Use of a Multivariate Analysis in the Search for Vector-Like Quarks at the LHC

Use of a Multivariate Analysis in the Search for Vector-Like Quarks at the LHC Ester Amaral Simões Mestrado em Física Departamento de Física e Astronomia 2014 Orientador Dr. Nuno Filipe da Silva Fernandes de Castro, Investigador Auxiliar no Laboratório de Instrumentação e Física Experimental de Partículas Todas as correções determinadas pelo júri, e só essas, foram efetuadas. O Presidente do Júri, Porto, ______/______/_________ Any device in science is a window on to nature, and each new window contributes to the breadth of our view. Cecil Frank Powell. There is no excellent beauty that hath not some strangeness in the proportion. Sir Francis Bacon. 3 Acknowledgements First of all, my sincerest thanks to Dr. Nuno Castro, the most supportive and understanding supervisor a student can have. Thank you for all the hours spent teaching me how one can do Physics. And for this tremendously great opportunity for me. I thank my colleague and friend Juan Pedro Araque for all the support given to me, in particular with the analysis code and the limits derivation. It was precious to learn so many things from a great programmer like you! I thank the whole LIP-Minho team, in particular António Onofre, for all the valuable insight. To Miguel Fiolhais goes a special word of appreciation, for all the feedback and support given from as far as the other side of the Atlantic ocean! Also, a word of gratitude towards those who taught me Physics and Mathematics since the very beginning. It has been a pleasure to learn from all of you. A special word goes to Professor José Leonardo - my Physics and Chemistry teacher - thank you for presenting me the wonderful world of thoughts, engines and stars. I thank all my friends and colleagues over the years, the patient and the not so patient ones, for their guidance and the fruitful discussions we had. A word of appreciation and friendship goes to my dear companions André Patrício, Artur Sousa, Catarina Cosme and José Vieira. Last but not least, I thank my mother Filomena, my father Casimiro, my sister Alice, my brother Sancho and my grandmother Júlia for all the support given during the roughest of times. It wasn’t easy for you as well, I know. And to you, Tiago. You’ve put up with all the storms, always by my side. Thank you again. I acknowledge Laboratório de Instrumentação e Física Experimental de Partículas (LIP) and the Portuguese ATLAS group for the significant financial support provided through the grants Bolsa de Iniciação Científica - Projecto ATLAS/LIP - CERN/FP/123595/2011 and Bolsa de Investigação (licenciado) - Projecto Estratégico nºFCOMP-01-0124FEDER037290 (ref.: Pest-C/FIS/LA0007/2013). 4 Resumo Esta dissertação teve como objectivo a pesquisa da produção de pares de novos quarks não quirais, designados de quarks vectoriais, a partir da análise de dados colectados pelo detector ATLAS do LHC (Large Hadron Collider), localizado no CERN, no período de Abril a Dezembro de 2012, relativos a colisões protão-protão a uma energia de centro de massa de 8TeV, correspondendo a uma luminosidade integrada de 20.3±0.6fb≠1. Com uma hipotética quarta geração sequencial de quarks quirais a ser excluída por dados do LHC, os quarks vectoriais são uma das adições ao Modelo Padrão ainda permitida por dados experimentais, sendo considerados em vários modelos de nova Física. Neste trabalho foi estudado o decaimento do quark vectorial T(B) a dar origem a um bosão Z e a um quark top (bottom). Foi considerada uma topologia dileptónica, em que um par de leptões carregados possui uma massa invariante compatível com o decaimento de um bosão de gauge Z, e em que pelo menos dois jactos são classificados como provenientes de um quark b(b-tagged jets). Foram identificadas algumas variáveis potencialmente úteis na separação de sinal e fundo: os momentos lineares no plano transverso dos dois jactos b-tagged de momento transverso mais elevado, pT(b1) epT(b2), a soma escalar do momento transverso de todos os jactos, HT(jets), a massa invariante do quark vectorial Treconstruído, M(T), e a distribuição angular R(b1b2) entre os dois jactos b-tagged de momento transverso mais elevado. Estas variáveis foram usadas como input em três classificadores multivariacionais: um discriminante linear (LD), uma boosted decision tree (BDT) e uma rede neuronal (MLPBNN), que se determinou serem os classificadores com melhor performance. Não sendo observada nenhuma evidência para a existência de quarks pesados, os resultados obtidos antes e depois de uma análise multivariacional foram usados para colocar limites inferiores de massa de 625 GeV e 665 GeV (a 95% C.L.), respectivamente, para quarks Tem singletos de SU(2). Este último melhora o primeiro limite, derivado antes da aplicação de métodos multivariacionais, melhorando também o limite recentemente publicado pela Colaboração ATLAS. 5 Abstract The subject of this dissertation is the search for the pair production of new non-chiral quarks, known as vector-like quarks, through the analysis of data collected by the ATLAS detector of the LHC (Large Hadron Collider), located in CERN, in the data-taking period between April and December of 2012, corresponding to an integrated luminosity of 20.3±0.6fb≠1of pp collisions at a center-of-mass energy Ôs=8TeV. With an hypothetical fourth sequential generation of chiral quarks being excluded by LHC data, vector-like quarks are one of the additions to the Standard Model still allowed by experimental data, being considered by several new Physics models. In this work was studied the decay of a vector-like T(B)toaZboson and a top (bottom) quark. A dileptonic topology was considered, in which a pair of charged leptons has an invariant mass compatible with the decay of a Zgauge boson, and in which at least 2 jets are classified as coming from a b≠quark (b-tagged jets). Some variables, potentially useful in the separation of signal from background, were identified: the linear transverse momenta of the two higher transverse momentum b-tagged jets, pT(b1) epT(b2), the scalar sum of all the jets transverse momentum, HT(jets), the invariant mass of the reconstructed T,M(T), and the angular distribution R(b1b2) between the two higher-pTb-tagged jets. These discriminating variables were the input of three multivariate classifiers: a linear discriminant, a boosted decision tree (BDT) and a neural network (MLPBNN), categorized as the best performance classifiers. No evidence for a heavy quark signal is observed when selecting events with topologies sensitive to heavy quark pair-production via the strong interaction. The results obtained before and after a multivariate analysis were used to set lower mass limits of 625 GeV and 665 GeV (at 95% C.L.), respectively, on vector like Tquarks when assuming the SU(2) singlet hypothesis. The latter improves the former, derived before employing multivariate methods, improving also the limit recently published by the ATLAS Collaboration. 6 Contents 1 Introduction 18 2 Theoretical Context 21 2.1 The Standard Model of Particle Physics: an overview ........... 21 2.2 The Lagrangian for the Standard Electroweak Model ........... 22 2.3 Presenting Vector-like Quarks ........................ 24 2.3.1 Why are they called “vector-like” quarks? ............. 25 2.3.2 Models with Vector-like Quarks ................... 26 2.3.3 VLQs Representations and Couplings ................ 26 2.3.4 VLQs Production and Decay ..................... 27 3 Experimental Apparatus 34 3.1 CERN ..................................... 34 3.2 Large Hadron Collider ............................ 35 3.3 ATLAS Detector ............................... 36 3.4 Worldwide LHC Computing Grid ...................... 39 4 Building the Analysis: TæZt and BæZb 41 4.1 Data Sample .................................. 41 4.2 Trigger ..................................... 42 4.3 Presenting Primary Physics Objects ..................... 43 4.4 Signal Modeling ................................ 45 4.5 Background Modeling ............................. 47 4.6 Search Strategy and Event Selection .................... 48 4.7 Discriminating Variables ........................... 58 5 Multivariate Analysis with TMVA 67 5.1 Multivariate Analysis Classifiers outlined .................. 67 5.2 Training/testing MVA Classifiers ...................... 70 7 5.3 Applying MVA Classifiers .......................... 75 6 Results 78 6.1 Limits On the Singlet TQuark Pair-Production Hypothesis ....... 78 6.1.1 Before MVA .............................. 78 6.1.2 After MVA .............................. 79 7 Conclusions and Further Work 82 Bibliography 82 8 List of Figures 2.3.1 Observed lower limits at 95% C.L. on the mass of vector-like T(a) and B(b) quarks for ATLAS searches with 14.3fb≠1and 20.3fb≠1of 8 TeV data. ...................................... 29 2.3.2 Observed lower limits at 95% C.L. on the mass of vector-like T(a) and B(b) quarks for CMS searches with 19.5fb≠1and with 19.6fb≠1of 8 TeV data, respectively (extracted from [1, 2]). ............... 30 2.3.3 A representative diagram illustrating heavy quark pair production and vector-like decay modes (extracted from [3]). ............... 30 2.3.4 The pair production cross section versus quark mass as predicted by HATHOR [4] for pp collisions at Ôs=7TeV and 8 TeV. The bottom panel shows the 8TeV/7TeV cross section ratio (extracted from [5]). .. 31 2.3.5 Vector-like Tquark branching ratios (a) to the Wb,Zt, and Ht decay modes as a function of the Tquark mass, computed with PROTOS [6] for an SU(2) singlet and two types of doublets. Likewise, vector-like B quark branching ratios (b) to the Wt,Zb, and Hb decay modes for a singlet and two types of doublets (extracted from [3]). ........... 32 3.2.1 Scheme of the LHC experiments ATLAS, ALICE, CMS and LHCb; and preaccelerators PS (Proton Synchrotron) and SPS (Super Proton Synchrotron); figure extracted from [7]. .................... 36 3.3.1 Representation of ATLAS coordinate system: the side-A of the detector is defined as the one with positive z and side-C as that with negative z. The azimuthal angle „is measured around the beam axis, and the polar angle ◊is measured from the beam axis (figure extracted from [7]). ... 37 3.3.2 Cut-away view of the ATLAS detector. The dimensions of the detector are 25 m in height and 44 m in length. The overall weight of the detector is approximately 7000 tonnes (figure extracted from [8]). ......... 