ATLAS detector

Reconstruction of challenging signatures characteristic to new physics beyond the Standard Model with the

ATLAS detector

Timmy Mattson Lindgren January 16, 2020

Supervisor: Dr. Venugopal Ellajosyula Examinators: Sophie Grape and Peter Jansson

Project in Applied Physics, 15.0 c Abstract

This project applied event reconstruction requirements on simulations at truth and reconstructed level of collimated photons in the final state of a signal based upon the Composite Higgs Model (CHM) in order to study the fraction of the signal that is lost due to isolation criteria in the ATLAS detector. Events of pair production of vector like tops, t

, from pp-collsions followed by the decay of t

→ St, S → γγ and t → W b with W decaying into everything allowed was generated using event generator Madgraph.

Showering and hadronization was simulated using Pythia and fast-simulation of the

ATLAS detector was simulated using Delpes. Collimated photons in the final state is

not unique to the CHM alone, but occur in several Beyond the Standard Model (BSM)

theories. Because conventional identification and reconstruction algorithms typically

fail for collimated particles, it is of high interest to study signatures characteristic to

BSM models in order to develop robust search strategies. The angular separation be-

tween the pair of collimated photons were calculated and compared to the total number

of events. Furthermore, this project tries to identify specific discriminating variables

in the electromagnetic calorimeter (EMC) to target in a future work to optimize iden-

tification algorithms in the attempt to not lose counts from collimated photons. The

rectangular separation was compared with the granularity of the cells in the EMC in

order to further collect information that can be used for this purpose. It was found that

the fraction of the signal that hit the same cell in η-direction of the first and second

layer did not change much as m

was increased. It was also found that the fraction of

the signal that hit the same cell in φ-direction of the first and second layer showed a

clear decrease as m

was increased. These tendencies exist on both truth and recon-

structed level. Based on these results, first layer discriminating variables E

, E

and w

and second layer discriminating variables R

and R

was found particularly

interesting.

1 Introduction

The Standard Model of Particle Physics (SM), describing the fundamental particles and the weak, strong and electromagnetic forces between their interactions, has proven to be success- ful over the years. In 2012, the Higgs boson was discovered which was the last piece of the SM puzzle [1] [2]. The Higgs mechanism was formulated independently by Brout, Englert and Higgs to explain the masses of the rest of the particles and predicted the existence of what is called the Higgs field [3] [4]. However, the SM fails to explain the large difference in strength between the four fundamental forces, the weak and strong force, the electromag- netic force and gravity. It also fails to explain the small neutrino masses, the presence of dark matter and gravity, and the small Higgs mass. New physics is to be expected in the attempt to explain these problems, which is extensively searched for at the Large Hadron Collider (LHC). In an attempt to resolve the fine-tuning problem of the Higgs boson mass, the Composite Higgs Model (CHM) is currently being developed [5]. It predicts the existence of vector like quarks (VLQ), that may decay into SM particles Zt, Ht and W b, but also into a spin-0 exotic (pseudo) scalar boson S with an additional top quark t, i.e. t

→ St, or ¯ t

→ S¯ t. S might in turn decay as S → {Zγ, γγ, ZZ, W W } and fermions, however we restrict ourselves to a parameter space where BR(S → f f ) ≈ 0 [6].

Multipurpose experiments such as ATLAS are, as of today, pushing the limits of the SM.

Through simulations, robust search strategies can be developed before the actual search is performed at the LHC. The signal under study is the pair production of vector like tops (VLT) from proton-proton collision pp → t

t ¯

at LHC [6]. This project focus exclusively on the decay channel t

→ S → γγ as photons are experimentally very clean in the detec- tor. As S and t

are not yet experimentally observed, their mass is unknown, so different signal hypotheses assume different masses of S. Conventional software based analysis in- clude reconstruction, identification and isolation. Reconstruction algorithms reconstructs the event while identification algorithms identify the reconstructed particle as background- like or signal-like. Additional isolation requirements are used for further discrimination between background-like and signal-like particles. In specific kinematic regions of the signal under study, the pair of photons lead to unconventional signatures in the detector, e.g. they deposit their energy too close to each other in the electromagnetic calorimeter (EMC) for conventional methods to identify the particles and isolation requirements will fail and the count disregarded. One step in the quest to test this signal is to improve the efficiency in counting collimated photons. Collimated particles, including photons, are not unique to this model alone, but occur in several Beyond the Standard Model (BSM) theories. So if successful, this work could help explore not only the model discussed above but several new theories yet to be searched for at the LHC.

