0) s, leading to cτ = μm [1]. The flight length l = βγ cτ of the generated tau leptons depends on their energy. That allows the measurement of its decay length with the ATLAS-detector. The information is provided by the inner detector and used during the τ identification. The leptonic decays have a branching ratio, B, of about 35%. The two most common decay modes are: τ μ ν μ ν τ (B = (17.39 ± 0.04)%) τ e ν e ν τ (B = (17.82 ± 0.04)%) The processes for τ + are the same but with inverted charges. Because it is not possible to detect neutrinos with the ATLAS detector, leptonic decay products are hard to distinguish from primary μ and e. Therefore, only hadronic decays are

17 5 considered for τ reconstruction and identification. The branching ratio of hadronic decays is about B = 65%. The Feynman diagram of the hadronic decay for τ is shown in Figure 1.2. Figure 1.2: Feynman diagram of hadronic τ decay. In hadronic decays an odd number of charged pions, π, or kaons, K, and the corresponding τ neutrino are generated. The modes are dominated by pions instead of kaons in the final states. Furthermore, additional decay products can be neutral pions, which decay most likely into 2 photons (B = (98.82 ± 0.03) %). Decays of the tau lepton including one electric charged hadron in the final state are called 1-prong (B = (49.5 ± 0.1) %), including 3 electric charged hadron are called 3-prong (B = (14.6 ± 0.1) %). The fraction of 5- or higher prong decays is about 0.1% [1]. An overview of the hadronic τ decay modes is shown in Table 1.1[1]. Type Decay products B [%] 1-prong π ν τ ± 0.07 π π 0 ν τ ± 0.09 π 2π 0 ν τ 9.29 ± 0.11 π 3π 0 ν τ 1.04 ± 0.07 K + + neutral 1.5 % 3-prong π π + π ν τ 9.31 ± 0.06 π π + π π 0 ν τ 4.61 ± 0.06 π π + π 2π 0 ν τ 4.95 ± 0.32 K π π % Table 1.1: Overview of hadronic τ decay modes.

18 6 1.5 Data and Monte Carlo samples 1.5 Data and Monte Carlo samples In this analysis ATLAS-data and Monte-Carlo generated samples for QCD background and Z ττ are used. The data were taken in 2011 corresponding to an integrated luminosity of L int = t 0 dt L = 4.66fb 1. The Monte Carlo samples were generated with PYTHIA.

19 2 Reconstruction and Identification The challenge of the tau reconstruction and identification algorithms is to distinguish between real hadronic tau decays and fake sources such as jets, electrons or muons. In the context of this work only the jet fake rates are discussed. One problem is the similarity of the structure of quark or gluon initiated jets and hadronic τ decays. However, there are slight differences in e.g the number of associated tracks to a vertex, the energy-deposits in the electromagnetic and hadronic calorimeter and the form of the shower. Hadronic τ decays are well collimated while QCD jets are spread out more in space. As already discussed in the introduction the tau leptons usually decay into one or three charged particles in the final state. In average for QCD jets this number is higher. In τ decays, the track of the particle with the highest transverse momentum, p T, reproduces the direction of the τ very well, which is not the case for most QCD jets because of the energy splitting in many uncollimated particles. After reconstruction, the step of identification is proceeded, because of the low separation of the reconstruction between QCD jets and showers of hadronically decaying tau leptons. Therefore, a set of different methods can be used to identify hadronic τ decays. 2.1 Reconstruction Around a seed cell in the calorimeter a group of cells with a signal above the noise level is formed, building a topological cluster. These clusters are then combined to jets, using the anti-k T algorithm [4]. With the information of the energy deposits and the track information provided by the inner detector a possible tau candidate axis can be calculated. This axis describes the flight path of the visible τ decay products. For information about geometric properties, cones around the τ candidate axis are defined, the core cone ( R 0.2) and the isolation annulus (0.2 R 0.4). The tracks within the core cone are associated to the candidate if they pass the following specific quality conditions:

20 8 2.2 Identification the transverse momentum has to be higher than 1 GeV a minimum of 2 hits in the pixel detector a minimum of 7 hits in the pixel detector and the SCT together the distance of the track to the corresponding primary vertex, d 0, has to be smaller than 1 mm the longitudinal distance to the vertex z 0 sin θ has to be smaller than 1.5 mm [4]. 2.2 Identification The aim of tau identification (ID) is the distinction between real τ leptons decays and jets originating from quarks and gluons as well as muons and electrons, inducing similar detector signals. To get quantitative criteria for separating real τ decays from background a set of variables is defined. They use both, tracking and calorimeter information. The distributions of these variables for different object categories should be sufficiently different, depending on whether it is signal or background. To increase the efficiency for selecting real τ decays, collections of variables are used There are three different τ identification methods used to distinguish the signal signatures of hadonically decaying τ leptons from background signatures caused by hadronical jets. A good signal and background separation is important for reducing uncertainties in later analyses. Cut based: Variables that are calculated from energy deposits and optionally variables that are based on tracking informations are used for the cut based identification. These variables have to be well understood in the early data taking phase. To separate signal from background, distributions of a specific variables like R track and f core are used. These variables are optimised for single- and multi-prong decays separately [5]. Boosted Decision Tree (BDT): The decision tree method uses a set of variables to separate signal from background. After picking a first variable or value, the element is tested if it is more signal or more background like. Depending on the decision, the next variable is taken to check the element again. Thus, the reconstructed particle passes a tree of decisions. Dependent on the final BDT score, it is treated as signal or background. The boosted decision tree instead weights misclassified events and builds a new tree. Hence, it generates a group of different trees ( forest ) with specific weights to increase the efficiency.