39 9 LHC Large Hadron Collider LHCb Large Hadron Collider beauty MC Monte Carlo MLP Multi-layer Perceptron MVA Multivariate Analysis NNLO Next-to-next-to-leading-order LO Leading Order PDF Parton Distribution Function PS Proton Synchrotron QCD Quantum Chromodynamics ROC Receiver Operating Characteristic RoI Region-of-Interest SCT Silicon Microstrip Trackers SM Standard Model SPS Super Proton Synchrotron SSB Spontaneous Symmetry Breaking SU Special Unitary SUSY Supersymmetry TMVA Toolkit for Multivariate Data Analysis TRT Transition Radiation Tracker UA1 Underground Area 1 UA2 Underground Area 2 VEV Vacuum Expectation Value 16 VLQ Vector-Like Quark WLCG Worldwide LHC Computing Grid 17 1 Introduction A centrepiece of the Standard Model of Particle Physics (SM), described by the SU(3)¢ SU(2) ¢U(1) gauge group, is the formulation of the electroweak interactions as arising from a spontaneously broken gauge symmetry. This hypothesis has been confirmed with incredible success by experimental physics programs over the past four decades, most notably by the LEP (Large Electron-Positron) and SLC (Stanford Linear Collider) collider programs [13,14]. Nevertheless, the nature of the symmetry breaking mechanism is not yet fully understood. The Higgs boson, as proposed within the frame of the Standard Model, is the simplest manifestation of the Englert-Brout-Higgs-Guralnik-Hagen-Kibble [15,16,17] mechanism. The ATLAS and CMS collaborations have discovered a convincing candidate for the Higgs boson with a mass around 126 GeV at the CERN Large Hadron Collider (LHC) [18,19]. Hence, the default electroweak symmetry breaking mechanism, whereby a weak isospin doublet of fundamental scalar fields obtains a vacuum expectation value, remains a valid assumption. Even though the Standard Model is currently the best description there is of the subatomic world, it is unlikely that it stands as the ultimate theory. It is of the uttermost importance to investigate what may lie beyond the SM and try to solve several unanswered questions, such as: how to explain the number of fermion generations and mass hierarchy? What is the origin of the matter-antimatter asymmetry? What is the nature of Dark Matter? Can we incorporate gravity in the SM? What is the mass of neutrinos, and do they follow Majorana or Dirac statistics? The Standard Model is generally regarded as a low-energy approximation of a more fundamental theory with new degrees of freedom and symmetries that would only manifest themselves at higher energies, i.e. we assume that the SM remains valid up to a cut-offscale . Indeed, the SM violates a concept of naturalness [20] when extrapolated to energies above the electroweak scale, as fine tuning is required to account for the quadratic mass-squared divergences of fundamental scalar fields (such as the Higgs). Hence, naturalness demands these divergences to be cancelled, typically at a scale below 1TeV. Models of physics beyond the SM (BSM models) typically address this issue by postulating a new symmetry, as in supersymmetry SUSY [21,22,23,24]. 18 In SUSY - a Bose-Fermi symmetry [25,26] - new states related to the SM fermions and bosons introduce new interactions (new symmetries) that cancel the quadratically divergent ones. This new symmetry could also be a spontaneously broken global symmetry of the extended theory, with the Higgs boson emerging as a pseudo-Nambu-Goldstone boson [27]. This “collective” symmetry breaking is the essential ingredient in Little Higgs [28,29] and Composite Higgs [30,31] models, which are weakly coupled extensions of the Standard Model with little or no fine tuning. These latter models (amongst many others) share one of the simplest additions to the Standard Model: the introduction of isosinglet vector-like quarks (VLQs) [32] - a strategy supported by several theoretical motivations [33,34,35]. Vector-like quarks are hypothetical color-triplet, spin-1 2 fermions, whose leftand right-handed chiral components have the same transformation properties under the weak-isospin gauge group SU(2), i.e. their leftand right-handed components have the same color and electroweak quantum numbers. Such quarks could mix with like-charge SM quarks [35,36,37,38], and the mixing of the SM top quark with a charge +2 3vector-like quark could play a role in regulating the divergence of the Higgs mass-squared. Hence, vector-like quarks emerge as an exciting subject in searches of new physics, since they are a characteristic feature of plenty non-supersymmetric natural models [39]. Furthermore, they are attracting a lot of attention since a fourth sequential generation of chiral quarks was excluded by experiments at the LHC [40], and by recent measurements for Higgs-mediated cross-sections [41,42], when combined with results of direct searches at the Large Hadron Collider [43,44]. Previous searches targetting a hypothetical fourth sequential generation of quarks were able to provide a vector-like quark interpretation [44]. Unlike chiral quarks, vector-like quarks are able to decay through neutral-current channels, since the GIM mechanism [45] ceases to operate with the addition of VLQs to the Standard Model. These extra heavy quarks, decaying through neutral-current channels, have been the aim of searches at the CERN Large Hadron Collider, by the ATLAS and CMS collaborations [46,47,48,49,50]. Since no evidence for a heavy quark signal was observed by these collaborations, the results obtained were used to set lower mass limits for the vector-like quarks in study [49,51,52]. Indeed, the CMS Collaboration published a vector-like Tquark search, setting lower mass limits in the range of 690 ≠780 GeV [1], at a 95% confidence level (C.L.). Furthermore, just recently, the ATLAS Collaboration published a vector-like quark search [3], in which results were used to set lower mass limits of 685 GeV and 755 GeV (at 95% C.L.) on vector like Bquarks, when assuming the SU(2) singlet and doublet hypotheses, respectively. Likewise, lower mass limits of 655 GeV and 735 GeV 19 (at 95% C.L.) were obtained for vector-like Tquarks when assuming the SU(2) singlet and doublet hypotheses, respectively, depending on the assumptions for the branching ratios. The present thesis is organized as follows: the SM and the addition of vector-like quarks to it are discussed in chapter 2; the experimental apparatus, including the ATLAS detector, is described in chapter 3; the construction of the analysis is described in chapter 4, the work with the multivariate techniques is explained in chapter 5and the results are presented in chapter 6. The conclusions of this work, as well as some future work ideas, are drawn in chapter 7. 20 2 Theoretical Context In this chapter, we briefly present and discuss the Standard Model of Particle Physics and the consequences of adding vector-like quarks to it. 2.1 The Standard Model of Particle Physics: an overview In 1961, Glashow [53] first proposed the idea that the electromagnetic and weak interactions may be unified in a gauge theory based on the group SU(2)¢U(1), which combines different massless chiral1states. Consider, for instance, a Universe in which quarks and leptons have no mass at all. At first, this could appear to be a surprising supposition. Nonetheless, the massless limit is where the present Standard Model begins. The seeming problem of generating masses in a manner consistent with gauge invariance was solved later by Weinberg and Salam, using the idea of “spontaneous symmetry breaking” (an expression coined by Baker & Glashow, in 1962), by introducing Higgs fields. The resulting theory, known as the Glashow-Weinberg-Salam model, was shown by ’t Hooft [54,55] to be a renormalizable quantum field theory. All these contributions combine to present us with what is known as the Glashow-Weinberg-Salam model gauge theory of the electroweak interactions, whose input fermionic degrees of freedom are massless spin one-half chiral particles. It has the group structure SU(2)L¢U(1)Y, where the SU(2)L,U(1)Yrepresent weak isospin and weak hypercharge, respectively. We define the hypercharge Yas Q=T3+1 2Y, in analogy with the original Gell-Mann-Nishijima [56,57] formula for strong interaction quantum numbers, where Qis the electric charge (in units of the positron charge, e) and T3is the third component of the weak isospin operator. The subscript “L” on SU(2)Lindicates that among fermions, only left-handed states transform nontrivially under weak isospin. In fact, only left-handed components 1Chirality is defined as the eigenvalue of “5(“5=i“0“1“2“3, in the Dirac basis); with “5=1corresponding to right-handedness, and “5=≠1to left-handedness, where leftand right-handed fermion fields may be written as: ÂL=1 2(1 ≠“5)Â,ÂR=1 2(1 + “5)Â. 21 are coupled in the charge changing sector, whereas right-handed components provide mass. The electroweak interactions that result from gauging SU(2) ¢U(1) reproduce all known phenomena (and predict new ones!), in particular the structure of neutral currents and the existence of gauge vector bosons, which have all been successfully verified experimentally. Aditionally, Quantum Chromodynamics (QCD) - the theory of strong interactions - was developed in parallel with the supracited model of weak interactions through the 60s and 70s. In 1964, Murray Gell-Mann and George Zweig independently suggested the existence of quarks with different flavors as the components of hadrons [58]. In 1965, Moo-Young Han with Yoichiro Nambu [59] and Oscar W. Greenberg [60] proposed an additional gauge degree of freedom, the color charge. Since each quark has now three possible colours (RGB: red, green and blue), we can describe any particular quark flavour by a three component field Â(x)=[Â(R, x),Â(G, x),Â(B,x)] and consider local gauge transformations where (x)is a 3◊3hermitian matrix operating on Â. These transformations can change the color and belong to the symmetry group SU(3)C. Now, to achieve local gauge invariance is required the introduction of eight massless gauge bosons - gluons - which carry pairs of colour labels. Quantum Chromodynamics reached its present form in 1973 with the discovery of asymptotic freedom of strong interactions by David Politzer [61,62] and David Gross, together with Frank Wilczek [63]. Combining QCD with the Glashow-Weinberg-Salam model gives an SU(3)C¢SU(2)L¢U(1)Y2 gauge invariant theory of the strong and electroweak forces, commonly known as the Standard Model of Particle Physics. 2.2 The Lagrangian for the Standard Electroweak Model3 All the pieces are now in place for presenting a model that is not simply an illustrative elegant “toy”, rather it appears to describe quite well the universe we inhabit. The standard electroweak model is based on the gauge group [64]SU(2) ¢U(1), with gauge bosons Wi µ,i=1,2,3, and Bµ, for the SU(2) and U(1) gauge groups, respectively, and 2The subscript “C” in SU(3) stands for color. 