CORSO DI LAUREA TRIENNALE IN FISICA. SEARCH FOR NEW PHYSICS IN PHOTON+JET EVENTS IN P-P COLLISIONS AT 13 TeV WITH THE ATLAS DETECTOR

Transcription

1 CORSO DI LAUREA TRIENNALE IN FISICA SEARCH FOR NEW PHYSICS IN PHOTON+JET EVENTS IN P-P COLLISIONS AT 13 TeV WITH THE ATLAS DETECTOR Codice PACS: i Relatore interno: Prof. Leonardo Carminati Correlatore: Dott. Miguel Villaplana Tesi triennale di: Davide Nolè Matricola N 8451 Sessione Autunnale, Secondo Appello Anno Accademico

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3 Contents Introduction v 1 LHC and p-p collisions The Large Hadron Collider Proton-proton collisions Phenomenology Pile-up and underlying events ATLAS detector Detector overview Inner Detector Calorimeters Muon and magnet system Trigger system and data acquisition Monte Carlo simulations Quantum gravity and photon+jet signature Quantum black holes Photon+jet channel Samples Photons and jets in the ATLAS detector Photon reconstruction Photon isolation Photon identification Jet reconstruction Event selection Di-jet contamination estimate The 2D sideband method iii

4 CONTENTS Theoretical basis for the method Sample selections Regions definition Systematic uncertainties Method validation Results Overall purity Purity as a function of p T,γ Purity as a function of η γ Purity as a function of m γj Photon isolation correction Results Searching for a signal Likelihood-based test for new physics Models from Monte Carlo samples Analysis Code validation Results Conclusions 57 Bibliography 59 iv

5 Introduction The aim of high energy physics is to study the main constituents of matter and their interactions. One of the main sources of data on this topics is represented by particles colliders, like the LHC ( Large Hadron Collider ) at CERN. Its focus is on hadron collisions, and it is currently collecting data on proton-proton collisions with a centre-of-mass energy s = 13 TeV. The data provided by the LHC are then analysed mainly by four large-scale experiments: ATLAS, CMS, LHCb and ALICE. Their purpose is to provide high precision measurements on Standard Model processes and searching for physics beyond that model. The Standard Model does not provide a theoretical explanation for the behaviour of gravity on a quantum scale. However, many theories explain this behaviour through the existence of one or more extra dimensions. The phenomenology predicted by these theories includes the existence of micro black holes, i.e. black holes with size analogous to the quantum scale, and gravitons, the hypothetical gauge bosons mediating gravitational force. One of the decay channels of these objects is the photon+jet channel, on which this thesis focuses. The aim is thus to search for an excess of events over the background predicted by the Standard Model. For this purpose photons with p T,γ > 150 GeV and pseudorapidity η γ < 1.37 and jets with p T,j > 150 GeV and are selected. In particular, in this thesis the background composition and the photon isolation systematics were studied. To estimate the di-jet contamination in the photon+jet sample the 2D sideband method was used. This is based on the classification of the photon candidates in one signal region and three control regions, by means of cuts on the isolation variable (ET iso ) and on the identification. The first variable is obtained from the sum of the energy depositions in a cone around the photon candidate in the Electromagnetic Calorimeter. The latter is based on a set of cuts on discriminating variables, used to define a photon as tight (passing all the cuts) or non-tight (failing one or more cuts). The signal region is the one having tight and isolated photon candidates, the control regions contain the candidates failing the cuts. In order to use the method one has to assume negligible correlation in the background in the four regions, as v

6 CHAPTER 0. INTRODUCTION well as negligible signal leakage in the control regions. While the second assumption was tested, evaluating the signal leakage through Monte Carlo (MC) simulations, the first was taken as true from the RUN1 analysis. After a code and method validation on a simulated sample of photons and jets of known composition, the method was applied on the data sample, studying the relative contamination from di-jet components as a function of some kinematic variables: the photon transverse momentum, pseudorapidity and the invariant mass of the photon+jet pair. fraction of di-jet events in the sample was found to be smaller than % and almost constant as a function of the studied kinematic variables. In the second part of the thesis the definition of the isolation cut for the photon candidates was studied. This is done a priori relying on a MC simulated sample of photons. The Even though the simulation is quite accurate, it is possible to find some differences in the ET iso distributions between data and MC. In particular, the difference in the distribution peak positions was studied through a two step analysis. Firstly, the di-jet component contributions were removed from the distributions by subtracting the normalised non-tight photon distributions from the tight ones. Then a fit with a Crystal Ball function was applied to the background-subtracted distributions and on the MC ones. This allows the extraction of the peak positions and thus the evaluation of the shifts between the functions. The data-mc shifts were found to be always below 1 GeV, having an impact on the signal efficiency smaller than 1%. Finally an estimate of the presence of a black hole signal in the selected sample was made. In order to do this a test statistic based on the profile likelihood ratio test was used. No evidence of a signal of new physics in the photon+jet channel was observed. This thesis is structured as follows. After a short introduction to the LHC and to proton-proton collisions in chapter 1, chapter 2 will focus on the ATLAS detector. Its main features will be described, together with an introductory report on Monte Carlo simulations. In chapter 3 two theoretical models of quantum gravity will be introduced, as well as the studied decay channel. Photon and jet reconstruction in ATLAS, with isolation and identification variables will be reported in chapter 4, with the analysis cuts. Chapters 5 to 7 will describe the analysis made in this thesis. The first will focus on the estimate of the di-jet component of the sample, describing also the used method. The study conducted on the isolation variable will be reported in chapter 6. The last chapter will describe the simplified signal searching process used in the reported analysis and its results on the data sample. vi

