Uppsala University. Department of Physics and Astronomy. Master s Degree Project 30hp

Transkript

1 Uppsala University Department of Physics and Astronomy Master s Degree Project 3hp Unfolding of multivariate tools and statistical analysis for Higgs boson pair production searches in the ATLAS detector at the Large Hadron Collider Student: Christina Dimitriadi Supervisors: Arnaud Ferrari Petar Bokan Subject Reader: Richard Brenner October 8, 219

2 Abstract Recently, searches for pair production of Higgs bosons in several final states have been carried out by the ATLAS exeperiment at the Large Hadron Collider (LHC). This study focuses on the search for non-resonant di-higgs production decaying to a final state with two b-jets and two τ-leptons using 36.1 fb 1 of data recorded by the ATLAS detector. The analysis for this process has already been performed. Boosted decision trees (BDTs) are used in the analysis to improve the separation of the signal from background processes and several variables that provide good discrimination between signal and background are used as inputs to the BDT. This study aims to unfold the BDT of the analysis and optimize a cut-based analysis so that the gain from using the BDT can be estimated. Two variables, related to the invariant masses and angular distances of the Higgs boson decay products, are defined and the optimal cuts are found to be X mττ m bb < 1.8 and X Rττ R bb < 4.. Then, the upper limits on the SM HH production cross section are set when fitting m HH with the cut-based analysis. An expected limit of.78 pb, 23 times the SM prediction is obtained when neglecting systematic uncertainties, compared to the limit of 15 times the SM as recomputed when using the BDT. Comparing the two results, the sensitivity is worsened by 5% when not using the BDT. 1

3 Sammanfattning Partikelfysik är den gren av fysiken som studerar de elementära beståndsdelarna i materia och interaktionerna mellan dem. Den kallas ofta högenergifysik, eftersom många partiklar skapas och upptäcks under energirika kollisioner mellan andra partiklar, såsom i partikelacceleratorer. Ett teoretiskt ramverk, Standardmodellen, som formulerades på 196- och 197-talet, beskriver materiens byggstenar och deras interaktioner med stor framgång. Standardmodellen innehåller sex leptoner och sex kvarkar, samt fyra bosoner som förmedlar den elektromagnetiska, svaga och starka växelverkan mellan leptoner och kvarkar. En ytterligare väsentlig komponent i Standardmodellen är Higgsbosonen, vars existens förutspåddes på 196-talet och observerades av ATLAS- och CMS-experimenten vid CERN:s Large Hadron Collider (LHC) den 4 juli 212. Denna elementära spin--partikel med en uppmätt massa på 125 GeV genererar alla partiklars massa genom Higgs mekanismen. Som en följd av Higgs-bosonens upptäckt har flera studier och mätningar av dess egenskaper genomförts för att verifiera huruvida dess beteende stämmer överens med Standardmodellens förutsägelser. En viktig studie är att mäta Higgsbosonens växelverkan med sig själv, som härrör från Higgs mekanismen. Detta kan göras genom att undersöka parproduktion av Higgsbosonen, H HH, vilken kan ge insikt i Higgs-potentialens faktiska form. I detta arbete studeras en analys som söker efter parproduktion av Higgsbosoner som sönderfaller till två τ-leptoner och två b-kvarkar (HH bbτ τ), där båda τ-leptonerna sönderfaller till hadroner. Analysen för detta sluttillstånd har redan utförts av ATLAS-samarbetet med hjälp av en multivariat analysteknik (MVA) som kallas Boosted Decision Tree (BDT) och används för att separera signalen från den relativa bakgrunden. MVA tekniker har blivit allt vanligare i högenergifysik, eftersom det finns en ständigt ökande produktion av stora datamängder vilket kräver mer avancerade analystekniker för att utvinna så mycket information som möjligt. Dessa involverar flera storheter eller variabler som vanligtvis är korrelerade. Fördelen med att använda MVA tekniker är att de tar hänsyn till sådana korrelationer. Ibland är dessa resultat emellertid svårtolkade, vilket medför att teoretiker har svårt att dra slutsatser av dem. Därför syftar denna studie till att omarbeta MVA-analysen genom att införa en snittbaserad analys så att vinsten från att använda MVA kan uppskattas. Metoderna vi använder oss av är avfaltning av BDT:n och granskning av inmatningen till BDT-n för att hitta de optimala snitten så att den största delen av bakgrunden tas bort, medan en stor del av signalen överlever. En rad signifikanstester genomförs följaktligen med de optimala snitten. Övre gränser sätts sedan på HH-produktionstvärsnittet genom anpassning av den invarianta massan hos di-higgs-systemet, m HH, i signal- och kontrollområden baserat på de optimala snitten. Den förväntade övre gränsen visar sig vara 23.4 gånger Standardmodellens förutsägelse vid 95% konfidensnivå, utan att beakta systematiska osäkerheter. Slutsatsen är att användningen av den snittbaserade analysen förvärrar känsligheten för HH bbτ τ med 5%. 2

4 Contents 1 Introduction Motivation Particle physics and the Standard Model Shortcomings of the Standard Model Beyond the Standard Model Higgs physics The Higgs mechanism Higgs boson pair production Higgs boson decay modes The ATLAS experiment at the LHC The Large Hadron Collider at CERN ATLAS Sub-detector systems Coordinate system and useful variables Trigger system Decay of Higgs boson pair to di-τ + di-b final state Data and simulation framework Object reconstruction in the ATLAS detector Tau-leptons Bottom quarks Missing transverse momentum Event selection Background processes Multivariate analysis in particle physics Boosted Decision Trees Input variables Existing upper limits Purpose Cut-based analysis Unfolding the BDT Fitting the BDT score distribution Fitting the m HH distribution Definition of variables Optimization of cuts Results and discussion 33 7 Conclusion 35 List of figures 36 List of tables 37 3

5 References 38 4

6 Chapter 1 Introduction 1.1 Motivation Particle physics seeks to understand the fundamental nature of the Universe and the building blocks of the matter created after the Big Bang. Although the underlying theory has been very successful, it only describes 4% of the known Universe. Hence, scientists and experimental laboratories all over the world are in constant search for answers to questions about dark matter, dark energy, anti-matter and more, in order to push back the frontiers of knowledge. The discovery of a Higgs boson by the Large Hadron Collider (LHC) at CERN in 212 [1, 2] was a big achievement for the particle physics society. Since then, measurements of its properties and behavior have been carried out. Searches for the production of pairs of Higgs bosons are very interesting and valuable since they can provide insight to the Higgs boson self-coupling, which is promptly linked to the shape of the Higgs potential in the Standard Model. The aim of this project is to re-interpret the recently published result of the bbτ had τ had final state in the search for Higgs boson pair production by the ATLAS experiment at the LHC, suggest and implement an alternative cut-based analysis and compare the results [3]. 1.2 Particle physics and the Standard Model Particle physics is the field studying the fundamental constituents of matter in the Universe and the forces between them. These are successfully depicted in a theoretical framework, the Standard Model (SM), which was formulated in the 196s and 197s. The SM of particle physics is based on a gauge quantum field theory (QFT) describing the unified electroweak (EW) interaction and quantum chromodynamics (QCD), based on a gauge symmetry group of SU(3) C SU(2) L U(1) Y. The SU(3) C group is associated to QCD, describing the strong force. The index C stands for the color charge, which is a property of the strong interactions. There are three colors, red, green and blue (r, g, b) followed by their anti-colors ( r, ḡ, b). The SU(2) L U(1) Y group is associated to the electroweak theory, where the SU(2) L group describes the interaction between left-handed (L) particles with the SU(2) gauge fields and U(1) Y is associated to the hypercharge Y, which is the conserved quantity in the unified electroweak interaction and is defined as Y = 2(Q I3 W ) (1.1) with Q being the electrical charge and I W 3 = ±1/2 the third component of the weak isospin [4]. The SM contains three generations of fermions (half integer spin) and four force carriers, the gauge bosons (integer spin), mediating the three fundamental forces. The electromagnetic force is carried by the photon (γ), while the W ± and Z bosons are the mediators of the weak interaction and the gluon (g) carries the strong interaction. Photons and gluons are both massless and electrically neutral, while the W ± and Z bosons are quite heavy compared to other elementary particles and carry an electrical charge of ±e. Gluons, unlike other gauge bosons, carry a color charge. Fermions are divided into leptons (l) and quarks (q) and they are called matter particles. The lepton family consists of three charged leptons, the electron e, the muon µ and the tau-lepton τ, their anti-particles as well as the corresponding electrically neutral neutrinos ν e, ν µ and ν τ. Quarks, like leptons, are divided in three 5