3For what comes next, our notation and conventions are as follows: The metric gµ‹in an inertial coordinate system has diagonal elements +≠≠≠; we use the Einstein’s summation convention over repeated indices; greek indices run over the four space-time inertial coordinate labels t, x, y, z; and unless otherwise indicated, c=~=1. 22 the corresponding gauge coupling constants gand gÕ4. The left-handed fermion fields of the ith fermion family transforms as doublets Âi=Q a ‹i l≠ iR band Q a ui dÕ iR bunder SU(2), where dÕ i©qjVijdj,Vis the Cabbibo-Kobayashi-Maskawa mixing matrix (which rules the mixing between quarks). The right-handed fields are SU(2) singlets. There is in Nature a replication of the fermion multiplets. Indeed, the number ngof fermion generations in the SM is not imposed by any symmetry principle. Experimentally, there is strong evidence that ng=3. So, the SM incorporates three fermion families (three quark generations and three lepton generations) and a single complex Higgs doublet = Q a + 0R b, which is introduced for mass generation5. After SSB (spontaneous symmetry breaking), the Lagrangian for the fermion fields, Âi, is given by [65]: LF=ÿ i ¯ Âi3i“µˆµ≠mi≠gmiH 2mW4Âi(2.2.1) ≠g 2Ô2ÿ i ¯ i“µ11≠“521T+W+ µ+T≠W≠ µ2i ≠eÿ i Qi¯ Âi“µAµÂi ≠g 2cos◊Wÿ i ¯ Âi“µ1gi V≠gi A“52ÂiZµ. The weak angle ◊W©arctan(gÕ/g), where g=e sin ◊Wand gÕ=e cos ◊W(eis the positron electric charge), is a parameter of the model. The following quantities are now defined: MW=A sin ◊W,A©Bcos ◊W+W3sin ◊Wis the (massless) photon field, whilst W±© (W1ûiW2)/Ô2and Z©≠Bsin ◊W+W3cos ◊Ware the massive charged and neutral weak boson fields, respectively. T+and T≠are the weak isospin raising and lowering operators, with T±=(T1+T2)/Ô2, where Ti=1 2·iand ·iare the Pauli matrices. The vector and axial-vector couplings are gi V©t3L(i)≠2Qisin2◊Wand gi A©t3L(i), where t3L(i)is the weak isospin of fermion i(+1 2for uiand ‹i;≠1 2for diand lirefer to table 2.1); Qiis the charge operator, it returns the charge value of Âiin units of e. 4For the strong interaction we would also have a similar description based on the SU(3) gauge group. 5When introducing a set of scalar fields , this set develops a U(1)em symmetric vacuum expectation value <>0so that we have the following pattern of symmetry breaking: SU(2)L◊ U(1)Y <>0 ≠æ U(1)em. Three of the original four SU(2 ◊U(1) gauge bosons acquire mass, while one (the photon) remains massless. 23 TT 31 2YQ ‹eL 1 2 1 2≠1 20 eL1 2≠1 2≠1 2≠1 uL1 2 1 2 1 6 2 3 dL1 2≠1 2 1 6≠1 3 eR00≠1≠1 uR00 2 3 2 3 dR00≠1 3≠1 3 Table 2.1: The electroweak quantum numbers for the first generation of quarks and leptons. The first term in LF(eq. 2.2.1) contains the Yukawa coupling of H6to Âi, and the usual free-field term, miis the mass of the ith fermion Âi. In non-minimal models it is also possible to include additional charged and neutral scalar Higgs fields. The second term in our Lagrangian describes the charged-current weak interaction [66,67]. For q2πM2 W, this term reduces to the four-fermion interaction7, with the Fermi constant given (at tree level) by GF/Ô2=g2/8M2 W. The third term represents the electromagnetic interaction (QED) and the last one is the weak neutral-current interaction. The Standard Model, as summarized by the Lagrangian in eq. 2.2.1, predicts a definite pattern of quark mixing: flavour-changing neutral currents (FCNC) are absent at tree level and suppressed at one loop by the GIM mechanism [45], with a branching ratio of the order of 10≠14, and the mixing in charged currents is given by the unitary CabbiboKobayashi-Maskawa (CKM) matrix [68]. 2.3 Presenting Vector-like Quarks Vector-like quarks present themselves as a very promising playground for searches of new physics. They are one of the simplest examples of extra (colored) fermions still allowed by experimental data. Vector-like quarks at the TeV scale are strongly motivated by (at least) two theoretical ideas, usually combined: they are required if the Higgs is a pseudo-Goldstone boson to induce electroweak symmetry breaking and account for the observed lightness of the Higgs [69,70,71], as they emerge as fermion ressonances in 6His the physical neutral scalar which is the only remaining part of after spontaneous symmetry breaking. A Yukawa coupling is the general term for an interaction between fermions and scalars of the form ¯ ÂÂ. 7Fermi’s theory involves a weak Lagrangian which is a product of four fermion fields: ¯ ÂpÂn¯ Âe‹. 24 flavour theories of partial compositeness [72,73]8. But how are these hipothetical new heavy fermions characterized? A fermion is defined to be vector-like if its leftand righthanded chiralities belong to the same representation of the symmetry group of the underlying theory: for the Standard Model, G©SU(3)c¢ SU(2)L¢U(1)Y. 2.3.1 Why are they called “vector-like” quarks? Vector-like quarks, as seen before, feature a striking characteristic: their left and right handed chiralites transform in the same way under the Standard Model (SM) gauge groups SU(3)c◊SU(2)L◊U(1)Y. But why are they called “vector-like”? A concise summary of the present knowledge of (charged) weak interactions is given by the following Lagrangian density[74]: LW=gWa(x)[Ja W(x)+ja W(x)] + h.c., (2.3.1) where the Ja W(x)is the quark weak current and ja W(x)is the lepton weak current, which are coupled to a massive charge vector field Wa(x). Now, if excluding the lepton charged currents, the Lagrangian density is of the form: LW=g Ô2ËJµ+W+ µ+Jµ≠W≠ µÈ,(2.3.2) Let us compare Standard Model chiral quarks with these vector-like quarks. The charged currents associated with chiral quarks are only left handed, i.e. Jµ+=Jµ+ L+Jµ+ R, with: Y _ ] _ [ Jµ+ L=¯uL“µdL=¯uL“µ(1 ≠“5)d=V≠A(vector-axial current) Jµ+ R=0 (2.3.3) On the other hand, vector-like quarks have both left and right handed charged currents: Jµ+=Jµ+ L+Jµ+ R=¯uL“µdL+¯uR“µdR=V, (2.3.4) which, unlike chiral quark currents, transform as a vector, henceforth justifying the designation attributed to these quarks. 8The quarks and leptons acquire a mass by mixing with composite fermions. 25 [GeV] T m 300 400 500 600 700 800 900 1000 Branching Ratio 0 0.2 0.4 0.6 0.8 1 Wb→T Zt→T Ht→T Wb→T Zt→T Ht→T SU(2) Singlet (X,T) Doublet (T,B) or (a) [GeV] B m 300 400 500 600 700 800 900 1000 Branching Ratio 0 0.2 0.4 0.6 0.8 1 Wt→B Zb→B Hb→B Wt→B Zb→B Hb→B Wt→B SU(2) Singlet (B,Y) Doublet (T,B) Doublet (b) Figure 2: Vector-like Tquark branching ratios (a) to the Wb,Zt, and Ht decay modes versus mass, computed with PROTOS [39] for an SU(2)singlet and two types of doublets. Likewise, vector-like B quark branching ratios (b) to the Wt,Zb, and Hb decay modes for a singlet and two types of doublets. The Xquark in an (X,T)doublet has charge +5/3, and theYquark in a (B,Y)doublet has charge 4/3. samples is set by the HATHOR prediction. The vector-like quarks were decayed in the charged- (W) and neutral-current (Z,H) modes assuming a 1/3 branching ratio for each. Arbitrary sets of branching ratios consistent with the three modes summing to unity are obtained by reweighting the samples using particle-level information. A SM Higgs boson with a mass of 125 GeV is assumed. The primary set of samples span quark masses between 350 GeV and 850 GeV in steps of 50 GeV and were produced assuming SU(2)singlet couplings. Additional samples were produced at two mass points (350 and 600 GeV) using SU(2)doublet couplings in order to confirm that the kinematic differences between singlet and doublet couplings are negligible in this analysis. The above samples were passed through a fast detector simulation [41], while additional samples with quark masses of 400, 600 and 800 GeV were also produced using full detector simulation [42] for validation. All signal samples were filtered at the generator level to require the presence of at least one electron or muon with pT>10 GeV and ||<2.8. 6 Background Modeling The SM backgrounds in this analysis are predicted primarily with simulated samples normalized to next-to-leading order or higher cross section calculations. Unless stated otherwise, all samples for SM processes are passed through a full detector simulation. Two leading-order multi-parton event generators, ALPGEN [43] and SHERPA [44], were compared at each stage of the analysis to provide a robust characterization of the dominant Z+jets background. The cross section normalization of both is set by the NNLO prediction calculated with the DYNNLO program [45]. In this note, the SHERPA predictions are shown throughout, as the statistical uncertainties when using these samples are significantly smaller than those associated with the ALPGEN samples, particularly in the final stages of the event selection. The ALPGEN Z+jets samples were produced using v2.13 with the CTEQ6L1 [46] PDF set and interfaced to PYTHIA [40] v6.421 for parton-shower and hadronization. Separate inclusive Z+jets and dedicated Z+c¯c+jets and Z+b¯ b+jets samples were simulated. Heavy flavor quarks in the former arise 5 Figure 2.3.5: Vector-like Tquark branching ratios (a) to the Wb,Zt, and Ht decay modes as a function of the Tquark mass, computed with PROTOS [6] for an SU(2) singlet and two types of doublets. Likewise, vector-like Bquark branching ratios (b) to the Wt,Zb, and Hb decay modes for a singlet and two types of doublets (extracted from [3]). 32 Despite the demanding environment of an hadron collider, such as the Large Hadron Collider (LHC), new heavy quark searches should be relatively clean, since these can be pair-produced through their gauge couplings to gluons (with a strength given by the strong coupling constant gs) with a large cross section and, being rather heavy, their signals can be distinguished from the backgrounds. 33 3 Experimental Apparatus In this chapter, the experimental infrastructure chain - the CERN laboratory (section 3.1), the Large Hadron Collider (LHC) (section 3.2), and the ATLAS detector (section 3.3) - is presented and briefly described. The functioning of the Worldwide LHC Computing Grid, in charge of the analysis of the LHC’s output data, is outlined in section 3.4. 