7 Chapter 1 LHC and p-p collisions The aim of this chapter is to summarise the features and main purposes of the LHC, its main experiments, and discuss the phenomenology of proton-proton (p-p) collisions, as well as the experimental challenges that must be faced in order to study the collisions. The descriptions are made following [11] 1.1 The Large Hadron Collider The Large Hadron Collider (LHC) is currently the world s biggest and most powerful circular particle accelerator. Located near Geneva, installed in the 27 kilometres long tunnel which contained the LEP, it is designed to provide p-p and heavy-ion collisions. Its 14 TeV designed pp centre-of-mass energy - about seven times larger than the previous largest centre-of-mass energy machine (the Tevatron) - and 34 cm 1 s 1 designed luminosity - about a hundred times larger than at the Tevatron and at the LEP - allow the attainment of searches for new particles up to masses of 5 TeV. The instantaneous luminosity is a measurement of the number of collisions per unit of time. In particular, it is defined as: L = 1 σ dn dt (1.1) where N is the number of collisions, t is time and σ is the interaction cross-section. The dn dt, i.e. the event rate, is usually reported as R. Apart from the cgs units already cited (cm 1 s 1 ) a non-si unit is usually used, b 1 s 1 where b is the barn ( 28 m 2 ). Fig 1.1 shows an exemplary plot of L during a typical working day. The 1

8 CHAPTER 1. LHC AND P-P COLLISIONS Figure 1.1: Example of plot of L during 1 November integrated luminosity L int, defined as: L int = Ldt (1.2) is used to report the total number of analysed collisions. Fig. 1.2 shows an exemplary plot of L int. In order to produce the collisions needed, two particle beams travel in opposite directions through two separated pipes kept at ultrahigh-vacuum, guided by superconductive magnets that need to operate at 1.85 K. Such a low temperature condition is obtained by cooling the magnets with liquid helium. Among the magnets, 1232 dipole ones bend the beams, and 392 quadrupole ones focus it. The beams are accelerated by 16 Radiofrequency cavities, whose frequency is chosen so that the beam is subjected to an accelerating field every time it passes through a cavity. When the energy of the particle beams is the designed one, ideally, they should receive no energy at each passage, if the frequencies of the RF cavities and the particle beams are perfectly tuned. However, if the beams are slower, or faster, they are subjected to an accelerating or a decelerating field respectively, thus tuning their speed to the ideal one. The data provided by the LHC are analysed mainly by four large-scale experiments: ATLAS and CMS are multi-purpose pp experiments, whose aims include search for new particles and better measurements of the properties the known ones; LHCb, which is focused on B-hadron physics and CP-violation; and ALICE, a heavy-ion experiment studying the nuclear matter behaviour at high energy and density, con- 2

9 1.1. THE LARGE HADRON COLLIDER Figure 1.2: Total L int recorded to 5 November. cerning in particular the formation of the quark-gluon plasma. One of the main purposes of the LHC was to understand the origin of the masses of the particles. In the Standard Model (SM) this is accounted for through the Higgs mechanism, so the discovery of the Higgs boson in 2012 was probably the greatest achievement made by the ATLAS and the CMS collaborations. This discovery was certainly not the end of the research the CERN has planned to do on that particle: its properties are to be measured with a high precision, in order to see if there is any deviation from the SM. Apart from the work on the Higgs boson, the LHC was built with other physics motivations, such as: Perform precision measurements on the known particles, as through this kind of measurement some deviation from the SM can be seen, becoming signals of new physics. This can be achieved because particles such as W and Z bosons, t and b quarks are produced with a high rate in the LHC p-p collisions. Look for physics beyond the SM, as there are several reasons not to believe it to be the ultimate theory of particle interaction. One of them is the little physical justification of the Higgs mechanism, which leads to divergent radiative corrections to the Higgs boson, unless fine-tuned cancellations occur. Furthermore, there are hints on the unification of the coupling constants of electromagnetic, weak and strong interactions for very high energies ( 16 GeV), leading to a simple physics model in which every force exists with the same strength. This is predicted by Grand Unified Theories (GUT) and more general theories 3

10 CHAPTER 1. LHC AND P-P COLLISIONS such as Supersymmetry (SUSY), some of which predict manifestation of new physics at energy scale accessible to the LHC. Answer to other open questions, such as if quarks and leptons are elementary particles, if there exist additional families of quarks, leptons, and gauge bosons, find a reason why the distribution of matter and antimatter are asymmetrical in the universe, and find out the composition of Dark Matter. 1.2 Proton-proton collisions Phenomenology At s = 14 TeV, the total inelastic p-p cross-section is 80 mb. Therefore the expected event rate is R = σ L 9 s 1 (1.3) Those events can be divided in two classes: Soft collisions. This class of events represents the large-distance interactions between incoming protons. In this case the momentum transferred is small, thus particles scatter at small angle, so that they have large longitudinal momentum but small transverse momentum p T ( 500 MeV). They represent by far the majority of collisions. Hard collisions. As proton beams can be seen as parton (quarks and gluons) beams, it is possible to observe, sometimes, head-on collisions between these constituents. They are small distance interactions, thus characterised by large momentum transfers. In this case, it is possible to produce particles with high p T and massive particles. Even though it is the most important one, this class of events is rare compared to the soft one. During hard collisions in hadron colliders, the effective centre-of-mass energy of the interaction ŝ is smaller than the centre-of-mass energy of the machine s. It is in fact given by: ŝ = xa x b s (1.4) where x a and x b are the fractions of the proton momenta carried by the interacting partons. The relation can be simplified if x a x b : ŝ = x s (1.5) 4