1.1 Objective

The first step is to understand the limitations of conventional methods to reconstruct colli-

mated photon signatures, characteristic to BSM theories. For this purpose, event generation

and simulation of the ATLAS detector response in well developed simulators are to be per-

formed and analyzed at truth and reconstructed level. Furthermore, the fraction of signal

lost when photons have an angular separation of delta R ¡ 0.2 is required to be quantified, both on truth and reconstructed level in order to understand how well conventional methods perform with collimated photons. At this stage, identification algorithms will not be used.

Instead, the analysis will aim at quantifying the loss of signal due to isolation criteria used in ATLAS. Using the same simulations, angular observables ∆φ

and ∆η

will be com- pared with the granularity of the cells in all layers of the EMC to see whether interesting information about what discriminating variables on identification level can be studied in a second step, however outside the scope of this project, or not.

2 Theory

This part is dedicated to develop a brief understanding of the theory involved in this project.

It includes a summary of the Standard Model of Particle Physics (SM), its symmetries and its limitations. Section 2.1. also includes a brief theoretical motivation to the model under study. It is not intended to explain the details but rather to touch upon the various concepts and terms that will frequently be used throughout the report. Section 2.2. is purposed to give the reader a brief understanding of the ATLAS detector and its layers that are relevant for this project. The section also includes a summary of the reconstruction and identification process involving electron and photon measurement in ATLAS.

2.1 The Standard Model of Particle Physics

The fundamental constituents of matter have during the last century been extensively stud- ied. Technological advancement of accelerators and detectors during the last few decades helped improve this knowledge. The SM is a modern theory describing the fundamental particles and the interaction between them. All particles in the SM are assumed to be ele- mentary, i.e. they have no internal building blocks and they are point like. The elementary particles in the SM can be divided into two groups; fermions and bosons. Fermions are spin-

particles and can be divided into two types; leptons and quarks. The leptons are further divided into three generations; electrons, muons and tauons as well as their respec- tive neutrinos. The second type, quarks, also consist of three generations. The first; up (u) and down (d ), the second; charm (c) and strange (s), the third; top (t ) and bottom (b).

All fermions have anti-particles with the same mass but with opposite charge, e.g. electric charge. The second group act as force carriers in the SM and are the spin-1 particles known as gauge bosons. Leptons are bound in atoms via the electromagnetic force mediated by the photon. The weak force, mediated by the Z and W bosons, is responsible for the decay of atoms. A well known example is the β-decay, which can only occur because of the weak force. The third and last force included in the SM is the strong force carried by the gluon.

The strong force is the reason to why quarks is observed in bound states, be it mesonic (two quarks) or baryonic (three quarks) bound states. The protons (uud) and the neutrons (udd) are examples of baryonic bound states and the pions (e.g. π

: u¯ u/d ¯ d) is an example of a mesonic bound state. Gravity is the fourth fundamental force but it is not observed in the SM. Gauge bosons also have anti-particles. However, Z and γ are their own anti-particles.

The generation of mass in the SM is due to the Higgs mechanism that also predicted the

existence of an additional boson, the Higgs boson.

Every particle in the standard model has a unique set of quantum numbers. Fermions have charge Q, strange S, charm C, beauty e B, truth T , baryon number B, isospin I, lepton number L, hypercharge Y = S + C + B + T + B and third component isospin I

= Q −

[7].

Beside these quantum numbers, fermions also have chirality [8] [9]. Chirality is related to the helicity of a particle, i.e. the sign of the spin vector’s projection onto the momentum vector.

For massless particles chirality and helicity is the same as they are allowed to travel at the speed of light and there is no real frame of reference where the helicity can be reversed. The chirality of a particle determines whether it is left handed or right handed. It is an impor- tant property as only weak bosons interact with left handed fermions and right handed anti fermions. In addition, quarks carry a color charge that require them to be confined in bound states color singlets [7].