3.1 CERN At the end of the Second World War, a handful of visionary scientists dreamed with the creation of an European atomic physics laboratory that would not only unite European scientists but also allow them to share the increasing costs of nuclear physics investigation. Among these enlightned pioneers were Raoul Dautry, Pierre Auger and Lew Kowarski in France, Edoardo Amaldi in Italy and Niels Bohr in Denmark. In 1952, eleven countries signed an agreement which established a provisional european council – the acronym CERN1was born. After some sessions of the provisional council, the CERN european laboratory was founded, in 1954, sitting astride the Franco-Swiss border near Geneva, and the exciting physics searches began! CERN has come a long way since its foundation in 1954. It was one of Europe’s first joint ventures and now has 21 member states. From the observation of the antideuteron in 19652, to the discovery of the W and Z bosons3the weak interactions mediators - 1The name CERN is derived from the acronym for the French "Conseil Européen pour la Recherche Nucléaire", or European Council for Nuclear Research, a provisional body founded in 1952 with the goal of establishing a world-class fundamental physics research organization in Europe. At that time, the physics research program focused on understanding the inside of the atom, hence the word "nuclear". 2The antideuteron was observed simultaneously by two teams, one led by Antonino Zichichi using the Proton Synchrotron (PS) at CERN, and the other led by Leon Lederman, using the Alternating Gradient Synchrotron (AGS) accelerator at the Brookhaven National Laboratory, New York . 3Carlo Rubbia and Simon van der Meer were the key scientists behind this discovery, having received the Nobel Prize in physics only a year after the discovery. Rubbia instigated the conversion of the SPS accelerator into a proton-antiproton collider and was spokesperson of the UA1 experiment while Van der Meer designed the stochastic cooling technique [91] crucial to the collider’s operation. 34 by the UA1 and UA2 (Underground Area 1 and 2) experiments at the SPS (Super Proton Synchrotron) in 1983, to the recent discovery (on the 4th July of 2012) of the long sought Higgs-consistent particle, with a mass around 126 GeV, by the ATLAS and CMS Collaborations at the Large Hadron Collider, the CERN laboratory is offering scientists and engineers all over the World the possibility to solve some of Nature’s most intriguing mysteries, probing the fundamental structure of the Universe. In addition to plenty scientific discoveries, some of which listed above, several technological breakthroughs took place at CERN, such as the invention of the World Wide Web by Sir Tim Berners-Lee, and the recent establishment of the global computer network infrastructure Worldwide LHC Computing Grid, which is discussed in section 3.4. 3.2 Large Hadron Collider At 10.28 am on 10 September 2008 a beam of protons was successfully steered around the 27-kilometre Large Hadron Collider (LHC) [92] for the first time. The Large Hadron Collider (LHC) at CERN extends the frontiers of particle physics with its unprecedented high energy and luminosity. It is the biggest and most powerful machine ever designed by mankind and was built in collaboration with over 10000 scientists and engineers from over 100 countries; lying in a tunnel 27 kilometres in circumference, at a depth ranging from 50m to 175m underground, beneath the Franco-Swiss border near Geneva, Switzerland. LHC’s tunnel was previously the functioning grounds of its predecessor: the lepton-positron collider LEP (Large Electron-Positron Collider). Inside the LHC, bunches of up to 1011 protons (p) collide 40 million times per second to provide several TeV proton-proton (pp) collisions at a design luminosity of 1034 cm≠2s≠1. The LHC also collides heavy ions (A), in particular lead nuclei, at 5.5TeV per nucleon pair, at a design luminosity of 1027 cm≠2s≠1. The LHC is currently in shutdown, in order to upgrade the accelerator to its design center-of-mass energy, Ôs=14TeV, resuming operations in early 2015, with run II of data-taking. The LHC contains two parallel beam pipes that intersect at four points, each containing a proton beam traveling in opposite directions around the circular tunnel. Each of the four collision points, depicted in fig. 3.2.1, correspond to one of the main LHC experiments: ATLAS (A Toroidal LHC ApparatuS), CMS (Compact Muon Solenoid), ALICE (A Large Ion Collider Experiment) and LHCb (Large Hadron Collider beauty). The LHC comprises more than one thousand dipole magnets, each 14.3meters long, to bend the beams in a circular trajectory, while an additional ≥400 quadrupole magnets 35 Figure 3.2.1: Scheme of the LHC experiments ATLAS, ALICE, CMS and LHCb; and preaccelerators PS (Proton Synchrotron) and SPS (Super Proton Synchrotron); figure extracted from [7]. are used to maintain the beams focused. These type-II superconducting magnets, made of copper-clad niobium-titanium (NbTi), operate at an average temperature of 1.9K, kept by approximately 96 tonnes of superfluid liquid helium He-II. The high interaction rates, radiation doses, particle multiplicities and energies, as well as the requirements for precision measurements that characterize the Large Hadron Collider, have definitely set new standards for the design of particle colliders. 3.3 ATLAS Detector The ATLAS (A Toroidal LHC ApparatuS) detector [8] is a general purpose particle physics detector that probes pp collisions at the LHC, identifying and measuring the momentum and energy of the particles created. This detector is nominally forwardbackward symmetric with respect to the interaction point, has a cilindrical geommetry covering a solid angle of ≥4fi, and consists of particle-tracking detectors (inner detector), electromagnetic and hadronic calorimeters, and a muon spectrometer. A cut-away view of the ATLAS detector is illustrated in fig. 3.3.2. 36 Figure 3.3.1: Representation of ATLAS coordinate system: the side-A of the detector is defined as the one with positive z and side-C as that with negative z. The azimuthal angle „is measured around the beam axis, and the polar angle ◊is measured from the beam axis (figure extracted from [7]). ATLAS uses a right-handed coordinate system (fig. 3.3.1) with its origin at the nominal interaction point (IP) in the centre of the detector, and the z-axis along the beam line. The x-axis points from the IP to the centre of the LHC ring, and the y-axis points upwards. Cylindrical coordinates (r, „)are used in the transverse plane, „being the azimuthal angle around the beam line. Observables labelled “transverse” are projected into the x≠yplane. The pseudorapidity is defined in terms of the polar angle ◊as h=≠ln tan(◊ 2) 4. The transverse momentum pT, the transverse energy ETand the missing transverse energy Emiss Tare defined in the x≠yplane. The distance Rin the pseudorapidityazimuthal angle space is defined as R=Ô÷2+„2. At small radii transverse to the beamline, approximately 1000 particles will emerge from the collision point every 50 ns within |÷|<2.5, creating a very large track density in the inner detector [93]. To achieve the momentum and vertex resolution requirements 4In the case of massive objects such as jets, the rapidity y=1 2ln[(E+pz)/(E≠pz)] is sometimes used. 37 imposed by the benchmark physics processes, high-precision measurements must be made with fine detector granularity. Pixel and silicon microstrip (SCT) trackers, used in conjunction with gas-filled straw tubes of the Transition Radiation Tracker (TRT) for larger radii, offer these features. The ID (inner detector) is surrounded by a thin superconducting solenoid which provides a 2T magnetic field, and by high-granularity liquid-argon (LAr) sampling electromagnetic calorimetry. The electromagnetic (EM) calorimeters employ lead absorbers and use liquid argon as the active medium. The barrel EM calorimeter covers |÷|<1.5and the end-cap EM calorimeters 1.4<|÷|<3.2. While the electromagnetic calorimeter was designed to identify and measure the energy of the particles that interact through the electromagnetic force, the hadronic calorimeter absorbs the energy of particles that interact via the strong force, after crossing the electromagnetic calorimeter, i.e. the particle shower resulting from the hadronization of the quarks (also known as jet). Hadronic calorimetry in the region |÷|<1.7is achieved using steel absorbers and scintillating tiles as the active medium. Liquid argon calorimetry with copper absorbers is employed in the hadronic end-cap calorimeters, which cover the region 1.5<|÷|<3.2. Forward liquid argon calorimeters employing copper and tungsten absorbers cover the region 3.1<|÷|<4.9. The muon spectrometer measures the deflection of muons with |÷|<2.7using multiple layers of high-precision tracking chambers located in a toroidal field of approximately 0.5T and 1T in the central and end-cap regions, respectively. The muon spectrometer is also instrumented with separate trigger chambers covering |÷|<2.4. ATLAS makes use of a trigger system with three distinct levels: L1, L2 and the event filter. Each trigger level refines the decisions made at the previous level, applying additional selection criteria if necessary. The L1 trigger searches for high transversemomentum muons, electrons, photons, jets, and ·≠leptons decaying into hadrons, as well as large missing and total transverse energy. In each event, the first-level trigger also defines Regions-of-Interest (RoI’s), recording sets of coordinates in ÷and „of these RoI’s within the detector. The RoI data include information on the type of feature identified and the criteria passed, e.g. a threshold. This information is subsequently used by the high-level trigger. L1 is implemented in custom electronics, using a subset of the detector information to reduce the event rate to a design value of 75 kHz. The secondlevel trigger selection is seeded by the RoI information provided by the L1 trigger over a dedicated data path. L2 selections use all the available detector data within the RoI’s (approximately 2% of the total event data), decreasing the trigger rate to approximately 3.5kHz. The last step of the event selection is performed by the event filter, which 38 Figure 3.3.2: Cut-away view of the ATLAS detector. The dimensions of the detector are 25 m in height and 44 m in length. The overall weight of the detector is approximately 7000 tonnes (figure extracted from [8]). reduces the event rate to approximately 200 Hz. The general performance goals for the ATLAS detector are summarized in table 3.1. 