11 1.2. PROTON-PROTON COLLISIONS The distributions of quark and gluon momenta inside the proton are described through parton distribution functions (PDFs). Thus a PDF gives the probability of finding a parton with a certain fraction x of the proton momentum. It is possible to distinguish two types of quarks: the valence and the sea ones. The first type contributes to the quantum numbers of the protons, and therefore valence quarks carry a large fraction of the proton momentum. The latter ones are mainly produced by gluon radiation from the valence quarks, subsequently splitting into quark-antiquark pairs. They carry a much smaller momentum fraction. The PDFs depend on the 4-momentum exchanged in the interaction (Q 2 ): at small Q 2 only the valence quarks are visible, and the PDFs peak at large x values, while at large Q 2 the partons interact with the short-distance structure of the protons, hence accessing to the sea. The cross-section of a generic hard collision interaction is thus: σ = f a (x, Q 2 )f b (x, Q 2 )ˆσ a,b (x a, x b )dx a dx b (1.6) a,b where ˆσ a,b is the cross-section of the elementary interaction between the two partons and f a and f b are the respective PDFs Pile-up and underlying events Protons travel in bunches containing 11 particles and colliding every 25 ns, which means that, at design luminosity, about 00 charged particles are expected to hit the detector every 25 ns over the pseudo-rapidity region η < 2.5. Every high-p T interesting event is expected to be overlapped with an average of 25 soft events, therefore called pile-up. In order to separate the interesting events from the pile-up ones, the difference in p T is exploited, using it as a threshold to select events. Before applying even a loose p T cut (such as 2 GeV) the hard collision events are not clearly visible, because they are surrounded by many soft ones. Only removing this background it is possible to study the interesting events in a much clearer environment. To prevent unwanted consequences arising from the pile-up events, the LHC detectors were built in such a way to exhibit: Fast response time, so that the signal from the detector is not integrated over many bunch crossings, determining a too high pile-up. The typical response times are ns, which correspond to integrating over 1-2 bunch crossings, contributing with about soft events for each hard one; 5

12 CHAPTER 1. LHC AND P-P COLLISIONS Fine readout granularity, in order to minimise the probability that a particle from a pile-up event traverses the same detector element of an interesting object; Radiation resistance, because the high particle flux can cause damages to the detector, leading to a reduction of the collected signal, or to a detector breakdown. In addition to the pile-up, other products of hard scattering can lead to problems in the reconstruction phase: the underlying events. They are usually defined as everything that was interested by a hard interaction, except the hard interaction itself. It is possible to consider them as the remnants of two protons that interacted with each other through a hard collision. These can then form the so-called beambeam remnants, they can radiate particles, contributing to the background, or they can interact with each other, causing other events that can cover the interesting ones. 6

13 Chapter 2 ATLAS detector The ATLAS (A Toroidal LHC ApparatuS) detector is one of the two general purpose detectors at CERN, whose aim is studying p-p and heavy ions collisions. In this chapter its main features will be described, for a more accurate report on the detector, see [1]. Figure 2.1: Cartesian and spheric frames of reference in the ATLAS detector. The coordinate system and the nomenclature used to describe the detector and the collision products are now summarized, and can be seen in 2.1. To define the origin of the coordinate system the nominal interaction point is taken. The z-axis is defined by the direction of the beam, thus defining the x-y plane as the one orthogonal to that same direction. The x and y axis are respectively defined as pointing to the centre of the LHC ring and upwards. The side-a of the detector is defined as the one with positive z, while side-c is its negative counterpart. As the ATLAS detector is formally forward-backward symmetrical with respect to the collision point, it is useful to define also spherical coordinates through the definition of φ and θ as the usual azimuthal and polar angles. The latter is usually described using the pseudorapidity η = ln[tan(θ/2)], or the rapidity y = 1/2 ln[(e + p z )/(E p z )] when talking about massive objects, such as jets. The transverse momentum p T, energy E T and missing momentum ET miss are defined in the x-y plane. The distance in the η - φ space is defined as R = η 2 + φ 2. 7

14 CHAPTER 2. ATLAS DETECTOR Figure 2.2: General view of the ATLAS detector. 2.1 Detector overview Fig. 2.2 shows the detector and underlines its main features. The geometry of ATLAS is driven by the configuration of its magnets. The magnet system comprises a 2T thin superconducting solenoid that surrounds the inner-detector and three large toroids (a barrel and two end-caps), around the calorimeters. In the inner part of the tracking volume, semiconductor pixels and strip detectors operate to recognize patterns, measure momenta of charged particles and vertices. In the outer part, straw-tube tracking detectors are capable of generating and detecting transition radiation. The calorimetric system is based mostly on liquid-argon (LAr) technology, using lead as passive material. The electromagnetic sampling calorimeters cover the region with η < 3.2, the hadronic calorimeters the end-caps ( η > 1.5) and the forward hadronic and electromagnetic calorimeters cover a region up to η = 4.9. The hadronic calorimetry in the region with η < 1.7 is made of scintillator-tile and iron absorbers, divided in a large central barrel and two smaller barrel cylinders on either side of it. In the outer side of the detector, the muon spectrometer surrounds the calorimeters. Three air core toroidal magnets provide a bending magnetic field, thus minimising multiple scattering. A high resolution is achieved due to three layers of tracking chambers. The trigger systems form a very important part of the detector, as the event rate at design luminosity (9 ev/s) is too high to be completely recorded, some events must 8