In the attempt to describe subatomic particles traveling at relativistic velocities, Quantum Field Theory (QFT) was developed. It combines Special Relativity and Quantum Mechanics.

QFT is a theoretical framework in high energy physics and describe particles as excitations of fields. Just as in classical mechanics, the Lagrangian for these fields can be used to find the equation of motion for particles in the SM. The Lagrangian can be acted upon by operators to find observables. In particle physics, transformation operators are particularly important.

If the Lagrangian is invariant under some transformation it is said to have a symmetry. Just like in classical mechanics where e.g. translational invariance implies conservation of linear momentum; if the Lagrangian is invariant under a transformation there exists a conserved quantity [9]. A group is a mathematical set of operations, e.g. transformations. The SM has the groups SU (3)

× SU (2)

× U (1)

combined [8]. Omitting details, SU (3)

is the symmetry of the strong interaction. The subscript C stands for color and it can be red (r), green (g) or blue (b). Only colorless particles are observed in nature. SU (2)

× U (1)

is the symmetry of electroweak (EW) interactions. It reflects the symmetry of the isospin and hypercharge quantum number and is the reason to that hadrons occur in families with approximately the same masses, e.g. (n,p) and (π

, π

, π

). The subscripts L, Y stands for color, left and hypercharge respectively, left because the symmetry only concerns the left handed fermions.

Gauge invariance in the SM implies that fermions and force carriers (W , Z) are massless.

This is, however, not what is observed in experiments [10]. In order to overcome this Brout,

Englert and Higgs predicted the existence of the Higgs field that interact with the SM parti-

cle fields to generate their mass [3] [4]. The story about the mass of the Higgs boson itself is

a different story. The SM is assumed to break down close to the Planck scale Λ = 10

GeV,

where new physics is expected. So the mass of the Higgs boson can in principle be as high

as 10

GeV as the SM does not provide any theoretical constraints that results in a Higgs

mass as little as m

= 125.18 ± 0.16GeV that was detected in 2012 [10] [7]. Such a light

Higgs in the SM cannot be achieved without significant fine-tuning. The fine-tuning problem

can either be accepted or solved in the attempt to go beyond the SM. This report focus on

a model based on the CHM.

The model starts with defining a new strong force in the ultracolor scale, Λ

, where free BSM ultrafermions exist. At some energy scale much larger than the EW scale the sym- metry is broken and the ultrafermions form mesonic and baryonic bound states including the exotic (pseudo) scalar S and the VLT t

. At EW scale, the EW symmetry is broken again to give the SM. The pair production of VLTs from pp collision is model independent, and the decays t

→ W b, t

→ Ht and t

→ Zt have been searched for in ATLAS [11] [12] [13] [14].

However, this model also considers the expected decay t

→ St. Details are explained in Ref. [6].

2.2 The ATLAS detector

The ATLAS detector is a multi-purpose detector, hence it is designed with several layers of different detector types around the interaction point in order to measure properties of particles originating from a wide range of physical processes. The first subdetector, the inner tracking system or the inner detector (ID) is used to measure position and momentum of charged particles. It is surrounded by a 2T magnetic field in the direction of the beam axis, generated by a thin superconducting solenoid. The system of detectors consist of three layers.

Closest to the beam pipe is an insertable b-layer (IBL) built to operate in a high radiation environment. The IBL is surrounded by a system of pixel detectors. The second layer is made up of strips of silicon detectors purposed to measure position of the charge particle passing through. The third layer is a transition radiation tracker (TRT) which is a system of straw drift tubes. The TRT gives additional information of whether the passing particle is an electron or a light charged hadron. The second ATLAS subdetector, the electromagnetic calorimeter (EMC), is used for energy and position measurements of electromagnetic showers from photons and electrons. It consist of three sampling regions with details explained below.