21 9 Log-likelihood (LLH): The probability density functions of each input variable, x i, are multiplied, defining the likelihood-function, for signal (L S ) and background (L B ) separately: L S/B = i p i,s/b (x i ). (2.1) With these two functions, the log-likelihood-score is calculated, which is defined as the natural logarithm of the fraction of L S over L B : d = ln L S L B = i ln ( ) p S i (x i ) p B i (x. (2.2) i) The larger the likelihood score the more likely the reconstructed particle is a real tau lepton. The variables used by the LLH and BDT method are listed in Table 7.1 [4]. Their definitions and descriptions can be found in the Appendix. After the identification is applied, the signal efficiency, ε, can be calculated as: ε = Number of τ candidates passing ID. (2.3) Number of total τ candidates For each of the 3 methods discussed above, 3 different working points are defined, corresponding to signal efficiencies of 60% (loose), 45% (medium), and 30% (tight) [4]. By choosing tighter cuts (decreasing the signal efficiency) the number of remaining tau candidates will be reduced in order to get an event-collection with a better separation from QCD background. For further analysis the background events in the full data sample are important. Therefore, a selection is proceeded to enrich the data sample with QCD background jets which are likely to fake hadronic tau decays. The signal and background separation based on the LLH method is shown in Figure 2.1. Therefore, the likelihood score for the simulated QCD background, the signal which consists of MC simulated Z ττ decays and data after the di-jet selection in plotted. The distribution of the data sample is in good agreement to the simulated QCD background. The likelihood score of the data sample is in good agreement with the simulated QCD background. For 1-prong τ candidates it can be seen that the score distribution for real τ leptons is sharper and peaks at a higher score than the distribution of QCD background. For 3-prong decays the QCD distribution is shifted to lower values, causing a better separation between data and Z ττ simulated decays. For tri-jet analysis the behaviour is basically the same.

22 Identification (a) 1-prong (b) 3-prong Figure 2.1: LLH score distributions for 1-prong (a) and 3-prong (b) tau candidates after applying the di-jet selection for data (black), QCD background (red) and Z τ τ decay signal (blue). variable LLH BDT 1-prong 3-prong 1-prong 3-prong R track f track f core N track iso R Cal m eff.cluster m tracks F light ST S leadtrack f 2leadcluster f 3leadcluster R max Table 2.1: Variables used in the Log-likelihood and BDT tau identification method [4].

23 3 Eventselection For the final analysis, an event selection is performed to enrich the sample with so called fake τ candidates. These are QCD jets misidentified as hadronic τ decays. For this, an event selection is applied and described in the following: 3.1 General quality criteria For further analysis, only data that which was taken under stable beam conditions and a during proper working of all relevant detector systems are used. 3.2 Conditions for reconstructed jets and events For the multi-jet analysis performed later it is necessary to choose a real jet to tag the event. Therefore, a trigger matching is applied. It removes every jet that did not fire a specific jet trigger. Different p T thresholds are applied between 15 GeV and 240 GeV. An additional requirement for the selected events is that there has to be at least one reconstructed vertex with four associated tracks. Further on, an object pre-selection is applied. After reconstruction, every reconstructed decay shower is treated as a jet, that means that the shower is caused by hadrons. To separate different objects, such as electrons, muons, taus and jets selection criteria are applied for those. If the initiating particle of the jet fulfils the specific conditions listed in Table 3.1, it will be treated as a corresponding candidate. During reconstruction it is possible that muons and electrons are mis-reconstructed as jets. For rejecting these from the sample a so called overlap removal is performed. If the particle passes a medium electron or a tight muon selection it will be removed.

24 Multijet selection selection p T η miscellaneous jet 15GeV 4.5 tau 15GeV or 3 assigned tracks BDT electron-veto medium muon 15GeV 2.5 electron 15GeV 2.47 excl medium++ identification Table 3.1: Object pre-selection conditions for jets, taus, muons and electrons 3.3 Multijet selection Di-jet selection In order to select di-jet events a tag-and-probe method is applied. There has to be at least one good quality jet in the event, which tags the event. After that, probe jets out of the list of tau candidates are taken with further requirements with respect to the tag jet. First, the jet with the highest p T ( leading jet ) is chosen as tag jet. In addition the p T difference of the leading jet and the τ candidate has to be less or equal to half the transverse momentum of the jet with the highest p T : p T = p leading jet T p τ cand. T p max T /2 (3.1) They also have to be back-to-back in the transverse plane. requiring: This property is ensured by φ(jet, tau) 2.85 π 0.3. (3.2) The number of tracks associated to the leading jet has to be greater than 4, because 4 and more track tau decays are very unlikely. Only if there is exactly one tau candidate in the event fulfilling all conditions it is chosen as probe tau candidate and used for further analysis. In Figure 3.1 the Feynman diagrams for 2 common interactions for di-jet production are displayed. They show that the QCD jets originate from both quarks and gluons. The p T distribution after applying all mentioned selections is shown in Figure 3.2. The data distribution is in good agreement with the Z ττ sample, peaking at a transverse momentum of approximately 30 GeV. For 3-prong tau candidates the same behaviour is observed.

25 3.3.2 Tri-jet selection 13 (a) 2 quarks in final state (b) 2 gluons in final state Figure 3.1: Possible Feynman diagrams for QCD di-jet production. Figure 3.2: Distribution of the transverse momentum, p T, for 1-prong tau candidates after applying the di-jet selection Tri-jet selection In the tri-jet selection, a tag-and-probe method is used as well. The event is tagged by the highest p T jet. Now every possible pair of τ candidates in the event is selected. The sum of both four-vectors of them is now treated like the four-vector of a new probe tau candidates. The pair of tau candidates has to be balanced in p T and back-to-back in the transverse plane to the leading jet. The number of tracks associated to the leading jet has to be greater than 4. Only if there is exactly one pair of tau candidates fulfilling these conditions, the event is chosen for further analysis. If not mentioned otherwise, the tau candidate with the lower p T is chosen as probe jet. It is likely generated by a radiated gluon, which causes the lower transverse momentum. This is shown in Figure 3.3 where the Feynman diagrams for 2 common interactions for tri-jet production are displayed. The p T distribution after applying all mentioned selection criteria including the tri-jet selection is shown in Figure 3.4. The data distribution is in good agreement with the QCD background, peaking at a transverse momentum of approximately 20 GeV. There is a distinct shift to lower