3.4 Worldwide LHC Computing Grid The Worldwide LHC Computing Grid (WLCG) project is a global network of more than 170 computing centres in 40 countries, linking up national and international grid infrastructures and designed to analyze the ≥30 Petabytes (30 million Gigabytes) of data annually generated at the LHC [94]. The data from the LHC experiments is distributed around the globe, according to a four-tiered model. Data coming from the experiment data acquisition systems is written to tape in the CERN Tier-0 facility, and a second copy of the raw data is simultaneously provided to the Tier-1 centers, in Europe, Asia, and North America, via dedicated 10 Gb/s links. Subsequently, the Tier-1 centers make data available to more than 150 Tier-2 centers, each consisting of one or several collaborating computing facilities able to store enough data and provide adequate computing power for the required analysis tasks. Individual scientists can access and further process the data through Tier-3 computing 39 Detector component Required resolution ÷coverage Measurement Trigger Tracking ‡pT/pT=0.05% ◊pTü1% |÷|<2.5≠ EM calorimetry ‡E/E =10%/ÔEü0.7% |÷|<3.2|÷|<2.5 Hadronic calorimetry (jets) Barrel and end-cap ‡E/E =50%/ÔEü3% |÷|<3.2|÷|<3.2 Forward ‡E/E =100%/ÔEü10% 3.1<|÷|<4.93.1<|÷|<4.9 Muon spectrometer ‡pT/pT=10%at pT=1TeV |÷|<2.7|÷|<2.4 Table 3.1: General performance goals of the ATLAS detector (extracted from [8,12]). For high-pTmuons, the muon spectrometer performance is independent of the inner-detector system. The unit employed for Eand pTis GeV. resources, which consist of local clusters. As an example of the data-processing chain, the analysis of the data presented in this dissertation involved the CERN Tier-0 facility (the origin of the raw data), the processing of LHC data at the PIC (Barcelona) Tier-1 center, local facilities in Coimbra and Lisbon (Portuguese ATLAS group Tier-2) and the cluster at Universidade do Minho (Braga), a Tier-3 facility. 40 4 Building the Analysis: TæZt and BæZb This chapter is devoted to the construction of the analysis, starting with the review of the results recently published by the ATLAS Collaboration [3]. This search analysis is focused on the pair production of new heavy quarks that decay to a Zboson and a third generation Standard Model quark. In the case of a new charge +2/3quark (T), the decay targeted is TæZt , while the decay targeted for a new charge ≠1/3quark (B) is BæZb. A dileptonic topology was considered, with exactly 2 leptons, in which a pair of charged leptons has an invariant mass compatible with the decay of a Zgauge boson, and in which at least 2 jets are classified as coming from a b≠quark (b-tagged jets). In the final stages of the event selection is required a high-pTZboson and a high value of HT(jets)1. 4.1 Data Sample The data analysed in this search were collected with the ATLAS detector, at the CERN Large Hadron Collider, between April and December of 2012 during LHC proton-proton (pp) collisions at Ôs=8TeV and correspond to an integrated luminosity of 20.3± 0.6fb≠1[93]. Figure 4.1.1 illustrates the total integrated luminosity as a function of time, in 2011 and 2012. Fig. 4.1.2 illustrates the luminosity-weighted distribution of the mean number of interactions per bunch crossing for 2012 (full pp collisions dataset). The mean value of µhere is <µ>=20.7, and corresponds to the mean of the Poisson distribution on the number of interactions per crossing for each bunch. It is calculated from the instantaneous luminosity per bunch as µ=(Lbunch ◊‡inel)/(nbunch ◊fr), where Lbunch is the instantaneous luminosity per bunch, svinel is the inelastic cross section which is 1The HT(jets) is defined as the scalar sum of the transverse momenta, qpT, of all the jets. 41 the CT10 PDF set. Parton shower and hadronization are performed with PYTHIA. The other small Standard Model background processes modeled with simulation include diboson, single top, t¯ t+W/Z, and W+jets processes. The diboson processes (WW, WZ and ZZ) are simulated with ALPGEN [123], another leading-order multi-parton event generator, interfaced to HERWIG [124] for parton shower and hadronization, and normalized to NLO cross section predictions [125]. Samples generated with MC@NLO [126] interfaced to HERWIG are used to estimate the Wtand s≠channel single top processes, while ACERMC [127] interfaced to PYTHIA is used to estimate the t-channel process. The single top processes are normalized to NLO cross sections [128]. The t¯ t+W/Z processes are generated with MADGRAPH [129], with parton shower and hadronization performed with PYTHIA, and also normalized to NLO cross sections [130]. For the production method of the W+jets samples refer to [3]. The multi-jet background is estimated using data samples satisfying the nominal trigger requirements but enriched in fake leptons obtained by requiring that both leptons fail the standard identification requirements. Other requirements are applied to reduce DrellYan and t¯ tcontamination. The multi-jet estimate is then obtained by applying the same kinematic selection to these samples as the nominal data sample with a normalization determined at the preselection level to account for the difference between data and all other backgrounds in the dilepton mass region between 50 and 75 GeV. In both the ee and mm channels, the difference is comparable or smaller than the uncertainty on all other backgrounds. No multi-jet events are predicted to pass the final event selection, but the estimate in the earlier stages of the analysis has a small influence on the data-driven Z+jets corrections, which was found to be negligible [3]. 4.6 Search Strategy and Event Selection At a first selection level is required that events contain a Zboson candidate and at least 2jets(Z+Ø2jets). Zboson candidates are formed if the invariant mass of same flavor and opposite charge lepton pairs (electron or muon)2differs from the known value for the Zboson mass (≥91 GeV [65]) by less than 10 GeV (Zcandidate invariant mass window). In order to better understand the selection cuts applied in the analysis, unit-normalized distributions of simulated signal and background events are presented in fig. 4.6.1, where 2One of the Zboson decay channels is Zæl¯ l,wherelstands for lepton. In this work lstands only for electrons or muons. 48 Z+Ø2jets Ø2b-jets pT(Z)>150 GeV HT(jets) >600 GeV TTS22.2±0.412.1±0.310.0±0.3 8.5±0.2 BBS36.7±0.618.7±0.416.5±0.414.2±0.3 Z+light 281776.3±1747.3298.8±128.8 5.6±1.0 0.1±0.1 Z+charm 207629.1±611.6598.1±30.857.6±3.2 3.9±0.6 Z+bottom 55372.6±104.74420.1±27.7380.8±4.819.4±1.0 t¯ t5982.1±42.62185.5±25.433.1±3.2 4.6±1.2 Other background 8643.9±29.4274.3±6.341.5±1.7 4.0±0.5 Total background 559403.9±1854.97776.9±137.8518.6±6.932.1±1.7 Data 560131 7790 542 31 Table 4.1: Listed are the predicted and observed number of events (ee+µµ channel), and the statistical uncertainties associated, after the indicated selection levels, for reference BBSand TTSsignal yields assuming mB/T =650GeV and SU(2) singlet branching ratios. SM backgrounds yields are listed by category, as well as the combined total. The events for the rightmost three selection levels contain at least two b-tagged jets (signal region). panels (a) and (b) display the jet and b-tagged jet multiplicity, and panels (c) and (d) present the pT(Z) and HT(jets)distributions, before applying a selection cut based on each of them, respectively. The following remarks apply to all the distributions shown throughout this chapter: the reference signals displayed correspond to BB and TT production assuming SU(2) singlet quarks with a mass of 650GeV. The hatched bands in the upper and lower panels represent the total background uncertainty; the leftmost bin in each histogram contains underflow events, and the rightmost bin contains overflow events. The kinematic distributions for the leptons and the Zboson candidate are plotted in figs. 4.6.2-4.6.3 and figs. 4.6.4-4.6.5. In fig. 4.6.6 is presented the b-tagged jets multiplicity. In table 4.1 is listed the predicted and observed number of events (ee +µµ channel) for the cut-flow implemented in this study, for reference BBSand TTSsignal yields assuming mB/T =650GeV and SU(2) singlet branching ratios. SM backgrounds yields are listed by category, as well as the combined total. All the values in the table must coincide with the ones in the upper captions of the distributions at the same selection level, concerning the number of signal, background and data events, to ensure the consistency of our study. Events passing the Z+Ø2jets selection are then separated according to the number of b-tagged jets in the event (Ntag). Vector-like quark pair-production signal events are expected to yield at least two b-jets (Ntag Ø2), whether produced directly from a heavy 49 Jet Multiplicity 0 2 4 6 8 10 12 Fraction of events -4 10 -3 10 -2 10 -1 10 1 10 ATLAS Work in Progress Simulation = 8 TeVs Backgrounds (650 GeV) S BB (650 GeV) S TT (a) b-tagged jet multiplicity 0 1 2 3 4 5 Fraction of events -4 10 -3 10 -2 10 -1 10 1 10 ATLAS Work in Progress Simulation = 8 TeVs Backgrounds (650 GeV) S BB (650 GeV) S TT (b) (Z) [GeV] T p 0 100 200 300 400 500 600 700 800 Fraction of events / 40 GeV -4 10 -3 10 -2 10 -1 10 1 10 ATLAS Work in Progress Simulation = 8 TeVs Backgrounds (650 GeV) S BB (650 GeV) S TT (c) ) [GeV] jet T (pΣ= T H 0 200 400 600 800 100012001400160018002000 Fraction of events / 40 GeV -4 10 -3 10 -2 10 -1 10 1 10 ATLAS Work in Progress Simulation = 8 TeVs Backgrounds (650 GeV) S BB (650 GeV) S TT (d) Figure 4.6.1: Unit-normalized distributions in the ee+µµ channel. Panel (a) displays the jet multiplicity, before requiring for 2 jets (after only requiring a Zboson candidate); panel (b) presents the b-tagged jets multiplicity, before requiring for two b-tagged jets (after a Z+Ø2jets selection); panels (c) and (d) present the pT(Z) and HT(jets)distributions, before a pT(Z)>150 GeV and HT(jets) >600 GeV selection, respectively. The filled histogram corresponds to SM backgrounds, while the red and blue solid lines correspond to the T¯ Tand B¯ Bsignal, respectively, assuming a heavy quark mass of 650 GeV with vector-like singlet branching ratios. 