The third subdetector, surrounding the EMC, is the hadronic calorimeter (HCAL). It is designed to detect particles that interact strongly, i.e. it measures the showers of secondary hadrons, e.g. n, p, π etc, produced from high energy hadrons interacting with nuclei in the detector. An additional subdetector, the muon spectrometer (MS), is needed to detect muons since they are weakly ionizing and pass through the calorimeters without depositing much energy. The ATLAS detector use a right handed coordinate system with its origin at the interaction point of the colliding particles, e.g. the p-p collision point. The z-axis goes along the beam direction, the x-axis points into the center of the LHC ring and the y-axis points upwards such that the transverse plane is the x-y plane. The angular separation between two particles is defined as,

∆R

= p

(η

− η

)

+ (φ

− φ

)

, (1) where φ is the azimuthal angle and η is the pseudorapidity defined as η = −ln tan(

), where θ is the polar angle. Differences in pseudorapidity is Lorentz invariant under boost in the beam direction, hence it is preferred over the polar angle θ.

2.2.1 The Electromagnetic Calorimeter

A photon or an electron incident on the EMC will interact with the electromagnetic field

produced by the detector material. Through this interaction, electrons and photons will emit

Figure 1: View of the ATLAS calorimeter system [15]. The schematic is modified to high- light the transition region between the barrel and endcap section in the electromagnetic calorimeter.

energy mainly through Bremsstrahlung which then leads to pair production of e

e

and thus

produce showers of particles in the detector. The mean length of a material required to reduce

the energy by a factor of 1/e is defined as the radiation length, X

[16]. The energy deposited

in the EMC by a photon or electron is used to measure its energy and position [16] [17]. The

EMC is divided into two sections. The barrel section, |η| ≤ 1.475, and an endcap section

on both sides 1.375 ≤ |η| ≤ 3.2, see Fig. 1. In between the barrel and the endcap there is

a transition region, covering the pseudorapidity 1.37 ≤ |η| ≤ 1.52. The region associated

with the barrel and the endcap section, excluding the transition region, will be referred to

as the fiducial region. For |η| ≤ 2.5, the EMC consist of three sampling regions of liquid

argon (LAr) with different longitudinal depths and cell sizes in the η × φ space. The first

layer is for |η| ≤ 1.4 and 1.5 ≤ |η| ≤ 2.4 segmented into cells (∆η × ∆φ) with granularity

0.003 × 0.0982. For 1.4 ≤ |η| ≤ 1.5 and 2.4 ≤ |η| ≤ 2.5 it is segmented into coarser cells with

0.025 × 0.0982. The thickness of the the first layer is 4.3X

at η = 0. The fine granularity

strips in the first layer are purposed for discrimination from overlapping showers of decays

from neutral hadrons in the fiducial region |η| ≥ 1.37 and 1.52 ≤ |η| ≤ 2.37. The second

layer has a thickness of 16X

at η = 0 and absorbs most of the energy of the electrons and

photons. It is segmented into cells with granularity 0.025 × 0.0245. The last layer is used

to correct for energy leaking into the HCAL. It has a thickness of 2X

and a granularity

of 0.05 × 0.0245. Prior to the three sampling layers is a presampler (PS) with granularity

0.024 × 0.0982. It is used to correct for energy loss upstreams from showering before the EMC and has a thickness of 1.1 cm in the barrel [16].

2.2.2 Electron and photon measurement

Electron and photon measurement in the ATLAS detector proceeds in several steps. Re- construction proceeds in parallell for both particles as they leave similar signatures in the EMC. Track information from the ID and energy deposit in the EMC are used in combi- nation with trigger systems to determine the particle type, which is done through a flow of reconstruction algorithms. The trigger system is twofold. The level-1 trigger is hardware based and use information from the calorimeters to select at most 100,000 of the 1.7 billion pp-collision events per second. The software based High-Level Trigger (HLT) reconstruct potential candidates and reject background early in order for more detailed analysis to be applied within reasonable computational time.

The basic idea is to first, through clustering algorithms, group the energy deposited in the cells of the EMC into clusters. The clustering algorithms used in the ATLAS experiment are explained in detail in Ref. [18]. The next step is to reconstruct the track, and the obtained track fit is matched to a cluster in the EMC with some particle hypothesis that also use information from the ID to complete the reconstruction procedure. Using information about the particle type and energy in the cluster, the four momentum can be computed. Details about the reconstruction flow for electrons is explained in Ref. [16].