26 Monte Carlo specific selections (a) 2 quarks, 1 gluon in final state (b) 3 gluons in final state Figure 3.3: Possible Feynman diagrams for QCD tri-jet production. p T values in comparison with the di-jet selection. With respect to the shape this implies a smaller number of probe tau candidates in the high-p T range. For 3-prong tau candidates the same behaviour is observed. Figure 3.4: Distribution of the transverse momentum, p T, for 1-prong tau candidates after applying the tri-jet selection. 3.4 Monte Carlo specific selections For MC samples, a pileup re-weighting is performed. Because of continuous changing beam conditions and hence different pile-up conditions the generated MC samples are re-weighted so that the distributions of the number of interactions found in the event match between them. Generating new MC samples matching the data conditions is too time-consuming. Further on, reconstructed particles are matched to MC generated particles. If the distance in

27 15 the η-φ plane between the reconstructed particle and the generated hadronically decaying tau lepton is smaller than 0.2 the reconstructed particle will be rejected. The third selection for the MC samples is testing the probe jet on its possible origin. It is verified if it is initiated by a gluon, quark, photon or other particle. According to the result, the particle receives a identification number (Particle ID). With this information it is possible to calculate the generated fraction of quark and gluon initiated jets in a sample. 3.5 Additional probe trigger matching A matching of reconstructed tau candidates and trigger objects can be applied optionally. Once the probe tau candidate is selected one checks if it has fired a given tau trigger. This leads to a strong bias to real τ leptons for the observed shape of the identification method variables because of the identification on trigger level. 3.6 Mis-identification rate After the eventselection step the mis-identification probability is calculated. In the following, this probability will be called fake rate, f ID, and is defined as [4]: f ID = Number of probe jets identified as tau lepton Number of probe jets reconstructed as tau leptons. (3.3)

28 4 Analysis 4.1 Distributions of identification variables for data, QCD background and Z ττ-signal Di-jet analysis The centrality fraction, f core, is defined as the fraction of the deposited energy of all tracks in the core cone with R < 0.2 and the sum of the energy deposited in the cone within R < 0.4 around the tau candidate axis. Therefore, f core is a measure of the collimation of energy deposit of the tau decay around the candidate axis. The more collimated the decay is, the larger f core is. This behaviour is shown in Figure 4.1. The distribution for Z ττ is asymmetric and shifted to the right with a maximum at higher values for 1-prong decays than for 3-prong decays, because of the lower collimation of 3-prong decays. As expected, for simulated τ decays the largest amount of energy is deposited in the core cone. However, the shape for QCD background is nearly symmetrically peaking at lower values than the Z ττ distribution because fake jets are not as collimated as the real tau decay products. There is a small bias of the data distribution to the Z ττ sample, so there is no good agreement between data and simulated QCD background. This is caused by the remaining real tau decays in the sample. Furthermore, one can define variables which measure the low track multiplicity. An example is the number of tracks in the isolation cone, Ntrack iso, which is only used for 1- prong tau decays. The distribution measured in data agrees very well with the prediction obtained from MC simulation (Figure 4.2). It can be seen that less than half of the chosen probe jets have no tracks in the isolation cone. With increasing number of tracks in the Figure 4.2: Number of tracks in the isolation cone, Ntrack iso, for 1-prong tau candidates after applying the tri-jet selection for data (black), QCD background (blue) and Z ττ decay signal (red).

29 4.1.2 Comparison between identification variables after di-jet and tri-jet selection 17 (a) 1-prong (b) 3-prong Figure 4.1: Centrality fraction, f core, for 1-prong (a) and 3-prong (b) tau candidates after applying the di-jet selection for data (black), QCD background (blue) and Z ττ decay signal (red). isolation cone, the relative amount of probe jets with this property is decreasing approximately linearly. In comparison, nearly every real tau decay of the Z ττ sample has no track in the isolation annulus. Only a small fraction of about 10 % has one track in the isolation cone Comparison between identification variables after di-jet and tri-jet selection Based on the two variables f core and R track, the differences between the di-jet and tri-jet events are discussed. For 1-prong tau candidates, in comparison to the di-jet selection, the shape of the f core distribution after tri-jet selection is asymmetrically shifted to lower values with a maximum at f core 0.25 which is shown in Figure 4.3. Thus, the selected tri-jet geometry is more spread out, reducing the relative energy deposition in the inner cone. For 3-prong tau candidates the same shift is observed. This shift can be explained by the domination of gluon initiated jets after the tri-jet selection, since gluon initiated jets cause a wider jet shower. The second variable is R track. It is the momentum weighted track distance of all tracks in a cone within R < 0.4 around the tau candidate axis. The distributions for this variable are shown in Figure 4.4. For real tau decays the R track distribution peaks at R track = 0.03 since the largest amount of energy is carried by one particle, traversing nearly into the same direction as the initially tau lepton. The looser collimation of gluon initiated jets selected by the tri-jet selection instead leads to energy deposits at higher radii. This explains the shift

30 Distributions of identification variables for data and quark and gluon initiated jets (a) 1-prong dijet selection (b) 1-prong trijet selection Figure 4.3: Centrality fraction, f core, for 1-prong tau candidates after applying the di-jet (a) and tri-jet (b) selection for data (black), QCD background (blue) and Z ττ decay signal (red). towards higher values after applying the tri-jet selection. (a) after dijet selection (b) after trijet selection Figure 4.4: Track radius, R track, for 1-prong tau candidates after applying the di-jet (a) and tri-jet (b) selection for data (black), QCD background (blue) and Z ττ decay signal (red). 4.2 Distributions of identification variables for data and quark and gluon initiated jets To examine the differences between quark and gluon initiated jets with respect to geometric properties of the decay, a classification of the jets relating to their origin is performed. For every identification variable there is a large overlap of the quark and gluon distributions.