7 generations, each one consisting of a +2/3 charged quark: up (u), charm (c), top (t), and a 1/3 charged quark: down (d), strange (s), bottom (b). They all have their own anti-particles and they also carry a color charge. Quarks form hadrons, which are color-neutral particles, containing either a quark and an anti-quark (mesons) or three quarks (baryons) [5]. In addition to the matter particles and the force carriers, an essential component of the SM is the Higgs boson, the existence of which was predicted in the 196s [6, 7, 8]. It was observed by the ATLAS and CMS experiments at CERN s Large Hadron Collider (LHC), as announced on 4th July 212 [1, 2]. The Higgs boson is an elementary spin- particle with a measured mass of 125 GeV 1. A summary of the SM particles is shown in Figure 1.1. Figure 1.1: The fundamental particles in the Standard Model [9]. 1.3 Shortcomings of the Standard Model The SM is undoubtedly a very successful theoretical model to describe particle physics. However, despite its consistency to nearly all experimental results and its accurate predictions of various phenomena, it cannot account for some observations []. One downside of the SM is the fact that it incorporates only three of the four fundamental forces in the Universe, excluding the weakest one of them, gravity. Besides, there is a hierarchy problem which cannot be explained by the SM, and it has to do with either the large spanning of masses in the SM or the fine-tuning needed to stabilise the Higgs boson mass. There is no interpretation of why the Higgs boson mass is much smaller than other energy scales and in particular the scale of gravity, m h 125 GeV M P lanck = 1 G = 19 GeV. (1.2) Moreover, the SM cannot account for the matter-antimatter asymmetry happening in the Universe. After the Big Bang equal amounts of matter and antimatter should have been created, yet today the Universe consists mostly of matter. Hence, physicists are studying this imbalance through experiments in order to discover the reasons why it exists. Another flaw of the SM is the lack of an explanation for the existence of dark matter that astrophysical observations have validated. Only 4% of our Universe is made of baryonic matter, while 21% is dark matter and the remaining 75% is dark energy. Nonetheless, no particle candidates for these phenomena can be provided by the SM. 1 In this thesis natural units are chosen, where c = = k B = 1. 6

8 Last, in the SM, neutrinos are massless particles. In 1998 it was discovered that neutrinos do have a very small, non-zero mass, giving rise to neutrino oscillations, which again contradicts the SM [11]. 1.4 Beyond the Standard Model Remaining unanswered questions and phenomena seeking explanation have motivated to extend the SM and develop theories beyond the Standard Model (BSM) in order to completely understand the Universe. Possible extensions of the SM are based on the principle of Supersymmetry (SUSY). The main point of SUSY is the prediction of a partner for each particle in the SM, which is rather essential since these new particles would stabilise the mass of the Higgs boson. The extra particles predicted by Supersymmetry would make a light Higgs boson possible and would interact through the same forces as SM particles. The SUSY links fermions and bosons since it predicts that each of the SM particles has a partner with a spin that differs by half of a unit. However, SUSY must be broken to allow the supersymmetric partners to acquire different masses than the SM fermions and bosons to which they are associated. The simplest supersymmetric extension of the SM is the Minimal Supersymmetric Standard Model (MSSM). Its Higgs sector must be described by the Two Higgs Doublet Models (2HDM). In comparison to the SM, an additional complex doublet and thereby four new Higgs bosons must be introduced [12]. It is noteworthy to mention that there are many more possible theoretical extensions of the SM and SUSY is only one of them. 7

9 Chapter 2 Higgs physics 2.1 The Higgs mechanism The mechanism responsible for explaining how particles obtain mass was developed by Robert Brout, François Englert, Peter Higgs, Gerald Guralnik, Carl Hagen and Tom Kibble [6, 7, 8]. A more detailed review of the subject can be found in [13]. As mentioned before, the SM is based on a QFT, where all fundamental particles are described as excitations of quantum fields. In QFT each non-interacting field is described by a Lagrangian density of the form L = L mass + L kin (2.1) However, having the L mass term in the Lagrangian density would violate gauge invariance. This problem is solved by a spontaneous electroweak symmetry breaking (EWSB), resulting in the attribution of mass to each particle. The Higgs mechanism postulates the existence of a complex scalar doublet ( ) φ Φ(x) = + (x) φ = 1 ( φ + 1 (x) + iφ + 2 (x) ) (x) 2 φ 1(x) + iφ, φ i R (2.2) 2(x) with a corresponding potential V (Φ) = µ 2 Φ Φ + λ(φ Φ) 2 (2.3) where λ > and µ 2 <. Due to those bounds on the parameters, the Higgs potential, as seen in Figure 2.1, does not have a minimum at Φ = and therefore the vacuum expectation value (vev, v) is shifted to a non-zero value for the ground state, µ 2 v = λ. (2.4) After expanding Φ around v and choosing a unitary gauge, Equation (2.2) can be rewritten as Φ(x) = 1 ( ), (2.5) 2 v + H where H is an electrically neutral scalar field, later identified with the Higgs boson. By spontaneously breaking the symmetry SU(2) L U(1) Y to U(1) Q, three massless gauge fields of the SU(2) are absorbed by the W ± and Z bosons which in turn get their masses. The fermion masses are also generated through the Yukawa coupling, via the interaction with the Higgs field. The electromagnetic U(1) Q symmetry stays unbroken, hence the photon remains massless. All in all, this Higgs potential, V (Φ), introduced in the Lagrangian density, adds couplings of the Higgs field to the gauge fields, to fermions and to itself, generating mass terms for all the particles that the Higgs field couples to [5, 15]. 8

10 Figure 2.1: The Higgs potential, in the shape of a Mexican hat, with the minimum energy not at Φ = [14]. 2.2 Higgs boson pair production The discovery of a particle consistent with the SM Higgs (H) boson by the ATLAS and CMS experiments at the LHC in 212 has been followed by numerous studies and measurements of its properties, which aim to verify if its behavior is in agreement with the SM predictions. However no significant deviation has been found up until now. Measuring the Higgs boson self-interactions that arise from the Higgs mechanism is an important next step of testing the EWSB. After the spontaneous symmetry breaking the Higgs potential takes the following form: V (Φ) = µ 2 Φ 2 + λφ 4 Φ 1 2 (v+h) V = V + λv 2 H 2 + λvh 3 + λ 4 H4, (2.6) where v = µ/ λ, λ = m 2 H /(2v2 ) and V is a constant term. The second term in the scalar potential is the mass term, 1 2 m2 H H2, and the other two are trilinear and quartic Higgs boson self-coupling terms. In order to further test the SM, experimental measurements of the Higgs boson self-coupling are necessary. This can be done by probing the Higgs boson pair production, H HH. The dominant production mode for a Higgs boson pair at the LHC is gluon-gluon fusion (ggf). Figure 2.2 shows three Feynman diagrams for Higgs boson pair production at leading order (LO) 2. In the first one (a), often called the box diagram, a Higgs boson pair is produced via the Higgs-fermion Yukawa interaction (mostly top-quarks), while in (b), often referred to as the triangle diagram, the Higgs boson pair production is mediated by an off-shell Higgs boson. Due to the fact that the box and triangle diagrams interfere destructively, the production cross section in the SM turns out to be very small, namely σ HH = 31.5 fb at 13 TeV, about three orders of magnitude less than for the single-higgs boson production rate [16]. Enhancements of the Higgs boson pair production cross section may occur in various BSM scenarios, introducing new couplings or deviations of the Yukawa- or self-coupling constants from their SM values. Another BSM scenario corresponding to Figure 2.2(c) shows a resonant Higgs boson pair production through the decay of an intermediate state X, which can be for example a spin-2 graviton or a scalar resonance. Figure 2.2: Leading-order Feynman diagrams for Higgs boson pair production in the SM via gluon-gluon fusion, (a) through a heavy-quark loop, (b) through the Higgs boson self-coupling. In (c) Higgs boson pairs are produced through an intermediate heavy resonance in a BSM scenario. This study covers only the non-resonant SM Higgs boson pair production mode. 2 The LO implies a diagram corresponding to the lowest order in couplings at which a process can occur. 9