The next step is to determine whether the reconstructed particle is signal-like or background-

Layer Object Definition

First layer w

Total shower width, E

Ratio of energy difference between the maximum and the sec- ondary maximum of energy deposit in the cluster to the sum of these,

E

Difference in energy in the second maximum and the minimum found in between two maxima in a cluster,

f

Ratio of energy deposited in the first layer to the total energy deposited in the EMC.

Second layer w

Lateral shower width, R

Ratio of energy in 3x3 cells over the energy in 3x7 cells centered around the cluster,

R

Ratio of energy in 3x7 cells over the energy in 7x7 cells centered around the cluster.

Table 1: Definition of some of the ATLAS detector discriminating variables used in recon- struction and identification in the electromagnetic calorimeter.

like. Background-like particles typically originate from light-flavor (LF) hadronic jets, photon

conversions and semileptonic decays from heavy-flavor (HF) hadrons, i.e. hadrons containing

charm and beauty quarks. Fig. 2 show the detector parts involved in data acquisition to compute the various variables used for reconstruction and identification. The variables are also designed to reject against different type of background. The variables that are collected from the first layer of the EMC are the shower width; w

, ratio of energy difference between the maximum and secondary maximum of energy deposit in the cluster to the sum of these;

E

, difference in energy in the second maximum and the minimum found in between two maxima in a cluster; E

and the ratio of the energy deposit in the first layer to the total energy deposited in the EMC; f

. w

give rejection against LF, photon conversion and HF. E

give rejection against LF and photon conversion, E

give rejection against LF and photon conversion, f

give rejection against LF. The variables that are collected in the second layer of the EMC are the lateral shower width; w

, ratio of energy in 3x3 cells over energy in 3x7 cells centered around the cluster; R

, ratio of energy in 3x7 cells over energy in 7x7 cells centered around the cluster; R

. w

and R

give rejection against LF and photon conversion and R

give rejection against LF, photon conversion and HF. From the third layer of the EMC, f

is computed. It is defined as the ratio of energy deposited in the last layer of the EMC over the total energy deposited in the EMC. It gives rejection against LF. The discriminating variables and their definition is summarized in Tab. 1

Figure 2: View of the ATLAS inner detector and electromagnetic calorimeter. The schematic show a simplified view of the reconstruction and identification process of an electron [16].

The identification algorithm is based on a multivariate likelihood (LH) method that

takes the discrimination variables as inputs in order to calculate signal and background

probabilities which are then used to compute a discriminant on which a requirement must

be fulfilled [16] [17]. However, w

is not used in LH but instead used as a stand-alone

selection. Typically, all analyses also need to fulfil an isolation requirement. The general

idea is to sum the transverse component of energy or momentum, excluding the candidate,

inside a cone around the candidate to compute an isolation variable for which a constraint must be met [16].

3 Methodology

3.1 Simulation method

This project consider a model where particles BSM, including t

and S are allowed to be produced in hadron-hadron collisions. The generated process was 10000 events of the pair production of VLTs, pp → t

t ¯

with the VLT decaying according to t

/¯ t

→ St/S¯ t. Further- more, S was required to decay into two photons, and the SM top into W b, with W decaying into everything allowed. This is done using Madgraph (MADGRAPH5 aMC@NLO [19]).

These events are called parton-level events. From a kinematic point of view, the Lorentz boost of the (pseudo) scalar boson S might in some regions become large enough to decay into two highly collimated photons in the final state. For these highly collimated photons, the opening angle between the trajectories become comparable to the granularity of the cells in the EMC which lead to problems in the reconstruction process as the size of the EM clusters corresponds to what would be expected from a single photon. The cause of the highly boosted S can be understood from the conservation of four momenta, starting from t

→ St we have,

P

= P

+ P

.