31 4.2.1 Di-jet analysis 19 Therefore, the variables are not qualified to separate jets with different origin with high efficiency. Nevertheless, slight differences between the two distributions are systematic due to a different geometry of the decay Di-jet analysis For every variable, except the track mass, m tracks, and the transverse flight path significance, S flight T, the distribution for data always fits best with the quark distribution, as shown in Figure 4.5 exemplary. This can be interpreted as an indication of the quark domination in the di-jet sample. On average the calorimetric radius, R cal, of the distribution of quark initiated jets is smaller compared to gluon initiated jets. This means that quark initiated jet yield to more collimated energy deposits than gluon initiated jets. Comparable observations can be made for f core and R track. Figure 4.5: Calorimetric radius, R cal, for 1-prong tau candidates after applying the di-jet selection from data (black), quark initiated jets (red) and gluon initiated jets (blue) Tri-jet analysis In the tri-jet analysis, the quark and gluon distributions differ less than in di-jet analysis. Furthermore, less available data statistics result in less significant conclusions. By choosing the tau candidate with the lower transverse momentum as probe jet, the selection of tri-jet events enhances the fraction of gluon initiated jets as predicted. This can be seen in Figure 4.6. For comparison the tau candidate of the pair of the tau candidates in the tri-jet selection with the higher transverse momentum is chosen as probe jet. The data distribution for the probe jet with the higher transverse momentum is in good agreement to the prediction of quark initiated jets, while the data distribution for the second leading probe jet is shifted towards the gluon dominated distribution.

32 Fake rates (a) first leading probe jet (b) second leading probe jet Figure 4.6: Track Radius, R track, for 1-prong tau candidates after tri-jet selection for first (a) and second (b) leading probe jet for data (black), quark initiated jets (red) and gluon initiated jets (blue). 4.3 Fake rates Given the difference in geometric and energetic properties of di-jet and tri-jet events, differences in the mis-identification rate are expected. Their differences will be discussed depending on the transverse momentum, p T, the pseudo rapidity, η, and the number of reconstructed vertices in the event, n vtx. The confidence limits of the fake rates are calculated, assuming a normal distribution. With the previous defined fake rate, f ID, the standard deviation, σ ε, is calculated as: f ID (1 f ID ) σ ε = total number of tau candidates. (4.1) Dijet analysis Fake rate depending on transverse momentum In Figure 4.7 the mis-identification rates for the 1-prong likelihood categories loose and tight are shown. For the loose working point the fake rate decreases slightly from approximately 20% to 10% in data with increasing transverse momentum in the range of 15 GeV to 80 GeV. In the low p T range, the shower width of real hadronic tau decays is small. Therefore, they are hard to distinguish from jets with a low collimation as well. This causes the increase of the fake rates for very low p T. In the p T bin between 40 GeV and 80 GeV, the fake rates reaches a minimum. For a higher transverse momentum the f ID increases again up to 25%.

33 4.3.1 Dijet analysis 21 This increase of the fake rate can be explained by the higher collimation of the jets, making them more tau like. The strong decline in the highest p T bin can be observed for all three working points. Choosing a tighter working point leads to a lower f ID. The minimal fake rate for the tight working point can be found at GeV bin with 2%. This is about a factor 10 smaller than for the loose ID. For higher p T the fake rate increases again up to 10 %. With increasing transverse momentum, the reduction of the fake rate by choosing tighter working points decreases. (a) LLH loose 1 prong (b) LLH tight 1 prong Figure 4.7: Mis-identification rate of the LLH-based identification method for 1-prong tau candidates after di-jet selection for data (red) and MC (blue) simulated background in dependence of p T for the loose (a) and tight (b) working point. The same behaviour can be seen in general for the BDT method, too. For this method, the f ID are smaller than for LLH at the same working points as it can be seen exemplary in comparison to Figure 4.8 (a). The strong decease of the fake rate in the high p T bin can only be seen for the tight working point. It became apparent that the fake rate for 3-prong LLH is lower than for 1-prong at the same working point. This behaviour is expected, due to the lower collimation of 3-prong decay in comparison to 1-prong decays. (This is amongst other things caused by the different target efficiencies for the two decay modes.) For all 3 working points, the mis-identification rate decreases with increasing p T reaching their minimum in the ( ) GeV bin (Figure 4.8 (b)). For the loose working point, the mis-identification rate decreases from 10% in the first p T bin to approximately 2%. As expected the fake rate decrease with tighter working points, reaching a minimum of about 0.3 % for the tight working point. An increase of the mis-identification rate in the p T range of ( ) GeV can be observed. This effect gets more dominant with tighter working points. For 3-prong tau candidates the fake rates of BDT are lower compared to LLH. For the loose and medium working point, with increasing p T the mis-identifcation rate decreases up to the

34 Fake rates (a) BDT tight 1-prong (b) LLH loose 3-prong Figure 4.8: Mis-identification rate of the BDT-based identification method for 1-prong tau candidates at the tight working point (a) and the LLH-based identification method for 3- prong tau candidates at the loose working point (b) after di-jet selection for data (red) and MC (blue) simulated background in dependence of p T. p T bin of ( ) GeV. This behaviour can not be observed for the tight working point, which is shown in Figure 4.9. There, increasing p T leads to smaller fake rates over the whole range of transverse momentum. This is not comparable to the MC prediction. (a) BDT medium 3-prong (b) BDT tight 3-prong Figure 4.9: Mis-identification rate of the BDT-based identification method for 3-prong tau candidates after di-jet selection for data (red) and MC (blue) simulated background in dependence of p T for the medium (a) and tight (b) working point. Fake rate depending on the pseudorapidity The 1-prong fake rate for the LLH method has a flat shape increasing with higher η and a local maximum in the central region. The average values for the different working points are: 20 % loose, 10 % medium, 4 % tight.