11 2.3 Higgs boson decay modes In general, Higgs bosons can decay to all massive SM particles. The branching ratios of the various decay channels of the Higgs boson, along with their uncertainties, as a function of the Higgs boson mass are illustrated in Figure 2.3. Next, Table 2.1 shows the SM expected branching ratios at m H = 125 GeV for the most relevant decay channels. Higgs BR + Total Uncert ττ cc bb γγ gg Zγ WW ZZ LHC HIGGS XS WG µµ M H [GeV] Figure 2.3: SM Higgs boson decay branching ratios and their total uncertainty as a function of its mass [17]. Table 2.1: The branching ratios and their uncertainty for a SM Higgs boson with mass m H = 125 GeV [18]. Decay Channel Branching Ratio Uncertainty H b b 58.4 % H W + W 21.4% H τ + τ 6.3% H ZZ 2.6% H γγ.23% +3.2% 3.3% +4.3% 4.2% +5.7% 5.7% +4.3% 4.1% +5.% 4.9% The final states of a Higgs boson pair are numerous, however the one of interest for this study is HH b bτ + τ. This decay process has a relatively clean final state compared to the most probable HH b bb b and a relatively large branching ratio (7.4%) compared to HH b bγγ, which has an even cleaner signature due to an excellent di-photon mass resolution. A statistical combination of searches for Higgs boson pairs in the above three decay channels can be found in Ref. [19]. The combined observed (expected) limit on the non-resonant Higgs boson pair cross section set by the ATLAS Collaboration is.22 pb (.35 pb) at 95% confidence level, corresponding to 6.7 (.4) times the predicted SM cross section.

12 Chapter 3 The ATLAS experiment at the LHC 3.1 The Large Hadron Collider at CERN The Large Hadron Collider (LHC) is the largest and most powerful existing particle accelerator. It consists of a 27 kilometer ring installed in a tunnel built at CERN in Geneva. Protons or ions are accelerated in opposite directions inside this ring and collide in four points at the intersection of the two beams. Their collision at energies in the TeV scale allows both the probe of new physics and precise measurements of known phenomena, enhancing our understanding of the fundamental constituents of matter in the Universe. The first data-taking period (Run I) was performed between 2 and 212, while the collision energy achieved was s = 7 8 TeV. The recorded integrated luminosity 3 was 5/fb in 211 and 23/fb in 212. A long shut down followed from 213 to 215. Then the LHC energy increased to s = 13 TeV. Run II was recently completed with a recorded integrated luminosity of nearly 14/fb being reached. Right now the LHC has stopped its operation for a second shut down so that beam optics near the interaction point are upgraded allowing for higher luminosities to be achieved. Two general purpose experiments, ATLAS and CMS, one dedicated to studies of b-quarks, LHCb, and one dedicated to studies of quark-gluon plasma, ALICE, are the four major experiments at the LHC, as seen in the overview of Figure 3.1. Figure 3.1: Overall view of the LHC experiments [2]. 3 The integrated luminosity, L, is a measure of the number of collisions that have happened over a period of time, usually expressed in fb 1. 11

13 3.2 ATLAS The ATLAS (A Toroidal LHC Apparatus) detector is one of the general-purpose detectors at the LHC designed to probe p p collisions and study the physical processes arising from them by measuring a wide spectrum of signatures. It is 25 m tall and 44 m long, with an overall weight of approximately 7 tons. A barrel part and two end-caps make up the detector, which is practically hermetic. In this way, the energy of neutrinos and weakly interacting particles, predicted by BSM theories, can be reconstructed and observed through the missing transverse energy. As can be seen in the layout of ATLAS in Figure 3.2, it consists of different sub-detector systems, each providing some level of particle identification and kinematic measurement Sub-detector systems An inner detector (tracker) is used for measuring the charged particle momenta by reconstructing their trajectories and it is also designed to detect secondary vertices from short-lived particles. Closest to the beam, it is placed inside a 2 T magnetic field, created by a solenoid magnet surrounding it, making the charged particles bend. The identification of electrons/positrons and photons as well as the measurement of their energy is performed by an electromagnetic (EM) calorimeter. In addition, a hadronic calorimeter, installed outside the EM calorimeter, is used for the energy measurement of charged and neutral hadrons. The calorimeters measure with high precision and granularity the energy, position and shower shape of electrons, photons and hadronic jets. The calorimeter system is able to disentangle the electrons/positrons and photons from showers coming from high-pt hadrons, τ -lepton decays and QCD-induced backgrounds up to an energy scale of TeV. Last, surrounding the hadronic calorimeter, there is a muon spectrometer used for muon identification, together with the track left in the inner detector. It is necessary to have this detector system, since muons escape the calorimeters usually undetected. The ATLAS muon spectrometer consists of three superconducting air-core toroids to create a strong magnetic field, necessary in order to bend the muon trajectories and thereby measure their charge and transverse momentum. The ATLAS detector and its predicted performance are reviewed in detail in Ref. [21]. Figure 3.2: Cut-away view of the ATLAS detector [21] Coordinate system and useful variables ATLAS follows a cartesian coordinate system with its origin being the nominal collision point. The z-axis defines the beam line direction, while the x y plane is transverse to the beam with the x-axis pointing towards the center of the LHC ring and the y-axis pointing upwards. The azimuthal angle φ defines the angle around the beam axis, while the polar angle θ is measured from the beam axis. At a proton-proton collider, the longitudinal momentum of the partons in collision is unknown, therefore it is necessary to define kinematic variables which are invariant under longitudinal boosts. Hence, the polar angle θ can be replaced by the pseudorapidity, defined as η = ln(tan( θ2 )). Another useful variable is the distance between 12

14 two variables in the η φ plane, defined as R = η 2 + φ 2. Last, two commonly used variables, also invariant under longitudinal boosts are the transverse energy, E T, and transverse momentum, p T = p 2 x + p 2 y. Table 3.1 shows some of the performance goals and characteristics of the ATLAS detector, such as the designed resolution of the EM and hadronic calorimeters. The expected momentum resolution for the tracking system and the muon spectrometer in specific pseudorapidity coverage is also reported. Table 3.1: Performance of the ATLAS detector. The units of E and p T are GeV [21] Trigger system A challenge of the LHC experiments is that the event production rate is too high to keep all events. In fact, according to Ref. [22], ATLAS is designed to observe up to 1.7 billion proton-proton collisions per second, while having a data volume of more than 6 million megabytes per second. At the same time the majority of the events are not interesting, thus the trigger system is used so that the data flow is reduced to a controllable level. The role of the trigger is to make the online selection of particle collisions potentially containing interesting physics. Trigger menus are used, which determine what events the system is supposed to accept. In Run II, the ATLAS trigger system performs the selection process in two stages. The Level-1 (L1) trigger, based on custom hardware, uses a subset of information from the muon spectrometer and the calorimeter systems and defines so-called Regions-of-Interest (ROI), which in turn are passed to the next level trigger. The L1 trigger searches for signatures of electrons/photons, high-p T muons, hadronic decays of τ-leptons, jets, as well as events with high missing transverse energy. A maximum of, events per second can be passed from the L1 trigger on to the High-Level Trigger (HLT). The HLT is a software based trigger, which improves the analysis of the L1 trigger. It makes use of the full granularity and precision data coming from the calorimeters, the inner tracker and the muon spectrometer or handles data in smaller and isolated regions of the detector. Thus, it is able to trigger on more complex signatures, like secondary vertices. The HLT selects approximately events per second and assembles them into an event record. Finally, these events are allocated to a data storage system for offline 4 analysis. 4 Offline analysis refers to the analysis which is performed on permanently stored events, i.e. after the processing by the trigger system. 13