50 Lepton E [GeV] 0 200 400 600 800 1000 1200 1400 1600 1800 2000 entries/bin 100 200 300 400 500 600 700 3 10× =1120262 D N =1118807.9 B N =73.4 BBS N =44.4 TTS N ATLAS Work in Progress = 8 TeVs -1 Ldt = 20.3 fb ∫ µµee + 2 b-tags, cut 3≥ data 2012 Z+light Z+charm Z+bottom tt Other bck. (650 GeV) S BB (650 GeV) S TT Uncertainty Lepton E [GeV] 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Data/MC 0.5 1 1.5 (a) Lepton E [GeV] 0 200 400 600 800 1000 1200 1400 1600 1800 2000 entries/bin -1 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 =1120262 D N =1118807.9 B N =73.4 BBS N =44.4 TTS N ATLAS Work in Progress = 8 TeVs -1 Ldt = 20.3 fb ∫ µµee + 2 b-tags, cut 3≥ data 2012 Z+light Z+charm Z+bottom tt Other bck. (650 GeV) S BB (650 GeV) S TT Uncertainty Lepton E [GeV] 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Data/MC 0.5 1 1.5 (b) [GeV] T Lepton p 0 100 200 300 400 500 600 700 800 entries/bin 200 400 600 800 1000 3 10× =1120262 D N =1118807.9 B N =73.4 BBS N =44.4 TTS N ATLAS Work in Progress = 8 TeVs -1 Ldt = 20.3 fb ∫ µµee + 2 b-tags, cut 3≥ data 2012 Z+light Z+charm Z+bottom tt Other bck. (650 GeV) S BB (650 GeV) S TT Uncertainty [GeV] T Lepton p 0 100 200 300 400 500 600 700 800 Data/MC 0.5 1 1.5 (c) [GeV] T Lepton p 0 100 200 300 400 500 600 700 800 entries/bin -1 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 =1120262 D N =1118807.9 B N =73.4 BBS N =44.4 TTS N ATLAS Work in Progress = 8 TeVs -1 Ldt = 20.3 fb ∫ µµee + 2 b-tags, cut 3≥ data 2012 Z+light Z+charm Z+bottom tt Other bck. (650 GeV) S BB (650 GeV) S TT Uncertainty [GeV] T Lepton p 0 100 200 300 400 500 600 700 800 Data/MC 0.5 1 1.5 (d) Figure 4.6.2: The Eand pTdistributions for leptons, in the ee +µµ channel, after requiring Z+Ø2jets. 51 ηLepton -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 entries/bin 10000 20000 30000 40000 50000 60000 =1120262 D N =1118807.9 B N =73.4 BBS N =44.4 TTS N ATLAS Work in Progress = 8 TeVs -1 Ldt = 20.3 fb ∫ µµee + 2 b-tags, cut 3≥ data 2012 Z+light Z+charm Z+bottom tt Other bck. (650 GeV) S BB (650 GeV) S TT Uncertainty ηLepton -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 Data/MC 0.5 1 1.5 (a) φLepton -3 -2 -1 0 1 2 3 entries/bin 5000 10000 15000 20000 25000 30000 35000 40000 45000 =1120262 D N =1118807.9 B N =73.4 BBS N =44.4 TTS N ATLAS Work in Progress = 8 TeVs -1 Ldt = 20.3 fb ∫ µµee + 2 b-tags, cut 3≥ data 2012 Z+light Z+charm Z+bottom tt Other bck. (650 GeV) S BB (650 GeV) S TT Uncertainty φLepton -3 -2 -1 0 1 2 3 Data/MC 0.5 1 1.5 (b) Figure 4.6.3: The ÷and „distributions for leptons, in the ee+µµ channel, after requiring Z+Ø2jets. quark decay, the decay of a top quark, or the decay of a Higgs boson. Furthermore, in order to effectively suppress the existent large Z+jets background, events are required to contain at least two b-tagged jets. Hence, to test the signal plus background hypothesis, it is useful to categorize events in two main regions: those belonging to the signal region, with Ntag Ø2; and the ones with Ntag <2, defining the control regions, whose purpose is to validate the modeling of the backgrounds. Indeed, analysing the signal and background event content listed in table 4.1, after requiring a Zboson candidate and at least two jets, where Ntag =0, it is straightforward to see that this is a background dominated region: there are only a few dozens of signal events (BBSand TTS), when compared to a total of approximately 5◊105background events. On the other hand, the ratio between the number of signal and background events is much larger for the signal region, after requiring pT(Z)>150 GeV: there are approximately three dozens of signal events, while the number of total background events is now reduced for ≥500 events. Figs. 4.6.7-4.6.8 are depicted the pTdistributions for the two higher-pTb-tagged jets, after a Z+Ø2jets, further requiring at least two b-tagged jets. The distribution of the transverse momentum of the Zboson candidate is also shown in fig. 4.6.9, at the same selection level, for Ntag =1and Ntag Ø2; refer also to table 4.1. 52 M(Z) [GeV] 82 84 86 88 90 92 94 96 98 100 entries/bin 10000 20000 30000 40000 50000 60000 =560131 D N =559403.9 B N =36.7 BBS N =22.2 TTS N ATLAS Work in Progress = 8 TeVs -1 Ldt = 20.3 fb ∫ µµee + 2 b-tags, cut 3≥ data 2012 Z+light Z+charm Z+bottom tt Other bck. (650 GeV) S BB (650 GeV) S TT Uncertainty M(Z) [GeV] 82 84 86 88 90 92 94 96 98 100 Data/MC 0.5 1 1.5 (a) M(Z) [GeV] 82 84 86 88 90 92 94 96 98 100 entries/bin -1 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 =560131 D N =559403.9 B N =36.7 BBS N =22.2 TTS N ATLAS Work in Progress = 8 TeVs -1 Ldt = 20.3 fb ∫ µµee + 2 b-tags, cut 3≥ data 2012 Z+light Z+charm Z+bottom tt Other bck. (650 GeV) S BB (650 GeV) S TT Uncertainty M(Z) [GeV] 82 84 86 88 90 92 94 96 98 100 Data/MC 0.5 1 1.5 (b) E(Z) [GeV] 0 200 400 600 800 1000 1200 1400 1600 1800 2000 entries/bin 50 100 150 200 250 300 3 10× =560131 D N =559403.9 B N =36.7 BBS N =22.2 TTS N ATLAS Work in Progress = 8 TeVs -1 Ldt = 20.3 fb ∫ µµee + 2 b-tags, cut 3≥ data 2012 Z+light Z+charm Z+bottom tt Other bck. (650 GeV) S BB (650 GeV) S TT Uncertainty E(Z) [GeV] 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Data/MC 0.5 1 1.5 (c) E(Z) [GeV] 0 200 400 600 800 1000 1200 1400 1600 1800 2000 entries/bin -1 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 =560131 D N =559403.9 B N =36.7 BBS N =22.2 TTS N ATLAS Work in Progress = 8 TeVs -1 Ldt = 20.3 fb ∫ µµee + 2 b-tags, cut 3≥ data 2012 Z+light Z+charm Z+bottom tt Other bck. (650 GeV) S BB (650 GeV) S TT Uncertainty E(Z) [GeV] 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Data/MC 0.5 1 1.5 (d) (Z) [GeV] T p 0 100 200 300 400 500 600 700 800 entries/bin 50 100 150 200 250 300 350 3 10× =560131 D N =559403.9 B N =36.7 BBS N =22.2 TTS N ATLAS Work in Progress = 8 TeVs -1 Ldt = 20.3 fb ∫ µµee + 2 b-tags, cut 3≥ data 2012 Z+light Z+charm Z+bottom tt Other bck. (650 GeV) S BB (650 GeV) S TT Uncertainty (Z) [GeV] T p 0 100 200 300 400 500 600 700 800 Data/MC 0.5 1 1.5 (e) (Z) [GeV] T p 0 100 200 300 400 500 600 700 800 entries/bin -1 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 =560131 D N =559403.9 B N =36.7 BBS N =22.2 TTS N ATLAS Work in Progress = 8 TeVs -1 Ldt = 20.3 fb ∫ µµee + 2 b-tags, cut 3≥ data 2012 Z+light Z+charm Z+bottom tt Other bck. (650 GeV) S BB (650 GeV) S TT Uncertainty (Z) [GeV] T p 0 100 200 300 400 500 600 700 800 Data/MC 0.5 1 1.5 (f) Figure 4.6.4: Distributions for the Zboson candidate, in the ee +µµ channel, after requiring Z+Ø2jets. Panels (a) and (b) show the invariant mass, M(Z), panels (c) and (d) show the energy E, while (e) and (f) show the transverse momentum, pT(Z). 53 (Z) η -6 -4 -2 0 2 4 6 entries/bin 10000 20000 30000 40000 50000 =560131 D N =559403.9 B N =36.7 BBS N =22.2 TTS N ATLAS Work in Progress = 8 TeVs -1 Ldt = 20.3 fb ∫ µµee + 2 b-tags, cut 3≥ data 2012 Z+light Z+charm Z+bottom tt Other bck. (650 GeV) S BB (650 GeV) S TT Uncertainty (Z) η -6 -4 -2 0 2 4 6 Data/MC 0.5 1 1.5 (a) (Z) φ -3 -2 -1 0 1 2 3 entries/bin 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 22000 24000 =560131 D N =559403.9 B N =36.7 BBS N =22.2 TTS N ATLAS Work in Progress = 8 TeVs -1 Ldt = 20.3 fb ∫ µµee + 2 b-tags, cut 3≥ data 2012 Z+light Z+charm Z+bottom tt Other bck. (650 GeV) S BB (650 GeV) S TT Uncertainty (Z) φ -3 -2 -1 0 1 2 3 Data/MC 0.5 1 1.5 (b) Figure 4.6.5: The ÷and „distributions for the Zboson candidate, in the ee+µµ channel, after requiring Z+Ø2jets. b-jet Multiplicity 0 1 2 3 4 5 6 7 8 9 entries/bin -1 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 =560131 D N =559403.9 B N =36.7 BBS N =22.2 TTS N ATLAS Work in Progress = 8 TeVs -1 Ldt = 20.3 fb ∫ µµee + 2 b-tags, cut 3≥ data 2012 Z+light Z+charm Z+bottom tt Other bck. (650 GeV) S BB (650 GeV) S TT Uncertainty b-jet Multiplicity 0 1 2 3 4 5 6 7 8 9 Data/MC 0.5 1 1.5 (a) Figure 4.6.6: Distribution of b-tagged jets multiplicity, in the ee +µµ channel, after requiring Z+Ø2jets. 54 [GeV] T p 1 b-Jet 0 100 200 300 400 500 600 700 800 entries/bin 1000 2000 3000 4000 5000 6000 =7790 D N =7776.9 B N =18.7 BBS N =12.1 TTS N ATLAS Work in Progress = 8 TeVs -1 Ldt = 20.3 fb ∫ µµee + 2 b-tags, cut 4≥ data 2012 Z+light Z+charm Z+bottom tt Other bck. (650 GeV) S BB (650 GeV) S TT Uncertainty [GeV] T p 1 b-Jet 0 100 200 300 400 500 600 700 800 Data/MC 0.5 1 1.5 (a) [GeV] T p 1 b-Jet 0 100 200 300 400 500 600 700 800 entries/bin -1 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 =7790 D N =7776.9 B N =18.7 BBS N =12.1 TTS N ATLAS Work in Progress = 8 TeVs -1 Ldt = 20.3 fb ∫ µµee + 2 b-tags, cut 4≥ data 2012 Z+light Z+charm Z+bottom tt Other bck. (650 GeV) S BB (650 GeV) S TT Uncertainty [GeV] T p 1 b-Jet 0 100 200 300 400 500 600 700 800 Data/MC 0.5 1 1.5 (b) Figure 4.6.7: The pTdistributions of the highest-pTb-tagged jet, in the ee+µµ channel, after requiring Z+Ø2jets and Ntag Ø2. [GeV] T p 2 b-Jet 0 100 200 300 400 500 600 700 800 entries/bin 1000 2000 3000 4000 5000 6000 =7790 D N =7776.9 B N =18.7 BBS N =12.1 TTS N ATLAS Work in Progress = 8 TeVs -1 Ldt = 20.3 fb ∫ µµee + 2 b-tags, cut 4≥ data 2012 Z+light Z+charm Z+bottom tt Other bck. (650 GeV) S BB (650 GeV) S TT Uncertainty [GeV] T p 2 b-Jet 0 100 200 300 400 500 600 700 800 Data/MC 0.5 1 1.5 (a) [GeV] T p 2 b-Jet 0 100 200 300 400 500 600 700 800 entries/bin -1 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 =7790 D N =7776.9 B N =18.7 BBS N =12.1 TTS N ATLAS Work in Progress = 8 TeVs -1 Ldt = 20.3 fb ∫ µµee + 2 b-tags, cut 4≥ data 2012 Z+light Z+charm Z+bottom tt Other bck. (650 GeV) S BB (650 GeV) S TT Uncertainty [GeV] T p 2 b-Jet 0 100 200 300 400 500 600 700 800 Data/MC 0.5 1 1.5 (b) Figure 4.6.8: The pTdistributions of the second higher-pTb-tagged jet, in the ee +µµ channel, after requiring after requiring Z+Ø2jets and Ntag Ø2. 55 (Z) [GeV] T p 0 100 200 300 400 500 600 700 800 entries/bin 5000 10000 15000 20000 25000 30000 =51291 D N =51299.1 B N =13.6 BBS N =7.9 TTS N ATLAS Work in Progress = 8 TeVs -1 Ldt = 20.3 fb ∫ µµee + 1 b-tag, cut 4 data 2012 Z+light Z+charm Z+bottom tt Other bck. (650 GeV) S BB (650 GeV) S TT Uncertainty (Z) [GeV] T p 0 100 200 300 400 500 600 700 800 Data/MC 0.5 1 1.5 (a) (Z) [GeV] T p 0 100 200 300 400 500 600 700 800 entries/bin -1 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 =51291 D N =51299.1 B N =13.6 BBS N =7.9 TTS N ATLAS Work in Progress = 8 TeVs -1 Ldt = 20.3 fb ∫ µµee + 1 b-tag, cut 4 data 2012 Z+light Z+charm Z+bottom tt Other bck. (650 GeV) S BB (650 GeV) S TT Uncertainty (Z) [GeV] T p 0 100 200 300 400 500 600 700 800 Data/MC 0.5 1 1.5 (b) (Z) [GeV] T p 0 100 200 300 400 500 600 700 800 entries/bin 500 1000 1500 2000 2500 3000 3500 4000 4500 =7790 D N =7776.9 B N =18.7 BBS N =12.1 TTS N ATLAS Work in Progress = 8 TeVs -1 Ldt = 20.3 fb ∫ µµee + 2 b-tags, cut 4≥ data 2012 Z+light Z+charm Z+bottom tt Other bck. (650 GeV) S BB (650 GeV) S TT Uncertainty (Z) [GeV] T p 0 100 200 300 400 500 600 700 800 Data/MC 0.5 1 1.5 (c) (Z) [GeV] T p 0 100 200 300 400 500 600 700 800 entries/bin -1 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 =7790 D N =7776.9 B N =18.7 BBS N =12.1 TTS N ATLAS Work in Progress = 8 TeVs -1 Ldt = 20.3 fb ∫ µµee + 2 b-tags, cut 4≥ data 2012 Z+light Z+charm Z+bottom tt Other bck. (650 GeV) S BB (650 GeV) S TT Uncertainty (Z) [GeV] T p 0 100 200 300 400 500 600 700 800 Data/MC 0.5 1 1.5 (d) Figure 4.6.9: The pTdistribution for the Zboson candidate, in the ee +µµ channel, after requiring Z+Ø2jets , Ntag =1(upper panel) and Ntag Ø2(down panel). 