15 2.2. INNER DETECTOR Figure 2.3: View of the Inner Detector of ATLAS. thus be rejected. The system is overall usually divided in two parts, the first one being the Level-1 (L1) Trigger system, hardware based. The second phase of eventtriggering is software based and operated by two levels, which are commonly known as High-level trigger. It provides a reduction up to the possible data recording rate. The forward region of the detector is covered by three smaller detector systems: LUCID, ALFA and ZDC. The first one, acronym for LUminosity measurement using Cherenkov Integrating Detector, is located at ±17 m. It is the main online source of information on the instantaneous luminosity delivered to ATLAS, detecting inelastic p-p scattering in the forward direction. ALFA (Absolute Luminosity For ATLAS) uses scintillating fibre trackers inside Roman pots approaching as close as 1 mm to the beam pipes to measure absolute luminosity, and is located at ±240 m. The last one is the Zero-Degree Calorimeter: it determines the centrality of the interaction point using alternating quartz rods and tungsten plates. It is located at ±140 m, near the point where the straight section of the vacuum tube divides in two independent beam pipes. 2.2 Inner Detector The Inner Detector (ID), shown in 2.3, has the fine granularity needed because of the track density created by the approximately 00 particles emerging from the collision point every 25 ns. It is immersed in the 2 T field generated by the central solenoid. Pixel and silicon microstrip (SCT) trackers are used in the η < 2.5 region to track charged particles; they are disposed in concentric cylinders around the z-axis 9

16 CHAPTER 2. ATLAS DETECTOR in the barrel, and on discs in the x-y plane in the end-caps. Silicon pixel detectors are placed around the vertex region. During the shut-down after RUN1 an additional layer of pixels (called IBL [9]) was inserted, reaching up to 3 cm from the interaction point in the R-direction. They are segmented in R-φ and z, and each track typically crosses four pixel layers, providing a single point of µm (R-φ) and 115 µm (e i ), where e i is the z-direction in the barrel and the R-direction in the end-caps. Around them, the SCT are disposed in a different geometry in the barrel and in the end-caps. In the first region, small-angle stereo strips set parallel to the z-axis are used to measure both coordinates, while in the latter ones two sets are used, one running in the R-direction, and a stereo one at a 40 mrad angle. Eight layers of theirs are typically crossed by each track providing an intrinsic accuracy of 17 µm (R-φ) and 580 µm (e i ) with the same notation used above. Transition Radiation Trackers (TRT) provide a very large number of hits per track (typically 36), allowing track following up to η = 2.0. They are disposed in straws in the e i -direction in each region, only giving R-φ information with an intrinsic accuracy of 130 µm per straw. All the above mentioned systems concur to a precise pattern recognition in each direction, where the less precise measurement of the TRT is compensated by the longer measured track length and the higher number of hits. The tracking measurements of the ID match the range of the electromagnetic calorimeter. The detection of transition-radiation photons in the straw tubes enhances the electron identification, while SCT provide vertexing and parameter measurements for heavy-flavour and τ-lepton tagging. 2.3 Calorimeters Covering the range η < 4.9, the calorimeters in the ATLAS detector use different techniques to suit the physics requirements in every region. A view of the calorimetric system is shown in fig Apart from the actual measurement requirements, the dimensions of the calorimeters have to be calibrated in order not to have electrons, photons and hadrons going through the muon detector. The EM calorimeter aims at measuring energy and directions of photons and electrons. It is divided into a barrel and two end-cap parts, with η < and < η < 3.2 respectively. Each of the parts is placed in its own cryostat, and all together, with the central solenoid, are placed in the same vacuum vessel, in order to reduce the material particles have to go through to access the calorimeters. The barrel is divided in two parts by means of a cut at z = 0. The end-caps consist

17 2.3. CALORIMETERS Figure 2.4: View of the calorimeters in ATLAS. of an inner and an outer coaxial wheels, covering different η-regions, discriminated by η = 2.5. The EM calorimeter is a lead-lar detector with accordion-shaped Kapton electrodes and lead absorber plates. This geometry configuration provides a complete φ symmetry without azimuthal cracks. In the region with η < 2.5, where the measurements have to be more precise, it is segmented in three sections in depth, while they are only two in the end-cap inner wheels. The strips section, which is the most internal one, has a typical granularity of ( η φ). It is the highest one, needed for the π 0 rejection. The middle and back sections have and granularities. To correct the energy lost by electrons and photons in the η < 1.8 region, a presampler upstream the calorimeter is used. The hadronic calorimeters have a coarser granularity, which still fulfils the physics requirements for jet reconstruction and ET miss measurements. They can be divided in three different sets: the tile, the LAr hadronic end-cap (HEC), and the LAr forward calorimeter (FCal). The first one is placed directly outside the EM calorimeter. It is divided into a central barrel and two extended barrels on each side, covering respectively the regions η < 1.0 and 0.8 < η < 1.7, each divided into 64 azimuthal modules and segmented in three layers in depth. As active material, scintillating tiles are used, and steel is used as absorber. The HEC is located behind the end-cap EM calorimeters and shares the same cryostats. It is composed of two independent wheels for both the end-caps, covering the 1.5 < η < 3.2 region. Built from 32 identical wedge-shape modules and 11