15 Chapter 4 Decay of Higgs boson pair to di-τ + di-b final state The published analysis of Ref. [3] searching for Higgs boson pair production in a final state with two b-quarks and two τ-leptons considers two decay sub-channels, τ lep τ had and τ had τ had. The subscripts, lep = lepton and had = hadron, denote the decay mode of the τ-lepton. The study presented in this report focuses on the search for SM pair production of Higgs bosons in the b bτ + τ final state, where both τ-leptons decay in a hadronic mode (τ had τ had ). 4.1 Data and simulation framework This analysis uses proton-proton collision data recorded in 215 and 216 by the ATLAS experiment at the LHC with a center-of-mass energy of s = 13 TeV, corresponding to an integrated luminosity of 36.1 fb 1. The data samples used for the analysis have previously gone through a process chain, illustrated in the left part of Figure 4.1. First, as long as the data taking is running, the ATLAS trigger system decides which events get written to the disk. As it has already been mentioned in subsection 3.2.3, the LHC delivers events with a rate of up to 4 MHz, while ATLAS can afford to record up to 1 khz, meaning that only one in 4. events can be kept. Hence, a clear-out among the events should be carried out by the two-step mechanism of the ATLAS trigger system, so that all interesting events are stored. Then, the output of the trigger, raw data, is organised into streams and used for reconstruction. The output produced by the reconstruction is AOD, which stands for analysis object data. The next step is the production of derived AOD (DAOD) files that are much smaller and contain the information specific to a targeted final state. Figure 4.1: The ATLAS data (left) and MC samples (right) processing chain [23]. Apart from the data samples, it is necessary to have Monte Carlo (MC) simulation samples for the signal and background processes. Several steps are included in the production of MC simulated samples, such as 14

16 event generation, parton showering, hadronization and detector simulation. These steps are presented in the right side of the sketch in Figure 4.1. The interactions between quarks and gluons in the proton-proton collisions are simulated during the event generation, while the interactions of outgoing particles, arising from the generator, with the detector material are computed during the detector simulation: the deposited energy in each sensitive element of the detector is determined. During the digitisation, the simulated energy deposits are turned into a detector response, looking similar to the raw data from the real detector. After this step, the process is the same as for real data. The signal and background samples used in this thesis are official ATLAS samples and have been used in the published analysis. The SM HH signal sample is simulated with MadGraph5 [24], while parton showers and hadronization are simulated with Herwig++ [25]. Table 4.1 shows how the different background MC samples are generated. All the plots presented in this thesis are edited with ROOT [26]. Table 4.1: Event generators for the different background samples. Background Processes Event Generators Parton Shower Simulation t t Powheg-Box [27], MadSpin [28] Pythia 6 [29] Single-top quark Powheg-Box, MadSpin Pythia 6 Z + jets Sherpa [3] W + jets Sherpa Diboson Sherpa Quark-induced ZH Pythia 8 [31] Gluon-induced ZH Powheg Pythia 8 tth MadGraph5 Pythia Object reconstruction in the ATLAS detector Tau-leptons Tau-leptons are the heaviest of the three charged leptons in the SM with a mass of ±.12 MeV and decay almost immediately with a mean life time of 29.3 fs [18]. Therefore, τ-leptons can only be reconstructed by their decay products, since they disappear before reaching any of the detector components. They are the only leptons heavy enough to decay both in lighter leptons and hadrons. As can be seen in the Feynman diagram of Figure 4.2, the τ-lepton decays into a neutrino ν τ and an off-shell W boson, where the W boson further decays into either lν l, where l is electron or muon, or two quarks. The former case is referred to as the leptonic decay mode and the latter as hadronic. The leptonic decay mode has a branching fraction of around 35%, while the hadronic decay mode is more common with a branching fraction of around 65%. Figure 4.2: Feynman diagram of τ-lepton decays by an emission of an off-shell W boson. 15

17 Hadronic τ-leptons Hadronically decaying τ-leptons, τ had, usually create final states of one or three charged pions π ± and some number of π. Depending on the number of charged tracks left in the inner detector, the hadronically decaying τ-leptons are referred to as 1-prong or 3-prong if they decay in one or three charged pions respectively. The most common 1-prong final state is τ π π ν τ. The τ had form jets in the calorimeter of the ATLAS detector at the LHC, which then have to be differentiated from quark- and gluon-initiated jets that are dominating at hadron collider experiments. The most essential difference is that τ had has a more narrow, collimated shape and lower charged track multiplicity (one or three tracks) in the inner detector. QCD-induced jets, in general, have a wider shape with more particles, which among other characteristics, is used to discriminate τ decays from other jets, as shown in Figure 4.3(a,b). The τ had candidates are reconstructed as jets in the ATLAS detector using the anti-k t algorithm [32] with a radius parameter R =.4 and calorimeter energy clusters as inputs. These jets are used as seeds for the reconstruction of visible products of hadronically decaying τ-leptons, τ had vis, which are required to have one or three tracks. Boosted decision trees (BDTs) 5 [33] are trained in order to distinguish τ had vis candidates from QCD-induced jets. Another challenge in the reconstruction of τ-leptons from detector objects is the existence of neutrinos, which escape detection. Many methods have been developed for the mass reconstruction of resonances decaying to τ-leptons. In the ATLAS experiment, the most usual method for calculating the invariant mass of particles that decay into two τ-leptons is the Missing Mass Calculator (MMC) [34] Bottom quarks Bottom quarks, with a mass of approximately 4.18 GeV [18], form B-hadrons that have sufficiently long lifetime to travel some distance before decaying. This lifetime on the other hand is short enough so that they decay before reaching the inner detector. b-jets Due to sufficiently long lifetime of B-hadrons, there is a displacement of their decay (secondary) vertex with respect to the primary vertex (interaction point), which can be reconstructed through the extrapolation of charged particle tracks. The decay products of the B-meson further form jets. Then, the presence of a secondary vertex within these jets indicates a presence of a B hadron and they are referred to as b-jets. The identification of heavy-flavor jets is also based on some impact parameter information. As can be seen in Figure 4.3(c), the transverse impact parameter, d, of a track is the closest distance between the track and the primary vertex in the plane perpendicular to the direction of collision. The longitudinal impact parameter, L, is the aforementioned closest distance in longitudinal direction. Similarly to hadronically decaying τ-leptons, b-jets are reconstructed using the anti-k t algorithm with a radius parameter R =.4. Then, they are identified using the MV2c multivariate discriminant, also based on BDTs [35, 36]. (a) (b) (c) Figure 4.3: Comparison of τ-jets and b-jets with regular jets [37]. 5 See Chapter 5. 16