35 4.3.1 Dijet analysis 23 The mis-identification rate for 3-prong tau decays shows the same behaviour like the misidentification rate for 1-prong tau decays, but with stronger increase of the fake rates for large absolute values of η. The average values for the different working points are 5 % for the loose, 3 % for the medium, 0.8 % for the tight working point. Thus, the fake rate for 3-prong events is approximately 3 to 4 times smaller than for 1-prong. The shape of the fake rate for the BDT-based identification method is in principle the same like for the LLH method (Figure 4.10). For comparison the average fake rates for the BDT method are: 1-prong: 10 %, 5 %, 1.5 % 3-prong: 2 %, 1 %, 0.3 % for the loose, medium and tight working point, respectively. (a) LLH medium 3-prong (b) BDT medium 3-prong Figure 4.10: Mis-identification rate of the LLH-based (a) and BDT-based (b) identification method for 3-prong tau candidates after di-jet selection for data (red) and MC (blue) simulated background in dependence of η for the medium working point. Fake rate depending on the number of reconstructed vertices The number of considered events with large number of reconstructed vertices is rather small. Hence, the statistical uncertainty rises with increasing number of reconstructed vertices. For 1-prong tau candidates passing the LLH loose identification (Figure 4.11) a logarithmic increase of the fake rate with n vtx from 10 % up to 30 % can be seen. For tighter working points the fake rate is reduced and the shape becomes more flat in n vtx, reaching a plateau at n vtx = 10 with a fake rate of about 10% (medium) and 5 % (tight). The fake rate for 3-prong decays shows the same behaviour but with lower fake rate. For the BDT identification working points, the fake rate differs from the LLH fake rate distributions in their shape.

36 Fake rates Figure 4.11: Mis-identification rate of the LLH-based identification method for 1-prong tau candidates after di-jet selection for data (red) and MC (blue) simulated background in dependence of n vtx for the loose working point. For 1-prong tau decays the fake rate remains approximately flat. In average the value of the fake rate is 10 % for the loose, 5 % for the medium and 2 % for the tight working point. Beginning at n vtx between 9 and 11 the fake rate decreases. For 3-prong events the fake rates decreases up to an n vtx between 6 and 8. For higher n vtx it increases again. (a) BDT medium 1 prong (b) BDT medium 3 prong Figure 4.12: Mis-identification rate of the BDT-based identification method for 1-prong (a) and 3-prong (b) tau candidates after di-jet selection for data (red) and MC (blue) simulated background in dependence of n vtx for the medium working point.

37 4.3.2 Tri-jet analysis Tri-jet analysis A general problem of the tri-jet analysis is the reduced number of selected events due to the tighter event selection conditions. The same problem occurs for the MC samples. Therefore, a separation of the tau candidates from MC samples with respect to their origin is not useful in most cases. An additional fact shall be mentioned here: In the tri-jet analysis, the chosen probe jet is one out of a pair of tau candidates, sharing the largest amount of the energy. Hence, the transverse momentum of the probe jet of the tri-jet selection is lower than for the di-jet probe jets. This also reduces the number of tau candidates with high p T. Fake rate depending on the transverse momentum For the LLH-based identification method and 1-prong decays there is a small reduction of the fake rate for p T between 40 GeV and 80 GeV in comparison to the previous p T range with a fake rate of about 20%. Increasing p T above 80 GeV increases the fake rate up to 30% (Figure 4.13). The same behaviour can be seen within the error bars for the medium working point. For the tight working point the fake rate decreases with higher p T between 25 GeV and 80 GeV. A comparison to the MC prediction is only possible for the first to bins, because no probe taus with a p T above 80 GeV from the MC sample passed the ID. Figure 4.13: Mis-identification rate of the LLHbased identification method for 1-prong tau candidates after tri-jet selection for data (red) and MC (blue) simulated background in dependence of p T for the loose working point. For the LLH-based identification method and 3-prong decays the fake rates for data and MC are decreasing with increasing p T, but the reduction of the fake rate for data is much higher than predicted by MC samples. For the tight working point for example, the fake rate of data is up to 100 times smaller than for the MC sample. The change of fake rate for the MC sample between the three working points above 80 GeV is low. For the data instead, the fake rate decreases significantly by choosing tighter working points. For the BDT-based identification method the behaviour of the fake rates is the same as it is for the LLH-based method and can be seen exemplary in Figure 4.14.

38 Fake rates (a) LLH medium 3 prong (b) BDT medium 3 prong Figure 4.14: Mis-identification rate of the LLH-based (a) and BDT-based (b) identification method for 3-prong tau candidates after tri-jet selection for data (red) and MC (blue) simulated background in dependence of p T for the medium working point. Fake rate depending on the pseudorapidity The fake rates depending on η have the same shape for both methods as well as for 1-prong and 3-prong tau candidates. For the LLH method, 1-prong and 3-prong tau candidates have the same fake rate. In the case of the BDT method, 3-prong has a 2% lower fake rate than the 1-prong for the same working point. The slight differences between the two methods can be seen in Figure (a) LLH medium 3 prong (b) BDT medium 3 prong Figure 4.15: Mis-identification rate of the LLH-based (a) and BDT-based (b) identification method for 3-prong tau candidates after tri-jet selection for data (red) and MC (blue) simulated background in dependence of η for the medium working point.

39 4.3.3 Comparison between the fake rates after di-jet and tri-jet selection 27 Fake rate depending on the number of reconstructed vertices For the LLH-based identification method for 1-prong tau decays and all working points, the fake rate increases for n vtx up to 14. For loose and medium working point a reduction of the fake rate for n vtx above 14 can be seen. In comparison to the 3-prong decays there are differences (Figure 4.16). The fake rates for the loose and the medium working point are increasing more with increasing n vtx than for 1-prong decays, but have the same magnitude. (a) LLH medium 1 prong (b) LLH medium 3 prong Figure 4.16: Mis-identification rate of the LLH-based identification method for 1-prong (a) and 3-prong (b) tau candidates after tri-jet selection for data (red) and MC (blue) simulated background in dependence of n vtx for the medium working point. For 1-prong decays, the behaviour of the mis-identification rates for the LLH-based and the BDT-based identification method is basically the same. A slight increasing of the fake rate for the BDT method for higher n vtx can be seen, but it is more stable than the increase of the fake rate for the LLH method. For 3-prong decays no significant increasing of the fake rates in the n vtx range can be observed (Figure 4.17) Comparison between the fake rates after di-jet and tri-jet selection Fake rate depending on p T For the LLH-based identification method and 1-prong decays, the fake rates after applying the di-jet and tri-jet selection for the loose and medium working point are in good agreement. For the tight working point, in p T range between 40 GeV and 120 GeV, the fake rate after

40 Fake rates (a) BDT medium 1 prong (b) BDT medium 3 prong Figure 4.17: Mis-identification rate of the BDT-based identification method for 1-prong (a) and 3-prong (b) tau candidates after tri-jet selection for data (red) and MC (blue) simulated background in dependence of n vtx for the medium working point. applying the tri-jet selection is lower then after the di-jet selection. For the LLH-based identification method and 3-prong decays, the fake rate for the tri-jet selection decreases with increasing p T. After applying the di-jet selection instead, the shape of the fake rate remains flat. The same behaviour can be seen for the BDT-based identification method. (a) 1-prong (b) 3-prong Figure 4.18: Mis-identification rate of the LLH-based identification method for 1-prong (a) and 3-prong (b) tau candidates after di-jet (red) and tri-jet (blue) selection for data in dependence of p T for the medium working point.