18 CHAPTER 2. ATLAS DETECTOR Figure 2.5: View of the Muon system of ATLAS. divided in two segments in depth, the wheels are constituted of copper plates and use LAr gaps between them as the active medium. The LAr technology is used in the forward region, as it is radiation tolerant Integrated in the end-cap cryostats, to have more uniformity in the calorimetry coverage, the LAr FCal consists of three modules for each end-cap. Each module is formed by a metal matrix with regular spaced longitudinal channels filled with the electrode structure. This consists of concentric rods in the z-axis direction. In the first module, copper is used to optimise electromagnetic measurements, whereas in the others, to measure energy of hadronic interactions, tungsten is used. As discussed before, calorimeters have to provide containment for electromagnetic and hadronic showers, limiting punch-through into the muon system. The total thickness of the EM calorimeter, higher than 22X0 (radiation lengths) in the barrel and than 24X0 in the end-caps, necessary to make precision measurement, provides the needed limitation. Whereas the hadronic calorimeter can provide precision measurements on high energy jets and ETmiss using the 9.7λ (interaction lengths) of active calorimeter in the barrel ( in the end-caps), and including 1.3λ from the outer support, is able to sufficiently reduce punch-through in the muon system. 2.4 Muon and magnet system The Muon system, shown in fig. 2.5, relies on the field generated by three toroid magnets, which bend the muon trajectories, then revealed by muon tracking chambers. The magnet system is divided in a central barrel magnet and two smaller end-caps, covering the η < 1.4 and 1.6 < η < 2.7 respectively; usually it is referred to the region in between as the transit region. The end-cap magnets are inserted in the first 12

19 2.4. MUON AND MAGNET SYSTEM one and rotated with respect to it in order to provide radial overlap of the fields and optimise the bending power in the transition region. This configuration was chosen to produce a field mostly orthogonal to the muon trajectory, while minimising the degradation of resolution due to multiple scattering. To characterise the performance in terms of bending power, the integral B dl is used, where the B term indicates the magnetic field perpendicular to the muon trajectory and the integral is evaluated along an infinitive-momentum muon trajectory, between the innermost and the outermost muon-chamber layers. The respective toroids provide a bending power of Tm in the barrel region, and of Tm in the end-caps. The bending power is lower in the transition region, where the fields overlap. The choice and design of the spectrometer instrumentation were made in order to optimise the detector performance in terms of rate capability, granularity, ageing properties and radiation hardness. The track-measuring chambers are disposed in three cylindrical layers around the z-axis in the barrel region, and in three planes perpendicular to the same direction in the end-caps. Over most of the η-range, Monitored Tubes (MTD s) provide measurements on the track coordinates in the principal bending direction, while for 2 < η < 2.7 Cathode Strip Chambers (CSC s), with higher granularity, are used. The chambers have to be aligned with respect to each other and to the overall detector in order to improve the detector performance. To reconstruct the chamber positions, as well as monitor the relative alignment, different techniques are used in the barrel and in the end-caps. For the stand-alone muon momentum measurement to be sufficiently accurate, a precision of 30 µm on the relative alignment of chambers within each projective tower and between consecutive layers in adjacent towers is necessary. In order to monitor the internal deformations and relative position of the MTD chambers, precision alignment sensor are used. To obtain adequate mass resolution for multi-muon final states, a precision of a few millimetres is necessary; this is achieved approximately during the installation of the chambers. To reconstruct the bending powers of the magnetic fields, with the goal precision of a few parts in a thousand, 1800 Hall sensors are distributed through the whole spectrometer volume. Comparing their measurements with simulations allows the reconstruction of the toroid coils position and accounts for its perturbations. The momentum resolution ranges from 1.7% at central rapidity and for p T GeV, to 4% at large rapidity and p T 0 GeV (for the details see [2]). The muon trigger system covers the region with η < 2.4, using Resistive Plate Chambers (RPC s) in the barrel and Thin Gap Chambers (TGC s) in the end-caps. It is used for three different purposes: identify the bunch-crossing, provide welldefined p T thresholds, and measure tracks in the direction perpendicular to the one 13

20 CHAPTER 2. ATLAS DETECTOR measured by the chambers. 2.5 Trigger system and data acquisition As already discussed, the design luminosity of the LHC accounts for a very high rate of interaction ( 1 GHz), while technology and resources limit the event data recording to 00 Hz; thus the Trigger system plays a key role in the data-taking process. Each of the three trigger levels refines the decisions made at the previous level, applying additional selections if necessary. The L1 trigger, hardware based, searches for high-p T particles such as electrons, photons, jets, muons and τ-leptons decaying into hadrons, as well as a large ET miss or total E T, using information collected by a subset of detectors. It also defines one or more Regions-of-Interest (RoI s), i.e. a certain η φ region which presents interesting features, including information on the features identified and the criteria passed. A decision is made in less than 2.5µs, reducing the event rate to 0 khz, thus the collected information is delivered to the higher level triggers. The information provided by the L1 trigger on the RoI s is used by these software triggers, which exploit all the available detector granularity in those regions to reduce the event rate to approximately the possible recording rate, using offline analysis procedures as implemented selections. 2.6 Monte Carlo simulations Monte Carlo (MC) simulations represent a very useful tool both for the detector calibrations and the analysis. They, in fact, provide information on the behaviour of the detector and estimate physical quantities of interest. A MC sample production starts with the generation of the collision of partons, following a theoretical model. Then, the interaction of the produced particles with the detector is simulated using GEANT4 [3]. This is a software capable of simulating the geometry and the composition of every part of ATLAS. It calculates the energy depositions in each detector volume. These deposits are converted into signals in the detector readout, and are reconstructed and analysed exactly as if they were coming from real particles. MC samples are produced in separate slices, depending on processes, final state particles, flavours or kinematic variables. For example events in which b-quarks or c-quarks are produced are particularly interesting for some analysis. Thus simulated samples accounting for these productions are divided from the others. In this thesis, large samples of simulated photon+jet events from SHERPA [12] and PYTHIA [17] 14