18 4.2.3 Missing transverse momentum The missing transverse momentum (and its magnitude ET miss ) account for the momentum imbalance in the plane transverse to the beam axis. Its measurement can allow the indirect detection of neutrinos. In this analysis, ET miss is defined as the magnitude of the negative vector sum of all reconstructed, calibrated objects together with a track-based soft term (TST), which is reconstructed from the transverse momentum deposited in the detector, but not associated with any of the aforementioned identified objects [38]. 4.3 Event selection Following the reconstruction of detector objects, an event selection is applied so that the selected final state consists of two τ had vis candidates of opposite charge satisfying the medium identification (ID) criteria, along with two b-tagged jets and ET miss. A BDT classification is applied on these events in order to separate the signal from background processes. Only events that pass the single τ had triggers (STT) and di-τ had triggers (DTT) are used. The event selection criteria depend on the trigger category. A minimum p T of 4 GeV for DTT events is required for the leading τ had vis candidate, while for STT events the minimum p T ranges between and 18 GeV 6. The sub-leading 7 τ had vis candidate is required to have a p T threshold of 2 GeV for STT and 3 GeV for DTT events. The selection also requires at least two jets, with the leading one having p T > 45 GeV for STT events, while for DTT the threshold is increased to 8 GeV, due to a L1 trigger requirement of the presence of a jet in the event. The minimum p T requirement for the sub-leading jet in both cases is 2 GeV. In addition,, which is calculated using the Missing Mass Calculator, is constrained to be higher than 6 GeV. Finally, the signal region (SR) is defined by selecting events that meet the above requirements and have exactly two b-tagged jets. The event selection is summarized in Table 4.2. the invariant mass of the di-τ system, m MMC ττ Table 4.2: Signal region event selection for the bbτ had τ had decay channel [3]. Preselection (had-had channel) Single-τ had trigger (STT) Di-τ had trigger (DTT) exactly 2 opposite-sign τ had s p τ 1(2) T > 18 (2) GeV p τ 1(2) T > 4 (3) GeV 2 central jets p T > 45, 2 GeV p T > 8, 2 GeV m MMC ττ > 6 GeV 2 b-jets Background processes The dominant background processes in the bbτ had τ had channel are t t, Z ττ produced in association with heavy flavour jets and multijet events. Background processes including real τ-lepton decays are derived from simulation, while data-driven methods are used to estimate backgrounds where jets are misidentified as τ had vis objects. In particular, t t events, where one or more reconstructed τ had decays are misidentified quark- and gluon-initiated jets, often referred to as fake-τ had background, are estimated in a semi-data-driven way. A set of probabilities for a jet to be misidentified as a medium τ had vis (fake rates) is measured in data in a control region enriched in fake τ had vis candidates with some very loose τ-id criteria applied. These fake rates are then applied to all 6 The p T threshold varies due to different trigger thresholds corresponding to different data-taking periods. 7 The leading τ had vis jet is the one with the highest transverse momentum, while sub-leading refers to that jet with the second highest transverse momentum. 17

19 non-truth-matched τ had vis candidates with the same identification criteria to estimate the fake medium τ had vis contribution from t t events in the SR. A data-driven method is used to estimate the multijet background. It is assumed that the probability for a jet to fake a τ had vis candidate is the same in the region where two τ had vis objects have the same electric charge (SS) and the region where they have opposite electric charge (OS). In both regions all non-multijet backgrounds are subtracted from data. A set of fake factors (FFs) are measured in the SS region as the ratio of the number of events where both τ had vis candidates pass the medium τ-id criteria to the number of events where at least one of them fails these criteria. These FFs are then applied to all events where at least one τ candidate fails the medium ID in the OS region to obtain the multijet estimate in the SR. A large background contribution is coming from processes involving the decay mode of the Z-boson in association with heavy-flavor jets, Z ττ +(bb, bc, cc). The jet emission is considered to be not well-modelled by the simulation, hence these processes are normalised to data in a control region. The production of jets should not depend on the decay mode of the Z-boson, hence Z µµ + (bb, bc, cc) jet events are selected from data. A dedicated control region is included in the final fit, so that the normalisation is derived. 18

20 Chapter 5 Multivariate analysis in particle physics In high energy physics experiments, there is an ever-increasing production of large data, which is followed by the demand for advanced analysis techniques, so that it is possible to extract the maximal amount of information from the data. These typically involve multiple quantities or variables, like transverse momentum, energy deposited in calorimeters, kinematic variables, and other more complicated variables aimed to describe characteristics of a specific final state. Since many variables can be correlated, the benefit from using multivariate techniques is that they take into account such correlations [39]. Multivariate analysis (MVA) methods, based on machine learning 8, are widely used in particle physics, mostly for signal and background classification. For this reason, a Toolkit for Multivariate Analysis (TMVA) [33], has been developed and integrated into the analysis framework ROOT. The TMVA includes different algorithms for multivariate classification, for instance Boosted Decision Trees (BDTs). 5.1 Boosted Decision Trees The multivariate analysis technique of BDTs is widely used by the ATLAS Collaboration. A decision tree is a binary classifier in the shape of a tree, as illustrated in Figure 5.1, consisting of nodes and leaves. Decision trees (DTs) consist of recursive left/right decisions which determine the classification of data, based on sequential cuts applied on a single variable at each time. At each step in the sequence, the best cut is looked for and used to split the data until in the end a terminal criterion is fulfilled. As shown in Figure 5.1, all decisions begin from an initial, root node, and each leaf gets assigned one of two classes, like for example signal or background, consequent to a binary decision taken at each node. The splitting of data stops when impurity cannot be further reduced. A measure of impurity is the Gini index, which is given by Gini = (s + b)p (1 P ) = sb s + b, (5.1) with P = s/(s + b) being the signal purity and s, b referring to the signal and background events respectively. In the end, all events are assigned to one of the classes and are given a score, which usually ranges between -1 and +1. Background-like events get a score near -1, while signal-like events have score close to +1. One shortcoming of a single decision tree is that its performance drops rapidly, if the dataset has a complex structure. However, a good solution is boosting, where the classification is repeated by creating many single trees, but the misclassified events in one tree are given a larger weight when the next tree is created. In more detail, the training procedure of a BDT includes building multiple decision trees and putting them in a forest to yield a combined score. This lets BDTs have an enhanced separation performance and stability compared to single DTs. For each individual tree, the best cut for each variable x i is found, so that the separation between signal and background is maximum. The process is repeated for each node. Next, misclassified events are checked for one classifier, and a higher weight is assigned to them. The next classifier, in turn, is trained on the reweighted dataset, and the procedure is repeated until all classifiers are trained. The weighted sum of all classifiers gives the final score. 8 Machine learning is the study of algorithms that learn from data, and then provide predictions for future data [39]. 19

21 Figure 5.1: Illustration of a binary decision tree [33]. Each branch of the decision tree represents a sequence of cuts, which classifies an event as signal (S) or background (B) Input variables The TMVA is used for the training and evaluation of various BDTs. Several variables that provide good discrimination between signal and background are used as inputs to the BDT, and are listed in Table 5.1 for the τ had τ had search channel [3].. Table 5.1: Variables used as inputs to the BDTs for the non-resonant di-higgs signal in the τ had τ had search channel [3]. Variables - τ had τ had channel m HH m MMC ττ m bb R(τ, τ) R(b, b) ET missφ centrality Explicitly, in the order they appear in Table 5.1, m HH is the invariant mass of the di-higgs system, which is reconstructed from the di-τ and di-b systems. Then, m MMC ττ is the invariant mass of the di-τ system, calculated using the Missing Mass Calculator, and m bb is the invariant mass of the di-b-jet system. The distance evaluated between two τ had vis decay products and the one between two b-jets are referred to as R(τ, τ) and R(b, b) respectively. The ET missφ centrality9 is a measurement of the angular position, φ, of the missing transverse momentum, ET miss, with respect to the visible decay products of the two τ objects. Its definition is given by: where A and B are defined as: E miss T φ centrality = A + B A2 + B 2, (5.2) A = sin(φ ET miss φ τ2 ) sin(φ τ1 φ τ2 ), B = sin(φ τ 1 φ ) Emiss T sin(φ τ1 φ τ2 ) (5.3) 9 In the plots below, it is referred to as MET φ centrality. 2