56 ) [GeV] jet T (pΣ= T H 0 200 400 600 800 1000 1200 1400 1600 1800 2000 entries/bin 200 400 600 800 1000 =3652 D N =3686.0 B N =11.7 BBS N =6.5 TTS N ATLAS Work in Progress = 8 TeVs -1 Ldt = 20.3 fb ∫ µµee + 1 b-tag, cut 5 data 2012 Z+light Z+charm Z+bottom tt Other bck. (650 GeV) S BB (650 GeV) S TT Uncertainty ) [GeV] jet T (pΣ= T H 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Data/MC 0.5 1 1.5 (a) ) [GeV] jet T (pΣ= T H 0 200 400 600 800 1000 1200 1400 1600 1800 2000 entries/bin 20 40 60 80 100 120 140 =542 D N =518.6 B N =16.5 BBS N =10.0 TTS N ATLAS Work in Progress = 8 TeVs -1 Ldt = 20.3 fb ∫ µµee + 2 b-tags, cut 5≥ data 2012 Z+light Z+charm Z+bottom tt Other bck. (650 GeV) S BB (650 GeV) S TT Uncertainty ) [GeV] jet T (pΣ= T H 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Data/MC 0.5 1 1.5 (b) Figure 4.6.10: The HT(jets)distribution, in the ee+µµ channel, after requiring pT(Z)> 150 GeV; for Ntag =1(a) and Ntag Ø2(b). The extraction of a T¯ Tand B¯ Bsignal in the presence of a large background can be boosted by knowing that vector-like quarks T/B are heavy, hence produced with relatively low momenta. Because of this, their decay products are often emitted with large momenta at large angles to the initial beam direction. This naturally defines a signal region that is characterized by a high-pTZboson, which justifies an additional requirement: pT(Z)>150 GeV. This requirement on the minimum transverse momentum of the Zboson is common in searches for heavy quarks (refer to [37] and experimental results in [52]), since it largely reduces the dominant t¯ tbackground in the signal region Ntag Ø2. Indeed, when analysing panel (c) in fig. 4.6.1, it is clear that there is an advantage in cutting the pTnear the 150 GeV, since there is a significant portion of the background that will not have to be dealt with. Signal events from VLQ pair production often produce several energetic jets (as seen in the jet-multiplicity distribution in fig. 4.6.1 (a)), which makes the scalar sum of the transverse momenta of all jets in the event, HT(jets), a powerful variable to further reduce the background, in particular the Z+jets fraction. The HT(jets)distribution is shown in fig. 4.6.10, after requiring pT(Z)>150 GeV. The final selection level of the current ATLAS analysis [3] is characterized by HT(jets) > 600GeV. The invariant mass for the Zb system, reconstructed with a Zboson candidate 57 Rl1b1∆ 0 1 2 3 4 5 6 entries/bin 50 100 150 200 250 =542 D N =518.6 B N =16.5 BBS N =10.0 TTS N ATLAS Work in Progress = 8 TeVs -1 Ldt = 20.3 fb ∫ µµee + 2 b-tags, cut 5≥ data 2012 Z+light Z+charm Z+bottom tt Other bck. (650 GeV) S BB (650 GeV) S TT Uncertainty Rl1b1∆ 0 1 2 3 4 5 6 Data/MC 0.5 1 1.5 (a) Rl1b1∆ 0 1 2 3 4 5 6 entries/bin -1 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 =542 D N =518.6 B N =16.5 BBS N =10.0 TTS N ATLAS Work in Progress = 8 TeVs -1 Ldt = 20.3 fb ∫ µµee + 2 b-tags, cut 5≥ data 2012 Z+light Z+charm Z+bottom tt Other bck. (650 GeV) S BB (650 GeV) S TT Uncertainty Rl1b1∆ 0 1 2 3 4 5 6 Data/MC 0.5 1 1.5 (b) Figure 4.6.17: The Rdistributions between the highest-pTb-tagged jet and the first lepton (used in the Zboson candidate reconstruction), in the ee +µµ channel, after requiring pT(Z)>150 GeV and Ntag Ø2. Rl2b1∆ 0 1 2 3 4 5 6 entries/bin 20 40 60 80 100 120 140 160 180 200 220 =542 D N =518.6 B N =16.5 BBS N =10.0 TTS N ATLAS Work in Progress = 8 TeVs -1 Ldt = 20.3 fb ∫ µµee + 2 b-tags, cut 5≥ data 2012 Z+light Z+charm Z+bottom tt Other bck. (650 GeV) S BB (650 GeV) S TT Uncertainty Rl2b1∆ 0 1 2 3 4 5 6 Data/MC 0.5 1 1.5 (a) Rl2b1∆ 0 1 2 3 4 5 6 entries/bin -1 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 =542 D N =518.6 B N =16.5 BBS N =10.0 TTS N ATLAS Work in Progress = 8 TeVs -1 Ldt = 20.3 fb ∫ µµee + 2 b-tags, cut 5≥ data 2012 Z+light Z+charm Z+bottom tt Other bck. (650 GeV) S BB (650 GeV) S TT Uncertainty Rl2b1∆ 0 1 2 3 4 5 6 Data/MC 0.5 1 1.5 (b) Figure 4.6.18: The Rdistributions between the highest-pTb-tagged jet and the second lepton (used in the Zboson candidate reconstruction), in the ee +µµ channel, after requiring pT(Z)>150 GeV and Ntag Ø2. 64 Rl1b2∆ 0 1 2 3 4 5 entries/bin 20 40 60 80 100 120 140 160 =542 D N =518.6 B N =16.5 BBS N =10.0 TTS N ATLAS Work in Progress = 8 TeVs -1 Ldt = 20.3 fb ∫ µµee + 2 b-tags, cut 5≥ data 2012 Z+light Z+charm Z+bottom tt Other bck. (650 GeV) S BB (650 GeV) S TT Uncertainty Rl1b2∆ 0 1 2 3 4 5 Data/MC 0.5 1 1.5 (a) Rl1b2∆ 0 1 2 3 4 5 entries/bin -1 10 1 10 2 10 3 10 4 10 5 10 6 10 =542 D N =518.6 B N =16.5 BBS N =10.0 TTS N ATLAS Work in Progress = 8 TeVs -1 Ldt = 20.3 fb ∫ µµee + 2 b-tags, cut 5≥ data 2012 Z+light Z+charm Z+bottom tt Other bck. (650 GeV) S BB (650 GeV) S TT Uncertainty Rl1b2∆ 0 1 2 3 4 5 Data/MC 0.5 1 1.5 (b) Figure 4.6.19: The Rdistributions between the second higher-pTb-tagged jet and the first lepton (used in the Zboson candidate reconstruction), in the ee+µµ channel, after requiring pT(Z)>150 GeV and Ntag Ø2. Rl2b2∆ 0 1 2 3 4 5 6 entries/bin 20 40 60 80 100 120 140 160 180 =542 D N =518.6 B N =16.5 BBS N =10.0 TTS N ATLAS Work in Progress = 8 TeVs -1 Ldt = 20.3 fb ∫ µµee + 2 b-tags, cut 5≥ data 2012 Z+light Z+charm Z+bottom tt Other bck. (650 GeV) S BB (650 GeV) S TT Uncertainty Rl2b2∆ 0 1 2 3 4 5 6 Data/MC 0.5 1 1.5 (a) Rl2b2∆ 0 1 2 3 4 5 6 entries/bin -1 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 =542 D N =518.6 B N =16.5 BBS N =10.0 TTS N ATLAS Work in Progress = 8 TeVs -1 Ldt = 20.3 fb ∫ µµee + 2 b-tags, cut 5≥ data 2012 Z+light Z+charm Z+bottom tt Other bck. (650 GeV) S BB (650 GeV) S TT Uncertainty Rl2b2∆ 0 1 2 3 4 5 6 Data/MC 0.5 1 1.5 (b) Figure 4.6.20: The Rdistributions between the second higher-pTb-tagged jet and the second lepton (used in the Zboson candidate reconstruction), in the ee +µµ channel, after requiring pT(Z)>150 GeV and Ntag Ø2. 65 [GeV] T p 1 b-Jet 0 100 200 300 400 500 600 700 800 entries/bin 20 40 60 80 100 120 140 160 180 200 220 240 =542 D N =518.6 B N =16.5 BBS N =10.0 TTS N ATLAS Work in Progress = 8 TeVs -1 Ldt = 20.3 fb ∫ µµee + 2 b-tags, cut 5≥ data 2012 Z+light Z+charm Z+bottom tt Other bck. (650 GeV) S BB (650 GeV) S TT Uncertainty [GeV] T p 1 b-Jet 0 100 200 300 400 500 600 700 800 Data/MC 0.5 1 1.5 (a) [GeV] T p 2 b-Jet 0 100 200 300 400 500 600 700 800 entries/bin 50 100 150 200 250 300 350 400 =542 D N =518.6 B N =16.5 BBS N =10.0 TTS N ATLAS Work in Progress = 8 TeVs -1 Ldt = 20.3 fb ∫ µµee + 2 b-tags, cut 5≥ data 2012 Z+light Z+charm Z+bottom tt Other bck. (650 GeV) S BB (650 GeV) S TT Uncertainty [GeV] T p 2 b-Jet 0 100 200 300 400 500 600 700 800 Data/MC 0.5 1 1.5 (b) ) [GeV] jet T (pΣ= T H 0 200 400 600 800 1000 1200 1400 1600 1800 2000 entries/bin 20 40 60 80 100 120 140 =542 D N =518.6 B N =16.5 BBS N =10.0 TTS N ATLAS Work in Progress = 8 TeVs -1 Ldt = 20.3 fb ∫ µµee + 2 b-tags, cut 5≥ data 2012 Z+light Z+charm Z+bottom tt Other bck. (650 GeV) S BB (650 GeV) S TT Uncertainty ) [GeV] jet T (pΣ= T H 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Data/MC 0.5 1 1.5 (c) Rb1b2∆ 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 entries/bin 20 40 60 80 100 =542 D N =518.6 B N =16.5 BBS N =10.0 TTS N ATLAS Work in Progress = 8 TeVs -1 Ldt = 20.3 fb ∫ µµee + 2 b-tags, cut 5≥ data 2012 Z+light Z+charm Z+bottom tt Other bck. (650 GeV) S BB (650 GeV) S TT Uncertainty Rb1b2∆ 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Data/MC 0.5 1 1.5 (d) T Invariant Mass [GeV] 200 400 600 800 1000 1200 1400 entries/bin 10 20 30 40 50 60 70 80 =542 D N =518.6 B N =16.5 BBS N =10.0 TTS N ATLAS Work in Progress = 8 TeVs -1 Ldt = 20.3 fb ∫ µµee + 2 b-tags, cut 5≥ data 2012 Z+light Z+charm Z+bottom tt Other bck. (650 GeV) S BB (650 GeV) S TT Uncertainty T Invariant Mass [GeV] 200 400 600 800 1000 1200 1400 Data/MC 0.5 1 1.5 (e) Figure 4.7.1: The chosen discriminating variables: (a) pT(b1), (b) pT(b2), (c) HT(jets), (d) R(b1b2) and (e) Tinvariant mass, in the ee +µµ channel, after requiring pT(Z)>150 GeV and Ntag Ø2. 66 5 Multivariate Analysis with TMVA In high-energy physics, with the search for ever smaller signals in ever larger data sets, it has become essential to extract a maximum of the available information from the data. The ATLAS experiment at CERN collects enormous amount of data, hence the use of data mining techniques can be a real help. In a Multivariate Analysis (MVA), variables potentially useful in signal-background discrimination are used as input in multivariate classifiers, which separate (classify) multidimensional data into categories, for instance signal and background. An MVA analysis is performed with the TMVA (Toolkit for Multivariate Data Analysis with ROOT) package [10], using as input the discriminating variables chosen in section 4.7. 5.1 Multivariate Analysis Classifiers outlined This section briefly outlines the multivariate analysis classifiers used in this work: a boosted decision tree (BDT), a linear discriminant (LD) and a neural network (MLPBNN). Boosted Decision Tree (BDT) A decision tree is a binary tree structured classifier that allows a straightforward interpretation, since it can be visualized by a single two-dimensional structure, as illustrated by fig. 5.1.1. Repeated left/right (yes/no) decisions are taken on one single variable at a time until a stop criterion is fulfilled. The phase space is separated this way into several regions that are eventually categorized in signal or background, depending on the majority of training events that end up in the final leaf node. For decision trees, each output node represents a specific value of the target variable. The boosting of a decision tree extends this concept from one tree to several trees, which constitute a forest. The trees are derived from the same training set by reweighting events, being finally combined into a single classifier which is given by a weighted average of all the individual 67 Figure 5.1.1: Schematic view of a decision tree. Starting from the root node, a sequence of binary splits using the discriminating variables xiis applied to the data. Each split uses the variable that at this node gives the best separation between signal and background when being cut on. The same variable may thus be used at several nodes, while others might not be used at all. The leaf nodes at the bottom end of the tree are labeled “S” for signal and “B” for background depending on the majority of events that end up in the respective nodes (figure extracted from [10]). decision trees. Boosting increases the statistical stability of the classifier trees, and also improves the separation performance, when compared to a single decision tree. Linear Discriminant (LD) The linear discriminant analysis provides data classification using a linear model, where linear refers to the discriminant function y(x)being linear in the parameters b, for y(x)=xTb+b0, where b0(denoted the bias) is adjusted so that for signal y(x)Ø0 and y(x)<0for background. It can be shown that this is equivalent to the Fisher discriminant (refer to [10] for a detailed description), which seeks to maximise the ratio of between-class variance to within-class variance by projecting the data onto a linear subspace. 