21 2.6. MONTE CARLO SIMULATIONS are used. These samples, among other divisions, are sliced in bin of p T,γ. These divisions are made in order to produce a sufficient number of events with a lower production rate without computing a very large number of events with higher production rates. Each MC sample comes with a cross-section weight that accounts for the real event production rate. Therefore, in order to see the real shape of a MC plot the sample must be weighted with the correct cross-section. Another weighting process must be applied to the MC sample, related to the pileup events. It is caused by the fact that the MC simulation are made by a priori consideration on the events, which can be different from the actual value observed in the data. In particular the variable that describes the pile-up incidence on the distributions is µ. It is defined as the average number of inelastic interactions per bunch crossing. As can be seen in fig. 2.6 the distributions of µ in the data sample and in the MC are quite different. In order to reproduce the real distribution of µ, it is necessary to re-weight the sample using the correct weight. As fig. 2.6 shows, after the re-weighting process, the distributions have a similar shape. Events s = 13 TeV, 3.25 fb µ Events s = 13 TeV µ Weighted events s = 13 TeV µ Figure 2.6: Plot of µ in the data sample (above left), and in the Monte Carlo sample before (above right) and after (below) pile-up re-weighting. 15

22 CHAPTER 2. ATLAS DETECTOR 16

23 Chapter 3 Quantum gravity and photon+jet signature While the Standard Model explains the behaviour of strong, weak and electromagnetic interactions, gravity still represents a challenge on a quantum scale. Many models try to explain the weakness of this interaction, compared to the other ones, through the existence of extra dimensions. In this chapter two of the theoretical models are introduced, in particular in relation to the production of micro black holes. The studied decay channel is also discussed, together with the selections applied to it. 3.1 Quantum black holes A Black hole (BH) is a region of space-time with a curvature so high that nothing can escape from it. Through Einstein s theory of General Relativity, the curvature of space-time is related to the presence of mass. It is possible to define a semiclassical object with an analogous behaviour, in fact we can define a BH as an object having a radius smaller the Schwarzschild radius r S. This is defined as the radius of the event horizon of a mass and can be obtained, in a semiclassical framework, equalising the escape velocity of the considered body to the speed of light in vacuum c. r S = 2 GM c 2 (3.1) where M is the mass of the considered object and G is the Gravitational constant. Therefore, it is possible to export this definition down to a quantum level. In that 17

24 CHAPTER 3. QUANTUM GRAVITY AND PHOTON+JET SIGNATURE condition, the Compton wavelength: λ C = h Mc (3.2) where h is the Planck constant, represents a limit on the minimum size of the localisation region for a mass M at rest. Comparing these quantities, it is possible to determine a threshold mass: if the body has a mass smaller than this threshold, it cannot form a BH. This threshold mass is (apart from a π 1 2 ) the Planck mass: M P = c G GeV (3.3) Such a mass is obviously out of the LHC range, thus no semiclassical BH is expected to be seen in ATLAS. However, two different theories ([4] [16]) propose to solve the Hierarchy problem (i.e. the problem of Gravity being much weaker than all the other forces) without relying on SUSY or technicolor. Such theories provide a different definition of the Planck scale, and allow, therefore, the production of quantum BH in ATLAS. In the first case, the weakness of gravity on distances 1 mm is justified by the existence of n 2 compactified extra spatial dimensions with radius R. The fundamental Planck scale in the (4+n)-dimensional space, M D, is related to the apparent mass scale M P by: M 2 P = M 2+n R n (3.4) where M P = M P 8. Gravitons freely propagate through the new dimensions, while the SM fields must be localized on a 4-dimensional manifold of weak scale thickness in the extra dimensions. For any number n it is possible for the experiments running at the LHC to observe quantum gravitational effects, at scales of TeV. In particular, in [4], a model with n = 6 extra dimensions is constructed. On the other hand, in the model proposed by Randall and Sundrum (RS), only one extra dimension is hypothesised. All the SM particles and forces, apart from gravity, are confined on a 4-dimensional subspace, while gravitons live in the 5-dimensional bulk. The metric in the extra dimension is supposed to be exponentially decreasing. Therefore, the wave-function of gravitons is exponentially suppressed when close to the SM manifold, causing a weak gravity. In this case M D = M P e kπrc (3.5) where r c is the size of the extra dimension.in the framework created by this model, 18

25 3.2. PHOTON+JET CHANNEL it is possible to observe quantum black holes for threshold energies as low as 1 TeV. 3.2 Photon+jet channel Among the possible decay channels for quantum BH there is the photon+parton(q,g) channel. As the hypothesised decaying particle is very massive, the focus is on a final state formed by a photon and a jet with high p T and low η. The spectrum for QCD photon+jet final state, is known to decrease exponentially as a function of m γj. The search for a possible new particle aims at measuring an excess of events above the expected QCD background. Thus, a particular interest is in finding the correct uncertainties of the background shape, as these affect the significance of a possible discovery. In the next chapters two uncertainties will be studied: the first given by the background composition, the second by the photon isolation definition on the signal yield. The studied model was, in particular, the RS one. Fig 3.1 shows the expected shapes of a hypothesised BH with mass M th = 3 TeV and the expected QCD background shape. Arbitrary units ATLAS Work in Progress s = 13 TeV m jγ Arbitrary units 1 1 s = 13 TeV m jγ Figure 3.1: Expected signal shape for a BH with 3 TeV mass in the RS model (left) and QCD background shape (right) Samples The analysed data sample has an L int = 3.25 fb 1. It corresponds to all the good data collected at 25 ns by the ATLAS detector at s = 13 TeV in 2015 The MC samples used as background sources are summarised in tab. 3.1, while the one used as signal sources are in