22 The E miss φ centrality should be equal to: T 2, when the E miss T 1, if the E miss T is exactly between the two τ has vis objects, lines up with either of the τ has vis objects, less than 1, if the ET miss lies outside of the angular region that the two τ has vis objects form. The BDT for the τ had τ had channel is trained against the dominant backgrounds, namely t t, Z ττ and multi-jet events. The training of the BDT has already been performed by the ATLAS Collaboration and the results can be found in Ref. [3]. In Figure 5.2, one can see the BDT score distribution using the SM HH signal in the training for the τ had τ had channel. Events / Bin ATLAS TeV, 36.1 fb 2 b-tags τ had τ had Data NR HH at exp limit Top-quark jet τ had fakes (Multi-jets) Z ττ +(bb,bc,cc) jet τ had fakes (tt) Other SM Higgs Uncertainty Pre-fit background 1 Data/Pred BDT score Figure 5.2: Distribution of the BDT score for non-resonant di-higgs signal in the τ had τ had channel, taken from the published analysis of Ref. [3]. The signal is scaled to the expected limit. The lower panel shows the ratio of the data to the sum of the backgrounds. The distribution of the BDT score is shown after a profile-likelihood fit [4] with the background-only hypothesis. The binning used for the fit is determined after fulfilling two conditions. First, the pre-fit relative background statistical uncertainty in each bin of the BDT score should be less than.5 times the signal fraction in that bin, and second, the minimum number of expected background events in each bin should be five [41]. Figure 5.2 shows a transformed BDT score after rebinning Existing upper limits Next, upper limits are set on the non-resonant Higgs boson pair-production at 95% confidence level (CL) using the CLs method [42]. The published analysis of Ref. [3] sets upper limits on the cross section for non-resonant HH production times the branching ratio of HH bbττ. These results, which pertain to both sub-channels, i.e. τ lep τ had and τ had τ had, and their combination, are presented in Table 5.2. The limits take into account both systematic and statistical uncertainties. The cross section times branching ratio for non-resonant Higgs boson pair-production is constrained to be less than 3.9 fb, corresponding to 12.7 times the SM expectation, at 95% CL for the combination, representing the most stringent limit on non-resonant HH set by an individual channel at the LHC. For the remainder of the thesis, we focus on the limit corresponding to the τ had τ had channel. In that case, still with both systematic and statistical uncertainties, the observed (expected) limit is 4. fb (42.4 fb), 16.4 (17.4) times the SM expectation. 5.2 Purpose The aim of this study is the rescoping of the multivariate analysis by introducing a cut-based analysis, in order to estimate the gain from using the MVA technique. Despite its limitations, a cut-based analysis offers 21

23 Table 5.2: Observed and expected upper limits on the non-resonant SM di-higgs production cross section times the branching ratio of HH bbττ at 95% CL, together with their ratios to the SM expectation [3]. more insight in the event selection, thus reinterpretations of the results become somewhat easier. This can be a benefit for theorists who can do MC simulations, mimic the cuts provided from these analyses and adapt the results to their theory. The objective is to learn from the BDT selection and use that to define an optimal cut-based analysis. The steps that are followed include unfolding the BDTs, looking at the BDT input variables and optimizing cuts. Then, signal and control regions are defined, after choosing a final discriminant and upper limits on the SM HH production cross section are set. 5.3 Cut-based analysis Unfolding the BDT At the first stage of the cut-based analysis, after having applied the SR preselection described in Section 4.3, distributions of the input variables used in the BDT analysis are shown, while considering only the last bins of the BDT. The effect of a cut on the BDT score on the shape of input variables is estimated by comparing the distributions before and after the cut. At first, this is done only for signal, as can be seen in Figure 5.3 and Figure 5.4. The blue line defines the distribution after the cut on the last one and the last two bins of the BDT score (as in Figure 5.2) for each variable, while the red line refers to the distribution when taking into account all bins of the BDT. Next, all background processes are included, and the distributions of BDT input variables are again shown without applying any cut on the BDT score (Figure 5.5). All these variables and especially the masses and distances R between the variables, offer very good discrimination power between signal and background. The non-resonant HH signal is scaled to the sum of backgrounds in every case, but in reality it would be much smaller. For the backgrounds, the pink color corresponds to multijet events with jets faking τ had, estimated using the Fake Factor method. Events with fake τ had objects from t t are shown in brown color, while backgrounds with truth matched τ had objects from t t are in yellow. The several shades of blue refer to events from Z τ τ + (bb, bc, cc) processes. The latter background is very signal-like, and hence dominant at high BDT score. This explains why a big contribution still remains after cutting on the last one and two bins of the BDT score. Looking at Figure 5.3, Figure 5.4 and Figure 5.5, the BDT appears to cut into the low-m HH region, where the background contribution is very large. It also cuts into the tails of the m MMC ττ, m bb, R(τ, τ) and R(b, b) variables, where the difference between the reconstructed and truth values is larger. There is no phase space of the SR that is completely removed by the cut on the BDT score. 22

24 (a) m HH (b) m MMC ττ (c) m bb (d) R(τ, τ) (e) R(b, b) (f) ET missφ centrality Figure 5.3: Distributions of BDT input variables for signal with and without a cut on the last two bins of the BDT score, overlaid. The blue line defines the distribution when the last two bins of the BDT are selected, while the red line refers to the whole distribution. 23

25 (a) m HH (b) m MMC ττ (c) m bb (d) R(τ, τ) (e) R(b, b) (f) ET missφ centrality Figure 5.4: Distributions of BDT input variables for signal with and without a cut on the last bin of the BDT score, overlaid. The blue line defines the distribution when only the last bin of the BDT is selected, while the red line refers to the whole distribution. 24

26 Events (Data Bkg)/Bkg ATLAS Work in Progress 1 Ldt = 36.1 fb s = 13 TeV hh bbτ had τ had, 2 tags, Presel., SR_SMRW m HH [GeV] Data hh (NR,RW) x fake ttbar (FF) ttbar (FT) ttbar (TF) ttbar (TT) single top (fake) single toptt Z Zττ+bb Zττ+bc Zττ+bl Zττ+cc Zττ+cl Zττ+l W+jets diboson tth VH (Data Bkg)/Bkg Stat Stat+Shape Stat+Sys Events (Data Bkg)/Bkg ATLAS Work in Progress 1 Ldt = 36.1 fb s = 13 TeV hh bbτ had τ had, 2 tags, Presel., SR_SMRW MMC m ττ [GeV] Data hh (NR,RW) x fake ttbar (FF) ttbar (FT) ttbar (TF) ttbar (TT) single top (fake) single toptt Z Zττ+bb Zττ+bc Zττ+bl Zττ+cc Zττ+cl Zττ+l W+jets diboson tth VH (Data Bkg)/Bkg Stat Stat+Shape Stat+Sys (a) m HH (b) m MMC ττ Events (Data Bkg)/Bkg ATLAS Work in Progress 1 Ldt = 36.1 fb s = 13 TeV hh bbτ had τ had, 2 tags, Presel., SR_SMRW m bb [GeV] Data hh (NR,RW) x fake ttbar (FF) ttbar (FT) ttbar (TF) ttbar (TT) single top (fake) single toptt Z Zττ+bb Zττ+bc Zττ+bl Zττ+cc Zττ+cl Zττ+l W+jets diboson tth VH (Data Bkg)/Bkg Stat Stat+Shape Stat+Sys Events (Data Bkg)/Bkg ATLAS Work in Progress 1 Ldt = 36.1 fb s = 13 TeV hh bbτ had τ had, 2 tags, Presel., SR_SMRW R(τ,τ) Data hh (NR,RW) x fake ttbar (FF) ttbar (FT) ttbar (TF) ttbar (TT) single top (fake) single toptt Z Zττ+bb Zττ+bc Zττ+bl Zττ+cc Zττ+cl Zττ+l W+jets diboson tth VH (Data Bkg)/Bkg Stat Stat+Shape Stat+Sys (c) m bb (d) R(τ, τ) Events (Data Bkg)/Bkg ATLAS Work in Progress 1 Ldt = 36.1 fb s = 13 TeV hh bbτ had τ had, 2 tags, Presel., SR_SMRW R(b,b) Data hh (NR,RW) x fake ttbar (FF) ttbar (FT) ttbar (TF) ttbar (TT) single top (fake) single toptt Z Zττ+bb Zττ+bc Zττ+bl Zττ+cc Zττ+cl Zττ+l W+jets diboson tth VH (Data Bkg)/Bkg Stat Stat+Shape Stat+Sys Events (Data Bkg)/Bkg 6 ATLAS Work in Progress 1 Ldt = 36.1 fb s = 13 TeV hh bbτ had τ had, 2 tags, Presel., SR_SMRW MET φ Centrality Data hh (NR,RW) x fake ttbar (FF) ttbar (FT) ttbar (TF) ttbar (TT) single top (fake) single toptt Z Zττ+bb Zττ+bc Zττ+bl Zττ+cc Zττ+cl Zττ+l W+jets diboson tth VH (Data Bkg)/Bkg Stat Stat+Shape Stat+Sys (e) R(b, b) (f) ET missφ centrality Figure 5.5: Distributions of all BDT input variables for the SM non-resonant signal model and the associated backgrounds in the bbτ had τ had channel. Only statistical uncertainties are shown. 25