68 pT b1 : pT b2 : HT(jets) : DeltaRb1b2 : T Invariant Mass : Bias node : Layer 0 Layer 1 Output layer Figure 5.1.2: Multilayer perceptron (MLP) neural network with one hidden layer. Artificial Neural Network (MLPBNN) An Artificial Neural Network (ANN) is defined as any simulated ensemble of interconnected neurons, with each neuron producing a certain response at a given set of input signals. By applying an external signal to some input neurons, the network is put into a defined state that can be measured by the response of one (or several) output neurons. One can therefore understand the neural network as a mapping from a space of input variables x1, ..., xnvar onto a one-dimensional space, in case of a signal-versus-background problem, or a multi-dimensional space of output variables y1, ..., ymvar . The mapping is nonlinear it at least one neuron has a nonlinear response to its input. In this study it is used an MLP (multi-layer perceptron) neural network 1. While in principle a neural network with nneurons can have n2directional connections, the complexity can be diminished by organising the neurons in layers and only allowing direct connections from a given layer to the following layer. This kind of neural network is named multi-layer perceptron (MLP). The first layer of a multilayer perceptron is the input layer, the last one is the ouput layer, and the ones between these are termed hidden layers. Fig. 5.1.2 illustrates the architecture of a MLP neural network with one hidden layer. 1In particular the MLPBNN extension, which employs the Broyden-Fletcher-Goldfarb-Shannon (BFGS) training method and a bayesian regulator (refer to [10] for a detailed description). 69 5.2 Training/testing MVA Classifiers In this study the problem to solve is one of classification: the goal is to separate signal from background. It is used a T¯ Tproduction signal sample, assuming SU(2) singlet quarks with a mass of 700GeV, and a background sample which includes all the distinct backgrounds used in the present analysis for vector-like quarks pair-production, whose modeling is explained in section 4.5. The signal sample for VLQs with a mass of 700GeV is assumed to be the benchmark, since it is in this mass region that limits are expected to be improved (as will be seen in section 6.1.1). The first step in a classification analysis is to define input variables, which correspond to the best discriminating variables chosen. In this case, the input variables used are the transverse momentum of the two higher-pTb-tagged jets, the total jet transverse momenta HT(jets), the Rdistribution between the two higher-pTb-tagged jets and the invariant mass of the T, as outlined in section 4.7. These variables are presented in fig. 5.2.1, in the ee +µµ channel, after requiring pT(Z)>150 GeV and Ntag Ø2, with a reference signal displayed corresponding to TT production, assuming SU(2) singlet quarks with a mass of 700 GeV. The linear correlation coefficients for the variables included in the signal and background training samples, as well for the data sample, are organised in three matrices as depicted in figs. 5.2.2 and 5.2.3. As expected, for all the samples, the correlations are stronger between the variables corresponding to the transverse momenta of the two higher-pTb-tagged jets and the total jet transverse momenta HT(jets). Take, for instance, the correlations for the signal sample in fig. 5.2.2 (a): it is approximately 42% between HT(jets)and pT(b1). This is due to the definition of the HT(jets)variable as the scalar sum of the transverse momenta of all the jets, which naturally includes the b-tagged ones. The correlation between HT(jets)and pT(b1) is stronger that the one between HT(jets)and pT(b2) (≥24%), as expected, since the higher the energy, the higher the contribution to the pTscalar sum HT(jets), which justifies a stronger correlation. Notice that the aforementioned correlations are more enhanced in the background (fig. 5.2.2 (b)). Nevertheless, none of the supracited correlation coefficients is high enough to justify the exclusion of any of the variables from the multivariate analysis. After training and testing, the most performing MVA methods are chosen and used to classify events in data samples with unknown signal and background composition. For the categorization of the multivariate methods trained and tested in terms of performance, it is useful to analyse the background rejection versus signal efficiency (efficiency=170 Figure 5.2.1: Unit-normalized input variable distributions, in the ee +µµ channel, after requiring pT(Z)>150 GeV and Ntag Ø2. The reference signal displayed corresponds to TT production assuming SU(2) singlet quarks with a mass of 700 GeV. Upper panel, from left to right: pT(b1),pT(b2) and HT(jets). Down panel, from left to right: R(b1b2) and the reconstructed Tquark invariant mass. The vertical text on the right-hand side of the plots indicates the underand overflows. 71 (a) (b) Figure 5.2.2: Linear correlation coefficients between the discriminating variables used: (a) for a T¯ Tproduction signal sample, assuming SU(2) singlet quarks with a mass of 700 GeV; for the total background sample (b). These coefficients are obtained after training (and testing) the classifiers with the aforementioned samples as input. 72 (a) Figure 5.2.3: Linear correlation coefficients between the discriminating variables used for the data sample. background rejection), also know as ROC (receiver operating characteristic) curve. The larger the area of the ROC curve, the better the performance. The BDT, the LD (linear discriminant) and the MLPBNN neural network were observed to deliver a good performance, as verified in fig. 5.2.4, hence are chosen to be used in the classification phase (section5.3). Notice, as well, the poor performance of the automatic cuts method implemented in the MVA algorithm, when compared to the other classifiers. These cuts are automatically performed and optimized by the MVA algorithm and correspond to the maximum performance in signal-background discrimination via this method, confirming the much lower gain when compared to the other methods presented. The training is followed by the testing phase, whose goal is to ensure there was no overtraining. Overtraining occurs when a machine learning problem has too few degrees of freedom, because too many model parameters of an algorithm were adjusted to too few data points. Hence, the sensitivity to overtraining depends on the MVA classifier used. For instance, a linear discriminant can hardly ever be overtrained, whereas, without the appropriate counter measures, boosted decision trees can suffer from at least partial overtraining, owing to their large number of nodes. Overtraining leads to a seeming increase in the classification performance over the objectively achievable one, if measured on the training sample, and to an effective performance decrease when measured with 73 300 400 500 600 700 800 900 -3 10 -2 10 -1 10 1 10 2 10 [GeV] T m ) [pb]T T→(pp σ Zb/t + X Dilepton SU(2) singlet -1 Ldt = 20.3 fb ∫ = 8 TeVs Theory (NNLO) 95% CL expected limit σ1±95% CL expected limit σ2±95% CL expected limit 95% CL observed limit (a) 300 400 500 600 700 800 900 -3 10 -2 10 -1 10 1 10 2 10 [GeV] T m ) [pb]T T→(pp σ Zb/t + X Dilepton SU(2) singlet -1 Ldt = 20.3 fb ∫ = 8 TeVs Theory (NNLO) 95% CL expected limit σ1±95% CL expected limit σ2±95% CL expected limit 95% CL observed limit (b) 300 400 500 600 700 800 900 -3 10 -2 10 -1 10 1 10 2 10 [GeV] T m ) [pb]T T→(pp σ Zb/t + X Dilepton SU(2) singlet -1 Ldt = 20.3 fb ∫ = 8 TeVs Theory (NNLO) 95% CL expected limit σ1±95% CL expected limit σ2±95% CL expected limit 95% CL observed limit (c) Figure 6.1.2: Predicted pair-production cross section as a function of the heavy quark mass and observed and expected upper limits for an SU(2) singlet Tquark, derived with the outputs of (a) BDT, (b) LD and (c) MLPBNN classifiers. 80 Tsinglet observed (expected) mass limit [GeV] Before MVA After MVA BDT LD MLPBNN 625(616) 599(630) 611(642) 665(667) Table 6.1: Observed (expected) 95% C.L. limits on the Tquark mass (GeV), assuming pair production of SU(2) singlet quarks, before (left) and after a multivariate analysis (right). obtained with the results of the MVA classification for a MLBNN neural network, since there is an improvement in the expected limit of 51 GeV, when compared to the limits set before the MVA classification. Furthermore, these results also improve the ones recently published by the ATLAS Collaboration [3], for a combined dilepton+trilepton channel: from an observed (expected) limit on the mass of an SU(2) singlet Tquark of 655 GeV (625 GeV) to 665 GeV(667 GeV), when considering the results obtained with the classification obtained with the MLPBNN, which translates to an improvement of 42 GeV, at a 95% confidence level. 81 7 Conclusions and Further Work A search for heavy quarks that decay to a Zboson and a third-generation quark has been performed, using a dataset corresponding to an integrated luminosity of 20.3fb≠1, collected by the ATLAS detector at the LHC in pp collisions at Ôs=8TeV. No evidence for a heavy quark signal is observed when selecting events with topologies sensitive to heavy quark pair-production via the strong interaction. Hence, the results obtained before and after a multivariate analysis using a MLPBNN neural network were used to set lower (observed) mass limits of 625GeV and 665 GeV (at 95% C.L.), respectively, on vector like Tquarks when assuming the SU(2) singlet hypothesis, which confirms the success of multivariate techniques in improving the previously set limits. The mass limit obtained after a MVA also improves the limit recently set by the ATLAS Collaboration [3] in 10 GeV. Several sources of systematic uncertainty affect the predicted Standard Model backgrounds and signal. However, since this is a search, in which statistical uncertainties dominate over systematics, they were not considered throughout the study. The former can be included in posterior studies. 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