If the pair t

t ¯

is produced nearly at rest, we find using conservation of relativistic energy and, in natural units, E

= m

+ p

that,

p

≈ m

− m

+ E

− 2m

E

. (2) For S → γ

γ

, we have,

(E

, ¯ p

) = f

(1, ˆ n

) + f

(1, ˆ n

) =⇒ ¯ p

= f

n ˆ

+ f

n ˆ

,

which shows that if S is in the boosted regime, ˆ n

≈ ˆ n

. Taking the zeroth component of the conservation of four momenta, with the Lorentz factor γ ≥ 1, we find kinematically allowed m

,

m

≤ m

− m

. (3)

The masses used in the simulations were m

= 1600 GeV and m

= 2000 GeV with m

=

100, 200, 400, 600 GeV for both cases. However, these parton events do not give a realistic

picture. In the event of hadron-hadron collision, e.g. pp-collision, quarks and gluons of the

hadron will collide with high momentum producing outgoing SM particles, or new exotic

particles if the model allow for it. The outgoing quarks and gluons, referred to as partons,

radiate virtual gluons much like accelerated electrons radiate photons. The virtual gluons

can in turn emit gluons or quarks, a process that is called parton showering. Eventually the

strong coupling will have increased to a level where partons form bound states of colorless

hadrons, a process that is called hadronization. However, these hadrons are in many cases

unstable and they will decay into allowed final state particles. To include showering and

hadronization giving rise to jets, further simulation is done using Pythia (Pythia 8.2 [20]).

After simulation in Pythia, the signal now has the particles of interest with additional jets. In order to study the signatures of these events in the detector, they need to be passed through a fast-simulation of ATLAS using Delphes (Delphes 3 [21]). The simulation provides two event file formats, HepMC and LHEF, where the latter does not include parton showering and hadronization. The ATLAS Delphes fast-simulation output were then used for further analysis on truth, using LHEF, and reconstruction level, using HepMC. The ATLAS Delphes card is modified to allow particles to be reconstructed without a minimum restriction on

∆R

.

3.2 Analysis

The LHEF event file provides information solely about the generated particles, hence the code required for efficiency analysis only need to find the branch to the photons, check if the grandmother is t

or ¯ t

, and thereafter store the kinematic variables p

, η, φ and E in a 4-vector. However, in order to properly compare truth level with reconstructed level, a detector cut was applied to account only for the photons in the fiducial pseudorapidity region. As the detector cut might ignore one of the two generated photons, an additional requirement is that the number of photons in every generated event after the detector cut must be two for truth level analysis. The diphotons that pass the cuts are counted as N

. The diphotons that further fulfil ∆R

< 0.2 are counted as N (∆R

< 0.2). Thus the fraction of the signal that might fail isolation criteria can be computed as,

N (∆R

< 0.2)

N

. (4)

Note that N (∆R

) < 0.2 is a simplified isolation requirement explained in Section. 2.1.2.

Depending on the constraint, photons might still fulfil isolation requirement even though their respective candidate cones overlap slightly.

Analysis of the HepMC event file is much less trivial. Reconstructed photons can be real or fake. Event reconstruction methods are required in order to search for the best candidate pair. Firstly, the number of reconstructed photons in every event is checked, and only if the number is at least two we proceed. Secondly, for every photon in the event the detector cut is applied along with the requirement that p

> 30, and kinematic variables are stored if and only if the photon pass. Thirdly, in order to find the best candidate pair coming from the same S, the invariant mass is computed for every possible diphoton. Then, the pair γ

γ

that fulfil |m

− M

|

is considered the best candidate. In order to account for the possibility that minimisation did not find a good candidate, the difference is not allowed to be larger than 20GeV, i.e. |m

− M

|

< 20. The diphotons that pass this last cut are counted as N

. The diphotons that further fulfil ∆R

< 0.2 are counted as N (∆R

< 0.2). Thus the fraction of the signal that might fail isolation criteria can be computed as Eq. (4). The cuts are summarized in Tab. 2.

Errors for statistical distributions were calculated according to Poisson error calculation, δ =

√

N (5)

Cut Truth Reconstructed

N

≥ 2 X X

|η| ≥ 1.37, 1.52 ≤ |η| ≤ 2.37 X X

p

> 30 X

|m

− M

|

< 20 X

Table 2: Cuts applied to photons on truth level and reconstructed level.

where N is the number of entries in a bin. For error calculations in efficiency, instead binomial error calculation was used because the numerator is a subset of the denomenator.

The efficiency is considered as a probability that ∆R

< 0.2. Then, δ = 1/N p

k(1 − k/N ), (6)

where k is the subset of N that passed ∆R

< 0.2.