27 5.3.2 Fitting the BDT score distribution As a next step, before deciding on the cuts that will later be applied, we recompute upper limits on the HH production cross section, while fitting the BDT score distribution. In this way, by comparing the results with the published ones, we can check the agreement and ensure that our set-up is working properly. The corresponding upper limits on the cross section are presented in Table 5.3. The whole BDT score distribution is fitted in order to have a reference point for comparing our later results. In this study the systematic uncertainties are not considered. However, statistical uncertainties on both data and MC simulations as well as normalisation uncertainties for the freely floating backgrounds are included. The normalisation of the simulated background samples from Z+heavy-flavor production is allowed to freely float in the final profile-likelihood fit, as described in Ref. [3]. Also, as mentioned in Section 4.3.1, there is a dedicated control region included in the fit, so that the Z+heavy-flavor jets background is constrained. As seen in Table 5.3, the expected upper limit on the non-resonant HH production cross section is estimated to be around 15 times the SM expectation. Table 5.3: Expected upper limits on the production cross section times the HH bbτ had τ had branching ratio for non-resonant HH at 95% CL, and their ratio to the SM prediction, when fitting the whole BDT score distribution. Only MC statistical uncertainties are considered. The ±1σ, ±2σ variations about the expected limit are also shown. 2σ 1σ Expected +1σ +2σ σ(hh bbτ τ) [pb] σ/σ SM Fitting the m HH distribution Next, we set again upper limits on the HH production cross section, but this time by fitting the m HH distribution in signal and control regions based on the BDT score. In this way, the benefit from using the BDT score as the final discriminant (which is a better final discriminant than any of the input variables by construction) is estimated. We begin by fitting the whole m HH distribution (Table 5.4). The result in that case is expected to be bad, namely 64.2 σ SM, because we do not apply any additional selection. Then, we define the last two BDT bins as a SR and the remaining ones as a CR, and we compute the limits by again fitting m HH (Table 5.5). This gives an expected limit of 73 fb, 21.7 times the SM prediction, hence it is clear that the BDT provides more separation power than m HH. As a matter of fact, the separation of m HH at high BDT score is slightly worse compared to the BDT itself. Finally, we define the last BDT bin as a SR and the remaining bins as a CR and we set limits by again fitting m HH (Table 5.6). The result of 53 fb, 16 times the SM prediction is quite close to the limit obtained when fitting the BDT. The difference comes from the separation power in lower BDT bins, that are used as a CR here. Table 5.4: Expected upper limits on the production cross section times the HH bbτ had τ had branching ratio for non-resonant HH at 95% CL, and their ratio to the SM prediction, when fitting the whole m HH distribution with no cut on the BDT score. 2σ 1σ Expected +1σ +2σ σ(hh bbτ τ) [pb] σ/σ SM Next step is to define good enough cuts in order to select only events that end up at high BDT score, and use m HH as the final discriminant in the fit. 26

28 Table 5.5: Expected upper limits on the production cross section times the HH bbτ had τ had branching ratio for non-resonant HH at 95% CL, and their ratio to the SM prediction, by fitting m HH while selecting the last two BDT bins as the SR. The other BDT bins make up the CR, also included in the fit of the m HH distribution to set upper limits. 2σ 1σ Expected +1σ +2σ σ(hh bbτ τ) [pb] σ/σ SM Table 5.6: Expected upper limits on the production cross section times the HH bbτ had τ had branching ratio for non-resonant HH at 95% CL, and their ratio to the SM prediction, by fitting m HH while selecting the last BDT bin as the SR. The other BDT bins make up the CR, also included in the fit of the m HH distribution to set upper limits. 2σ 1σ Expected +1σ +2σ σ(hh bbτ τ) [pb] σ/σ SM Definition of variables We move on by defining some new variables, based on which we will later define signal and control regions instead of BDT bins while fitting the final discriminant. We now want to cut on the input variables, but instead of making a rectangular cut in the m ττ and m bb plane, we define a variable that will allow us to make an elliptical cut, so that some of the correlations are taken into account. The same applies for the angular distances of di-τ and di-b objects. Thus, these variables associate the mass and R of di-τ and di-b objects, since m ττ and m bb (and similarly R ττ and R bb ) are very correlated. They are defined as follows: (mττ ) 2 ( ) GeV mbb 112 GeV X mττ m bb = + (5.4).1 m ττ.1 m bb ( Rττ ) 2 ( ) Rbb X Rττ R bb = + (5.5).1 R ττ.1 R bb where the numerical values in the numerator are obtained after a Gaussian fit on the signal distributions of m ττ, m bb, R ττ and R bb, and correspond to the mean values of each distribution. The definition of those variables follows the definition of the cuts introduced in the publication of Ref. [43]. Figure 5.6(a,b) shows the signal and background distributions for these variables, while in (c) the signal distributions are shown in a two-dimensional histogram. We conclude that there is no strong correlation between X mττ m bb and X Rττ R bb. 27

29 Events ATLAS Work In Progress TeV, 36.1 fb τ had τ had 2 b-tags Top-quark Fakes (Multi-jets) Z->ττ + (bb,bc,cc) SM Higgs Diboson Other Signal Events ATLAS Work In Porgress TeV, 36.1 fb τ had τ had 2 b-tags Top-quark Fakes (Multi-jets) Z->ττ + (bb,bc,cc) SM Higgs Diboson Other Signal X mττm bb X Rττ R bb (a) X mττ m bb (b) X Rττ R bb X Rττ R bb ATLAS Work In Progress 13 TeV, HH bbτ had τ had Events X mττ m bb (c) X mττ m bb vs X Rττ R bb Figure 5.6: Signal and background distributions of the X mττ m bb and X Rττ R bb variables (a,b), and two-dimensional signal distribution between those variables (c) Optimization of cuts After having defined the X mττ m bb and X Rττ R bb variables, the next step is to find optimal cuts on these variables, so that most of the expected background events are removed while at the same time most of the signal survives. For that reason, a series of significance tests are conducted and different combinations of cuts are tested. The aim is to find the combination of cuts that gives the highest significance. The significance is defined as the ratio of the total signal event yield to the square root of the total background event yield, s/ b, with s and b being the number of signal and background events respectively, as mentioned earlier in Section 5.1. First, the significance is computed as a function of the X mττ m bb variable. Also, the signal efficiency is plotted as a function of the same variable, and cuts on X mττ m bb corresponding to 7% (X mττ m bb < 2.4), 8% (X mττ m bb < 3.2) and 9% (X mττ m bb < 4.4) signal efficiency are later applied. Table 5.7 shows the initial signal and background event yields as well as those after the cuts mentioned above. The cut yielding the Signal yield is the expected number of events after the selection. It is normalized to the luminosity of 36.1 fb 1 and the HH cross section of fb. 28