41 4.3.3 Comparison between the fake rates after di-jet and tri-jet selection 29 Fake rate depending on the pseudorapidity For the LLH-based method and 1-prong decays no significant differences between the values of the fake rate after the di-jet selection and tri-jet selection is observed. For 3-prong decays, the fake rates after the tri-jet selection are between 2 and 5 times higher than after applying the di-jet selection (Figure 4.20). The same behaviour can be seen for the BDT-based method. (a) 1-prong (b) 3-prong Figure 4.19: Mis-identification rate of the LLH-based identification method for 1-prong (a) and 3-prong (b) tau candidates after di-jet (red) and tri-jet (blue) selection for data in dependence of η for the medium working point. Fake rate depending on the number of reconstructed vertices As already observed for η as variable, for both methods, the shape of the fake rates after di-jet or tri-jet selection for 1-prong decays are in very good agreement. For 3-prong decays the fake rate after the tri-jet selection is about 2 to 3 times higher than after the di-jet selection.

42 Influence of performing probe trigger matching (a) 1-prong (b) 3-prong Figure 4.20: Mis-identification rate of the LLH-based identification method for 1-prong (a) and 3-prong (b) tau candidates after di-jet (red) and tri-jet (blue) selection for data in dependence of n vtx for the tight working point. 4.4 Influence of performing probe trigger matching If a probe trigger matching is applied, tau candidates that do not pass a tau trigger with a p T threshold of 29 GeV will be rejected. Therefore, the remaining tau candidates are are more tau like, which should cause a higher fake rate for 1-prong and 3-prong decays as well. The specific changes of the fake rates will be discussed in the following section Fake rate depending on the transverse momentum After applying a trigger matching on the probe taus, the shapes of the fake rates after di-jet selection and tri-jet selection are equalized and shifted to higher values for the LLH-based identification method. The shapes of the fake rates are now comparable to the shapes of the fake rates after di-jet selection without applying the probe trigger matching. One observes an decreasing fake rate for increasing transverse momentum. In particular for 3-prong decays after applying the di-jet selection, the shapes of the fake rates before and after the tau trigger matching are greatly resembling each other. For the low p T range the fake rates with probe trigger matching are approximately one order of magnitude higher than without. For higher transverse momenta, the values differ by a factor of about 2.5. This can be seen in Figure By applying the additional matching, for the BDT-based identification method the fake rates increased up to 10 times, with unchanged shape for the di-jet selection. The behaviour for tri-jet selection is now consistent with the shape of the fake rate for di-jet selection.

43 4.4.2 Fake rate depending on the pseudorapidity 31 (a) without probe trigger matching (b) with probe trigger matching Figure 4.21: Mis-identification rate of the LLH-based identification method for 3-prong tau candidates after di-jet (red) and tri-jet (blue) selection for data in dependence of p T for the medium working point without (a) and with (b) applied probe tau trigger matching Fake rate depending on the pseudorapidity A good agreement between di-jet and tri-jet fake rates can be seen for the LLH-based method for the loose and medium working points. In contrast to the di-jet distribution the tri-jet distribution shows an asymmetric behaviour and is in average higher. For 1-prong decays and the tight working point the fake rate after the tri-jet selection is significant smaller than after the di-jet distribution. For the BDT method and the loose and medium working points the fake rates after the di-jet and tri-jet selection show the same behaviour (Figure 4.22). The reduction of passing events for tri-jet selection after the probe trigger matching makes it difficult to evaluate the behaviour after trijet selection for tight working points. For both methods an increase of the fake rate up to 10 times higher values as a consequence of the additional trigger matching can be seen Fake rate depending on the number of reconstructed vertices After probe trigger matching, the shape of the mis-identification rates did not change, but the values of the fake rate are increased. The decrease of the fake rate for higher n vtx for di-jet selection can still be observed (Figure 4.23).

44 Influence of quark and gluon initiated jets on the mis-identification rate (a) without probe trigger matching (b) with probe trigger matching Figure 4.22: Mis-identification rate of the BDT-based identification method for 3-prong tau candidates after di-jet (red) and tri-jet (blue) selection for data in dependence of η for the medium working point without (a) and with (b) applied probe tau trigger matching. (a) without probe trigger matching (b) with probe trigger matching Figure 4.23: Mis-identification rate of the LLH-based identification method for 1-prong tau candidates after di-jet (red) and tri-jet (blue) selection for data in dependence of n vtx for the medium working point without (a) and with (b) applied probe tau trigger matching. 4.5 Influence of quark and gluon initiated jets on the mis-identification rate The influence of quark and gluon initiated jets on the mis-identification rate is mainly discussed for the di-jet selection. The fake rate for gluon initiated jets should be smaller than for quark initiated jets, because these are more collimated, faking a real tau lepton decay more likely than gluon jets. This fact can be observed for the three variables p T, η and n vtx. If it is possible to gain data samples with a well known fraction of quark and gluon initiated jets, a fake rate study could by done for them. The results for the fake rates could then be