4 Result

In this section the result from the simulation of efficiency both at truth and reconstructed level according to Eq. (4) is presented. ∆R, ∆η and ∆φ are plotted in Fig. 3-5 respectively.

Fig. 6 and 7 in Appendix show the invariant mass for the photon pair at truth and recon- structed level used to construct these distributions. The simulation returned 8332, 8449, 8763 and 8890 events that passed the cuts on truth level and 8445, 8507, 8166 and 7879 events that passed the cuts on reconstructed level in Tab. 2 for m

= 100, 200, 400, 600 GeV respectively.

0 1 2 3 4 5 6 7

γ) γ

∆R ( 0

500 1000 1500 2000 Events 2500

= 100 GeV mS

= 200 GeV mS

= 400 GeV mS

= 600 GeV mS

(a) Truth

0 1 2 3 4 5 6 7

γ) γ

∆R ( 0

200 400 600 800 1000 1200 1400 1600 1800 2000 2200

Events = 100 GeV_Sm

= 200 GeV mS

= 400 GeV mS

= 600 GeV mS

(b) Reconstructed

Figure 3: Simulation at truth (a), and reconstructed (b) level for m

= 2000 GeV. The figures show the distribution of angular separation between the two photons from S → γγ

The error bars included in the angular plots are based on Poisson statistics and calculated according to Eq. (5) discussed in Section 3.2. The error bars were computed using the ”E1”

option in Root.

−5 −4 −3 −2 −1 0 1 2 3 4 5 γ) γ η (

∆ 0

500 1000 1500 2000 2500 3000

Events

= 100 GeV mS

= 200 GeV mS

= 400 GeV mS

= 600 GeV mS

(a) Truth

−5 −4 −3 −2 −1 0 1 2 3 4 5

γ) γ η (

∆ 0

500 1000 1500 2000 2500

Events

= 100 GeV mS

= 200 GeV mS

= 400 GeV mS

= 600 GeV mS

(b) Reconstructed

Figure 4: Simulation at truth (a), and reconstructed (b) level for m

= 2000 GeV. The figures show the distribution of ∆η between the two photons from S → γγ

−5 −4 −3 −2 −1 0 1 2 3 4 5

γ) γ φ (

∆ 0

500 1000 1500 2000 2500 3000

Events

= 100 GeV mS

= 200 GeV mS

= 400 GeV mS

= 600 GeV mS

(a) Truth

−5 −4 −3 −2 −1 0 1 2 3 4 5

γ) γ φ (

∆ 0

200 400 600 800 1000 1200 1400 1600 1800 2000

Events

= 100 GeV mS

= 200 GeV mS

= 400 GeV mS

= 600 GeV mS

(b) Reconstructed

Figure 5: Simulation at truth (a), and reconstructed (b) level for m

= 2000 GeV. The figures show the distribution of ∆φ between the two photons from S → γγ

Based on these simulations Tab. 3 and 4 summarize the resulting efficiencies, where Tab. 3 is a similar simulation but for m

= 1600 GeV. The plots for the simulation with m

= 1600 GeV add no additional information, hence they were excluded from the report.

At masses greater than 400GeV for S, all photon pairs fulfil the isolation requirement. Note that the efficiency value are close to zero for m

= 200 GeV, so it is likely that for masses not much greater than 200 GeV, on truth as well as reconstructed level, all photon pairs fulfil the isolation requirement. The statistical error are based on binomial statistics according to Eq. (6) discussed in Section 3.2.

From information about the separations ∆η and ∆φ, Fig. 4 and 5, the collimated pho-

tons can be compared to the granularity of the EMC in the fiducial region. Tab. 5 and 6

show the fraction of collimated photons that are possibly incident on the same EMC cell in

either η or φ-direction.

Mass m

Truth Reconstructed 100GeV 0.111(3) 0.079(3) 200GeV 0.0011(3) 0.0010(3)

400GeV 0 0

600GeV 0 0

Table 3: Efficiencies according to Eq. (4) for truth and reconstructed level and m

= 1600 GeV.