26 CHAPTER 3. QUANTUM GRAVITY AND PHOTON+JET SIGNATURE Table 3.1: Summary of the photon+jet QCD background samples generated with Sherpa. The filter efficiencies listed are related to the flavour filters. dataset ID p T,γ range flavour σ [pb] filter efficiency CVetoBVeto CFilterBVeto BFilter CVetoBVeto CFilterBVeto BFilter CVetoBVeto CFilterBVeto BFilter CVetoBVeto CFilterBVeto BFilter CVetoBVeto CFilterBVeto BFilter CVetoBVeto CFilterBVeto BFilter CVetoBVeto CFilterBVeto BFilter inf CVetoBVeto inf CFilterBVeto inf BFilter

27 3.2. PHOTON+JET CHANNEL Table 3.2: Summary of the photon+jet signal samples generated with the QBH generator and Pythia. The branching ratios (BR) account for the probability of a produced BH to decay in the γ + j channel. dataset ID signal mass [TeV] σ BR [fb]

28 CHAPTER 3. QUANTUM GRAVITY AND PHOTON+JET SIGNATURE 22

29 Chapter 4 Photons and jets in the ATLAS detector In this chapter the processes of photon and jets reconstruction are summarised, while a description of the two variables which allow distinction of photon from other particles, like jets, is made. 4.1 Photon reconstruction Photon reconstruction [5] is initiated through a sliding window algorithm. It searches for clusters whose energy is above 2.5 GeV in the η < 2.5 region. Once a candidate fitting this selection is found, reconstruction is carried on looking for matching tracks. It is possible to select either candidates having two tracks pointing to a secondary vertex, or a single track missing a hit in the innermost layer of the pixel detector. If a cluster cannot be matched to a well-reconstructed track, it is classified as unconverted photon candidate, whereas candidates are classified as converted if they can be matched. Photon candidates initially classified as electron ones, for instance because unconverted candidates were matched to fake electron tracks, can be recovered by a final algorithm. The tracking, vertexing and matching processes require different approaches in order to be optimised for different s, to cope with different levels of pile-up. To measure the final photon energy, information from the calorimeters is used. Different calibration constant are applied for converted and unconverted candidates. 23

30 CHAPTER 4. PHOTONS AND JETS IN THE ATLAS DETECTOR 4.2 Photon isolation In order to evaluate an isolation variable for the photon, the sum of the E T of all the threedimensional positive-energy topological clusters is built in the cone of size R = 0.4 around the photon candidate. After the subtraction of the contribution from the photon itself, the underlying events and the pile-up, another correction is applied to the isolation distribution, using signal leakage coefficients [6]. These coefficients account for the energy deposited by the photon outside the region already removed. Fig. 4.1 shows a visual representation of the process. A photon candidate is defined as isolated if this energy variable, called E iso T is: Figure 4.1: A visual representation of the construction of the variable. E iso T E iso T,γ < p T,γ (4.1) This cut was adopted in order to guarantee a constant photon efficiency above 98% for photons with p T up to a few TeV. 4.3 Photon identification A photon identification algorithm ensuring high photon acceptance and background rejection is needed to distinguish true photons from jets, from p T 15 GeV, up to the TeV scale. In ATLAS, such identification is based on a set of rectangular cuts on several discriminating variables (DVs). These are computed from the lateral and longitudinal shower developments in the EM calorimeter, as prompt photons are expected to have a narrower deposit in it, and from the leakage fraction in the hadronic calorimeter, expected to be small for prompt photons. Pile-up broadens the distributions of the DVs, reducing the separation between prompt and fake photons. Two reference selections are defined, a loose and a tight one. The loose selection is based on the shapes of the showers in the EM calorimeter and on the energy deposit in the hadronic calorimeter. It is designed in order to provide a prompt photon efficiency, with respect to the reconstruction, rising from 97% at E T,γ = 20 GeV to above 99% for E T,γ > 40 GeV. The tight selection, adding information from the finely segmented strip layer of the calorimeter, provides good rejection of 24

31 4.3. PHOTON IDENTIFICATION hadronic jets. The selected criteria provide a photon identification efficiency of 85% for photon candidates with p T > 50 GeV, with a corresponding rejection factor of approximately Both selections do not depend on p T,γ but different criteria are applied in seven different intervals of the reconstructed η. Tab. 4.1 shows the DVs in relation to the reference selections. 25

32 CHAPTER 4. PHOTONS AND JETS IN THE ATLAS DETECTOR Table 4.1: Discriminating variables used for loose ad tight photon identification. Category Description Name Loose Tight Acceptance η < 2.37, 1.37 < η < 1.52 excluded Hadronic leakage Ratio of E T in the first sampling of the hadronic calorimeter to E T of the EM cluster (used over the range η < 0.8 or η > 1.37) Ratio of E T in all the the hadronic calorimeter to E T of the EM cluster (used over the range 0.8 < η < 1.37) EM Middle layer Ratio in η of cell energies in 3 7 over 7 7 cells EM Strip layer - R had1 R had R η Lateral width of the shower ω η2 Ratio in φ of cell energies in 3 3 over 3 7 cells Shower width for three strips around the strip with maximum energy deposit R φ ω s3 Total lateral shower width ω stot Energy outside the core of the three central strips but within seven strips divided by the energy within the three central strips Difference between the energy associated with the second maximum in the strip layer and the energy reconstructed in the strip with the minimal value found between the first and the second maxima Ratio of the energy difference associated with the largest and second largest energy deposits over the sum of these energies F side E E ratio 26