45 33 compared with fake rates caused by MC generated samples with associated quark and gluon initiated jet fractions. This will give the possibility to determine scale-factors for MC samples for physics analysis. In comparison to the MC samples, the data samples after applying the di-jet and tri-jet selections do not yield to a clean sample of either quark or gluon initiated jets over a large range of p T. Therefore, in the following sections only the fake rates for MC generated samples are discussed in general without comparison to a real data sample. In the plots the fake rates for quark and gluon initiated jets are shown, as well as the fake rate for the MC sample without applying the distinction between the origin of the jets. Fake rate depending on the transverse momentum For the transverse momentum no functional relation between the fake rates for di-jet and tri-jet selection can be seen. Depending on the chosen identification method and working point the fake rate ratio of the quark and the gluon initiated jets changes. Nevertheless, for increasing p T the fake rate of the whole MC sample approaches the fake rate of the quark initiated jets (Figure 4.24). This implies that for higher p T the sample is enriched with quark initiated jets. This will be compared with the predicted fraction of quark and gluon initiated jets in the sample. (a) loose (b) tight Figure 4.24: Mis-identification rate of the BDT-based identification method for 3-prong tau candidates after di-jet selection for QCD background (black), quark initiated jets (red) and gluon initiated jets (blue) in dependence of p T for the loose (a) and tight (b) working point. In Figure 4.25 it can be seen that in the low p T range the sample is dominated by gluon initiated jets. For higher p T, the fraction of quark initiated jets increases up to 80% and is

46 Influence of quark and gluon initiated jets on the mis-identification rate conform to the above statement. The increase of the fraction of quark initiated jets can be understood with an increasing cross section for elastic gluon scattering for high transverse momenta. One reason for this effect is that probe taus belonging to the gluon initiated jets have in average a lower transverse momentum than the probe taus belonging to the quark initiated jets. Another reason is that with higher transverse momenta of the probe tau the collimation of the jet increases. This causes that more jets are identified as quark initiated jets because they are typically more collimated than gluon initiated jets. After applying the probe Figure 4.25: Quark (black) and gluon (red) fraction in the generated QCD background sample after di-jet selection without (a) and with (b) proceeded probe trigger matching (both in sum normalized to unity in each p T bin). trigger matching, the sample is dominated by quark initiated jets for the whole p T range. The number of quark initiated jets in comparison to the number of gluon initiated jets is more than 2 times higher than without the trigger matching. This is caused by the higher probability to remove gluon initiated jets with their tau decay unlike shower profile. In order to compare the fractions of quark and gluon initiated jets in dependence of the chosen jet selection, the same plots are shown for the tri-jet selection as well (Figure 4.26). It can be seen that after tri-jet selection without probe trigger matching, the sample is dominated by gluon initiated jets in the low-p T range as well as after dijet selection. With increasing p T the fraction of the gluon initiated jets decreases, but not as strong as it was observed after the di-jet selection. After applying the probe trigger matching most of the gluon initiated jets are removed, which increases the fraction of quark initiated jets enormously. Fake rate depending on the pseudorapidity The fake rate caused by quark and gluon initiated jets remains for the loose working point over the whole range of η roughly constant. For tighter working points no stable fraction can be observed, but in general the fake rate for quark initiated jets it approximately 2 to 4 times

47 35 Figure 4.26: Quark (black) and gluon (red) fraction in the generated QCD background sample after tri-jet selection without (a) and with (b) proceeded probe trigger matching (both in sum normalized to unity in each p T bin). higher than for gluon initiated jets (Figure 4.27). The tighter the working points is, the higher the fake rate ratio of quark- to gluon- initiated jets is. This can be explained by the fact, that choosing tighter working points, most of the gluon initiated jets are already removed while for the quark initiated jets a tighter working point still leads to a significant reduction of the jets that remain in the sample. A difference in the shape of the fake rates between 1-prong and 3-prong could not be observed. (a) loose (b) tight Figure 4.27: Mis-identification rate of the BDT-based identification method for 3-prong tau candidates after di-jet selection for QCD background (black), quark initiated jets (red) and gluon initiated jets (blue) in dependence of η for the loose (a) and tight (b) working point.

48 Influence of quark and gluon initiated jets on the mis-identification rate Fake rate depending on the number of reconstructed vertices The fake rate of gluon initiated jets is in general between 3 and 5 times smaller than the fake rate of quark initiated jets but over the range of n vtx no significant functional relation between the two fake rates is seen. (a) loose (b) tight Figure 4.28: Mis-identification rate of the BDT-based identification method for 3-prong tau candidates after di-jet selection for QCD background (black), quark initiated jets (red) and gluon initiated jets (blue) in dependence of n vtx for the loose (a) and tight (b) working point.

49 5 Conclusion In this thesis, the tau identification fake rates depending on the transverse momentum, the pseudorapidity and the number of reconstructed vertices were studied with data taken by the ATLAS detector for p-p collisions at s = 7 TeV centre-of-mass energy. It was observed that the fake rates for the di-jet and tri-jet selections are in the case of 1-prong decays almost the same. This takes effect for the LLH-based and the BDT-based identification method. For 3-prong decays differences between the fake rates for the two selections occurred. There, the mis-identification rate depending on η after the tri-jet selection was up to 2-5 times higher compared to the di-jet selection. For a different number of vertices the same performance could be observed. In the case of p T as variable the f ID after the tri-jet selection reached significantly smaller values than after the di-jet selection. Instead of reaching a plateau like the fake rate for di-jet selection, a continuously decrease of the fake rate for increasing p T after the tri-jet selection was observed. After applying the probe trigger matching, the fake rates for both selections where equalized. Additionally it was shown that the fake rate of quark initiated jets is higher than the fake rate of gluon initiated jets, as it was expected. This is caused by the lower collimation of the gluon initiated jets. This has been seen by observing the tau identification variables for MC simulated quark and gluon initiated jets separately. To study the influence of the origin of the jets based on data, a p T range should be selected where the data samples after di-jet and tri-jet selection differs a lot. The comparison of the quark and gluon fractions in dependence of p T showed that it could be possible to use the high-p T range for the study, because the fraction of gluon initiated jets after tri-jet selection seems to be higher than after di-jet selection. Currently, the statistics after the tri-jet selection is not sufficient for significant analysis.