30 highest significance, X mττ m bb < 1.8, is also considered. In addition to signal efficiency plots, ROC (Receiver Operating Characteristic) curves are shown to illustrate the background rejection rate as a function of the signal efficiency. Figure 5.7 includes significance and signal efficiency distributions, as well as a ROC curve for the X mττ m bb variable. Figure 5.8 shows significance distributions for the X Rττ R bb variable after cuts on X mττ m bb corresponding to 7%, 8% and 9% signal efficiency are applied. Table 5.7: Signal (s) and background (b) yields before applying preselection cuts, and after applying a cut on X mττ m bb corresponding to the maximum significance and corresponding to 7%, 8% and 9% in signal efficiency. Initial X mττ m bb < 1.8 X mττ m bb < 2.4 X mττ m bb < 3.2 X mττ m bb < 4.4 s.78 ±.3.41 ±.2.53 ±.3.6 ±.3.68 ±.3 b ± ± ± ± ± 12.5 Significance ATLAS Work in Progress 1 13 TeV, 36.1 fb, τ had τ had 2 b tags Signal Efficiency ATLAS 1 13 TeV, 36.1 fb, τ had τ had Work in Progress 2 b tags Background Rejection Rate ATLAS Work in Progress 1 13 TeV, 36.1 fb, τ had τ had 2 b tags X mττm bb X mττm bb Signal Efficiency (a) significance (b) signal efficiency (c) ROC curve Figure 5.7: Significance and signal efficiency as a function of the cut on the X mττ m bb variable, and corresponding ROC curve. The cut value for the highest significance is 1.8 (a), while the cut values for 7%, 8% and 9% in signal efficiency (b) are found at 2.4, 3.2 and 4.4 respectively. 29

31 Significance ATLAS Work in Progress 1 13 TeV, 36.1 fb, τ had τ had 2 b tags Significance ATLAS Work in Progress 1 13 TeV, 36.1 fb, τ had τ had 2 b tags Significance ATLAS Work in Progress 1 13 TeV, 36.1 fb, τ had τ had 2 b tags X R(τ,τ) R(b,b) X R(τ,τ) R(b,b) X R(τ,τ) R(b,b) (a) after cutting on X mττ m bb < 2.4 (b) after cutting on X mττ m bb < 3.2 (c) after cutting on X mττ m bb < 4.4 Figure 5.8: Significance versus the cut value for the X Rττ R bb variable after a cut on X mττ m bb is applied corresponding to the three aforementioned cases of signal efficiency. The reverse procedure was tested, meaning that the significance and signal efficiency are plotted as a function of the cut on the X Rττ R bb variable and a ROC curve is computed in Figure 5.9. Then significance plots for X mττ m bb are shown after applying cuts on X Rττ R bb corresponding to 7%, 8% and 9% in signal efficiency (Figure 5.). Table 5.8 shows the corresponding event yields as well. Table 5.8: Signal (s) and background (b) yields before applying preselection cuts, and after applying a cut on X Rττ R bb corresponding to the maximum significance and corresponding to 7%, 8% and 9% in signal efficiency. Initial X Rττ R bb < 2.8 X Rττ R bb < 4.8 X Rττ R bb < 5.5 X Rττ R bb < 6.3 s.78 ±.3.27 ±.2.49 ±.3.57 ±.3.64 ±.3 b ± ± ± ± ±

32 Significance ATLAS Work in Progress 1 13 TeV, 36.1 fb, τ had τ had 2 b tags Signal Efficiency ATLAS Work in Progress 1 13 TeV, 36.1 fb, τ had τ had 2 b tags Background Rejection Rate ATLAS Work in Progress 1 13 TeV, 36.1 fb, τ had τ had 2 b tags X R(τ,τ) R(b,b) X R(τ,τ) R(b,b) Signal Efficiency (a) significance (b) signal efficiency (c) ROC curve Figure 5.9: Significance and signal efficiency as a function of the cut on the X Rττ R bb variable, and corresponding ROC curve. The cut value for the highest significance is 2.8 (a), while the cut values for 7%, 8% and 9% in signal efficiency (b) are found at 4.8, 5.5 and 6.3 respectively. Significance ATLAS Work in Progress 1 13 TeV, 36.1 fb, τ had τ had 2 b tags Significance ATLAS Work in Progress 1 13 TeV, 36.1 fb, τ had τ had 2 b tags Significance ATLAS Work in Progress 1 13 TeV, 36.1 fb, τ had τ had 2 b tags X mττm bb X mττm bb X mττm bb (a) after cutting on X Rττ R bb < 4.8 (b) after cutting on X Rττ R bb < 5.5 (c) after cutting on X Rττ R bb < 6.3 Figure 5.: Significance versus the cut value for the X mττ m bb variable after a cut on X Rττ R bb is applied corresponding to the three aforementioned cases of signal efficiency. 31

33 This study suggests that the combination of cuts for which the highest significance can be achieved is when X mττ m bb < 2.4 (corresponding to a 7% signal efficiency). In that case the cut value of X Rττ R bb corresponding to the maximum significance is at 2.2. Therefore, the next step is to apply both those cuts and check the event yields. We get only.14 ±.1 events for signal and 1.6 ±.5 background events, which is too low and does not follow the binning criteria used to ensure meaningful statistics. Another definition for the significance, which is more robust in the low statistics limit, is now used, called the Asimov significance [4], defined by: Z = 2 ((s + b) ln(1 + s ) s). (5.6) b The uncertainty on the Asimov significance is given using error propagation: σ Z = 1 Z (ln(1 + s b ) σ s) 2 + ((ln(1 + s b ) s b ) σ b) 2. (5.7) By maximizing the Asimov significance, the optimal cuts are chosen. A two-dimensional scan to compute the significances versus cuts on the X mττ m bb and X Rττ R bb variables is performed in Figure 5.11 where the uncertainties are also computed. Two conditions are applied, requiring that the value of the significance is filled only when more than five background events exist and that the relative background uncertainty in a given range is less than.5 times the signal fraction. X Rττ R bb ±.1.8 ±.1.9 ±.1 ATLAS Work in Progress.8 ±.1.9 ±.1.8 ±.1.8 ±.1.9 ±.1.7 ±.1.8 ±.1.8 ± TeV, 36.1 fb, τ had τ had 2 b tags.7 ±.1.7 ±.1.7 ±.1.6 ±..7 ±.1.7 ±.1.6 ±..6 ±.1.7 ±.1.7 ±.1.6 ±..6 ±.1.6 ±.1.7 ±.1.6 ±..6 ±.1.6 ±.1.7 ±.1.6 ±..6 ±..6 ±.1.6 ±.1.5 ±..6 ±..6 ±.1.6 ± Significance X mττ m bb Figure 5.11: Asimov significance and its uncertainty versus cut values for both X mττ m bb and X Rττ R bb. 32

34 Chapter 6 Results and discussion Three points are selected from the two-dimensional histogram of Figure 5.11 so that signal and control regions can be defined accordingly and limits on the HH production cross section can be set. The three points are shown in Figure 6.1 with red color. Figure 6.1: Illustration of the three selected points from the distribution of Asimov significance for the cuts on X mττ m bb and X Rττ R bb. They correspond to the following set of X mττ m bb and X Rττ R bb cut values: Cut 1: X mττ m bb < 1.8 and X Rττ R bb < 4. Cut 2: X mττ m bb < 2.7 and X Rττ R bb < 4. Cut 3: X mττ m bb < 2.7 and X Rττ R bb < 3. The signal and background yields after each of the cuts are presented in Table 6.1. Having decided that these are the optimal cuts in the mass and R planes between di-τ and di-b objects, a signal region, that is an event selection mostly sensitive to the signal, can be defined, as well as a control region so that the backgrounds can be constrained. For each different combination of cuts, the SR is defined by the specific cuts, while the CR is defined by simply inverting the cuts. 33