33 4.4. JET RECONSTRUCTION 4.4 Jet reconstruction Jet reconstruction is based on data collected by the calorimeters. It is an experimental challenge, as a jet is not a single object, but rather a collection of particles produced through hadronisation. In order to reconstruct a jet, Topoclusters [13] are used as an input of the anti-k t algorithm [8]. A final selection discards the candidates with p T < 20 GeV and in the η > 2.8 region. 4.5 Event selection Once physics objects are correctly reconstructed and calibrated, the event selection proceeds as follows: The highest E T,γ photon passing tight identification and isolation selection with η γ < 1.37 and p T,γ > 150 GeV is taken. The η γ cut is found to be useful to reduce the signal/background ratio, as signal events tend to have a smaller η than background ones. The event is rejected if the photon and the jet reconstructed from the photon (overlap jet) are not well aligned, i.e. if R(γ overlap jet ) > 0.1. This might happen if there were problems in the reconstruction of the event. Also in cases where there was additional energy scattered around the photon, this additional energy could pull the reconstructed centroid of the jet away from the photon center. Objects like photons, electrons or muons can also appear in the jet collection. Overlap among reconstructed objects is treated according to recommendations via the package AssociationUtils In the used setup, the overlap removal tool does not take into account taus nor b-jets. Events with R(γ, j) < 0.8 for any jet with p T,j > 30 GeV are rejected. This is required to avoid possible contamination of jet energy in the photon isolation cone (see 4.2). The leading jet is selected requiring p T,j > 150 GeV. Events are rejected if η(γ, j) > 1.6. This requirement is found to be useful to discriminate between QCD di-jet production and the signals. Tabs. 4.2 and 4.3 show the efficiency of the above listed cut on the used MC and the data sample. 27

34 CHAPTER 4. PHOTONS AND JETS IN THE ATLAS DETECTOR Table 4.2: Efficiency of selection cuts for 1 TeV RS signal. RS QBH 1 TeV Cuts Cumulative Relative PV + Trigger Baseline photon Tight photon Photon p T > 150 GeV Photon η < Isolated photon One jet with R < Jet overlap removal jets with R < Jet quality Jet p T > 150 GeV η <

35 4.5. EVENT SELECTION Table 4.3: Efficiency of selection cuts in the data sample. The cuts that are listed in this table but not in tab. 4.2 have efficiency 1 on MC samples. Data Cuts Cumulative Relative Events GRL LAr cleaning Tile cleaning Incomplete events removal PV Trigger Baseline photon Tight photon Photon p T > 150 GeV Photon η < Isolated photon One jet with R < Jet overlap removal jets with R < Jet quality Jet p T > 150 GeV η <

36 CHAPTER 4. PHOTONS AND JETS IN THE ATLAS DETECTOR 30

37 Chapter 5 Di-jet contamination estimate Even though the identification and isolation selections applied to the photon candidates provide a high rejection for hadronic jets, it is still possible for a jet to be misidentified as a photon. As the analysis is based on the photon+jet final state, it is necessary to estimate the di-jets events contamination in the selected sample. In order to do this, an almost fully data-driven technique is used, where only a particular correction relies on a Monte Carlo (MC) simulated sample of photon+jets QCD events. In this section a short description of the method is reported, based on [14], as well as the results obtained on the analysed sample. 5.1 The 2D sideband method Theoretical basis for the method In the basic 2D sideband method photon candidates are distributed in a 2D plane formed by an isolation variable (x) and an identification variable (y). The plane is divided in four regions by means of rectangular cuts on these variables. Therefore, the regions are defined as follows: signal region (S): candidates passing both the x and y cuts; control region 1 (R 1 ): candidates passing the x cut but failing the y one; control region 2 (R 2 ): candidates failing the x cut but passing the y one; control region 3 (R 3 ): candidates failing both the x and y cuts; N S,N R1,N R2 and N R3 are defined as the number of events in each region, N sig S and N sig R 3 the number of true signal events in each region, and N bkg S 31 sig,nr 1,N sig R 2 bkg,nr 1,N bkg R 2 and

38 CHAPTER 5. DI-JET CONTAMINATION ESTIMATE Figure 5.1: A visual representation of the 2D sideband method plane division used in the discussed analysis N bkg R 3, the corresponding numbers of true background events. The interest is thus in evaluating N bkg S, which is exactly the number of candidates passing both the isolation and the identification cuts, but being actually background events (i.e. jets). Two basic hypotheses can be made; they simplify the estimate of N bkg S : 1. Negligible correlation for the background between the isolation and identification variables 2. Negligible number of signal candidates in the three control regions: N bkg R i N sig R i for i = 1, 2, 3 (5.1) These basic hypotheses lead to the following relations: N bkg S N bkg R 1 = N bkg R 2 (5.2) N bkg R 3 Thus, combining the previous equations: N Ri N bkg R i for i = 1, 2, 3 (5.3) N bkg S = N R1 N R2 N R3 (5.4) providing a fully data-driven estimate of the background events in the signal region. To indicate the relative contamination of the signal region of the sample, the purity (P ) is used: 32 P = N sig S N S = 1 N R 1 N R2 N S N R3 (5.5)