50 6 Outlook Redoing the analysis with data and MC samples of higher integrated luminosity would decrease uncertainties in the calculation of the fake rates. Especially for the tri-jet selection, MC samples with higher statistic are required to study the influence of the quark and gluon initiated jets on the fake rates. Additionally, algorithms for determination of the origin of gluon and quark initiated jets in data could be created. Therewith, it would be possible to select directly samples dominated by quark or gluon initiated jets. For a better understanding of the influence of geometric and kinematic conditions of the decays with respect to the fake rates, one could investigate correlation plots for the LLH and BDT variables in comparison to the transverse momentum as well as the number of reconstructed vertices. Taking into account these correlation would help to investigate the quantitative influence of e.g. increasing transverse momentum on the fake rates.

51 7 Appendix 7.1 Definition of used identification variables Variable & Description Electromagnetic radius E T weighted shower width in EM calorimeter Track radius p T weighted track width Leading track momentum fraction Fraction of p T of leading p T core track and p T of τ candidate Core energy fraction Fraction of E T within ΔR 0.1 of τ candidate Number of isolation tracks Number of tracks in isolation cone Calorimetric Radius Shower width in EM and hadronic calorimeter weighted by E T of each calorimeter part Cluster mass Invariant mass computed from constituent clusters of seed jet Track mass Invariant mass of track system Transverse flight path significance Decay length significance of secondary vertex First two leading cluster energy ratio Ratio of energy of first two leading clusters over all clusters associated to τ candidate R EM = R track = f core = R Cal = Definition ΔR<0.4 i (EM0 2) EEM T,i ΔR i ΔR<0.4 i (EM0 2) EEM T,i ΔR<0.4 i p T,i ΔR i ΔR<0.4 i p T,i f track = ptrack T,i p τ T ΔRi <0.1 E i [all] T,i ΔR j <0.4 E j [all] T,j N iso track ΔRi <0.4 E i [all] T,i ΔR i ΔRi <0.4 E i [all] T,i m eff.cluster = ( clst E)2 ( clst p)2 m tracks = ( tracks E)2 ( tracks p)2 S flight T = Lflight T δl flight T f 2leadclusters Maximum ΔR max Maximal ΔR between a core track and τ candidate axis Electromagnetic fraction Fraction of E T of τ candidate deposited in EM calorimeter f EM = ΔRi <0.4 i [Em0 2] E T,i ΔR j <0.4 E j [all] T,j Table 7.1: Description of variables used in the Log-likelihood and BDT tau identification method [4].

52 LLH scores after di-jet and tri-jet selection 7.2 LLH scores after di-jet and tri-jet selection (a) di-jet 1-prong (b) di-jet 3-prong (c) tri-jet 1-prong (d) tri-jet 3-prong Figure 7.1: LLH score after applying the di-jet and tri-jet selection for 1- and 3-prong tau candidates without probe trigger matching for data (black), QCD background (red) and Z ττ decay signal (blue).

53 Comparison of LLH variables between data, QCD background and Z ττ signal (a) f core 1-prong (b) f core 3-prong (c) R track 1-prong (d) R track 3-prong (e) R cal 1-prong (f) f 2 lead cluster 3-prong Figure 7.2: LLH-based identification variables f core, R track, R cal and f 2 lead cluster for 1- prong and 3-prong decays after di-jet selection without probe trigger matching for data (black), QCD background (blue) and Z ττ decay signal (red).

54 Comparison of LLH variables between data, QCD background and Z τ τ signal (a) N iso track 1-prong (b) ΔR max 3-prong (c) m tracks 3-prong (d) S flight T 3-prong Figure 7.3: LLH-based identification variables Ntrack iso, m tracks, S flight T for 1-prong and 3- prong decays after di-jet selection without probe trigger matching for data (black), QCD background (blue) and Z ττ decay signal (red).

55 43 (a) f core 1-prong (b) f core 3-prong (c) R track 1-prong (d) R track 3-prong (e) R cal 1-prong (f) f 2 lead cluster 3-prong Figure 7.4: LLH-based identification variables f core, R track, R cal and f 2 lead cluster for 1- prong and 3-prong decays after tri-jet selection without probe trigger matching for data (black), QCD background (blue) and Z ττ decay signal (red).

56 Comparison of LLH variables between data, QCD background and Z τ τ signal (a) N iso track 1-prong (b) ΔR max 3-prong (c) m tracks 3-prong (d) S flight T 3-prong Figure 7.5: LLH-based identification variables Ntrack iso, m tracks, S flight T for 1-prong and 3- prong decays after tri-jet selection without probe trigger matching for data (black), QCD background (blue) and Z ττ decay signal (red).

57 Comparison of LLH variables between data, quark and gluon initiated tau candidates (a) f core 1-prong (b) f core 3-prong (c) R track 1-prong (d) R track 3-prong (e) R cal 1-prong (f) f 2 lead cluster 3-prong Figure 7.6: LLH-based identification variables f core, R track, R cal and f 2 lead cluster for 1-prong and 3-prong decays after tri-jet selection without probe trigger matching for tau candidates from data (black), quark initiated jets (red) and gluon initiated jets (blue).

58 Comparison of LLH variables between data, quark and gluon initiated tau candidates (a) N iso track 1-prong (b) ΔR max 3-prong (c) m tracks 3-prong (d) S flight T 3-prong Figure 7.7: LLH-based identification variables Ntrack iso, m tracks, S flight T for 1-prong and 3- prong decays after tri-jet selection without probe trigger matching for tau candidates from data (black), quark initiated jets (red) and gluon initiated jets (blue).

59 47 (a) f core 1-prong (b) f core 3-prong (c) R track 1-prong (d) R track 3-prong (e) R cal 1-prong (f) f 2 lead cluster 3-prong Figure 7.8: LLH-based identification variables f core, R track, R cal and f 2 lead cluster for 1-prong and 3-prong decays after tri-jet selection without probe trigger matching for tau candidates from data (black), quark initiated jets (red) and gluon initiated jets (blue).

60 Comparison of LLH variables between data, quark and gluon initiated tau candidates (a) N iso track 1-prong (b) ΔR max 3-prong (c) m tracks 3-prong (d) S flight T 3-prong Figure 7.9: LLH-based identification variables Ntrack iso, m tracks, S flight T for 1-prong and 3- prong decays after tri-jet selection without probe trigger matching for tau candidates from data (black), quark initiated jets (red) and gluon initiated jets (blue).