Mass m

Truth Reconstructed 100GeV 0.226(5) 0.146(4) 200GeV 0.0027(5) 0.0026(6)

400GeV 0 0

600GeV 0 0

Table 4: Efficiencies according to Eq. (4) for truth and reconstructed level and m

= 2000 GeV.

Mass m

First Second Third First Second Third 100GeV 0.508(5) 0.539(5) 0.570(5) 0.607(5) 0.512(5) 0.512(5) 200GeV 0.497(5) 0.512(5) 0.562(5) 0.599(5) 0.505(5) 0.505(5) 400GeV 0.490(5) 0.499(5) 0.509(5) 0.442(5) 0.424(5) 0.424(5) 600GeV 0.497(5) 0.508(5) 0.514(5) 0.406(5) 0.396(5) 0.396(5)

Table 5: Fraction of photon pairs that are possibly incident on the same EMC cell on truth level for m

= 2000 GeV. Columns 2-4 consider the cells in η-direction and columns 5-7 consider the cells in φ-direction. ”First”, ”Second” and ”Third” indicate layer in the EMC.

Mass m

First Second Third First Second Third 100GeV 0.502(5) 0.526(5) 0.552(5) 0.518(5) 0.460(5) 0.460(5) 200GeV 0.504(5) 0.516(5) 0.530(5) 0.458(5) 0.431(5) 0.431(5) 400GeV 0.502(6) 0.510(6) 0.517(6) 0.409(5) 0.398(5) 0.398(5) 600GeV 0.516(6) 0.512(6) 0.531(6) 0.391(5) 0.381(5) 0.381(5)

Table 6: Fraction of photon pairs that are possibly incident on the same EMC cell on

reconstructed level for m

= 2000 GeV. Columns 2-4 consider the cells in η-direction and

columns 5-7 consider the cells in φ-direction. ”First”, ”Second” and ”Third” indicate layer

in the EMC.

5 Discussion

Fig. 3 (a) and (b) show similar result. The most notable difference is the tendency of a peak at ∆R

≈ 3 in (b). Also in Fig. 5 this is notable, so it is clear that this peak originate from the distribution of ∆φ at reconstructed level. This peak could turn up if two photons from two different S are selected as the best candidate pair, in cases where one photon from each S is lost. The other notable difference in all resulting figures are the maximum number of events in the peaks. This can be deduced from the fact that the distribution is more smeared out on reconstructed level. Also, for smaller mass difference m

− m

the number of events passing the cuts are considerably less on reconstructed level than on truth level.

The former is due to the way that the particles are reconstructed, i.e. inaccuracies in the computation of kinematic variables will affect the angular observables that are plotted in Fig. 3-5. The latter is arguably mostly due to the applied cuts, Tab. 2 on analysis level.

p

< 30 GeV was applied to account for the ATLAS triggers having a p

cut, i.e. the trig- gers does not store the event in the ATLAS detector if p

< 30 GeV. |m

− M

|

< 20 was applied to find the best candidate pair coming from S. This cut is visible in Fig. 7.

However, there is of course still a possibility that the program for analysis picked a bad pair in an event. Also, the algorithms for reconstruction and identification have an efficiency of successfully reconstructing and identifying a particle. Another interesting observation from Fig. 3 is the poorer ability to find collimated photons with ∆R

, compare (a) and (b). In this project, event reconstruction requirements were applied at reconstructed level to give an idea of what fraction of photons are lost due to isolation, but no variables on identification level were used. The result can be seen in Tab. 3 and 4 and the cuts are summarized in Tab. 2. The truth level simulations give the ideal or best case picture of the events in the ATLAS detector. Adding to it parton showering and event reconstruction at reconstructed level provides a more realistic picture. If conventional identification algorithms were to be included while keeping the relaxed isolation requirement, counts would again be lost. By targeting specific discriminating variables the idea is to optimize the identification algorithm to retrieve the counts for ∆R

< 0.2. Note also that the fraction for calculating the ef- ficiencies in these tables are simplified. As explained in Section 2.2.2 and 3.2., there exist more sophisticated methods for calculation of efficiency. These methods will allow for slight overlap of the individual particle’s respective cones, and will therefore decrease the numbers by a bit. However, this project was partly to compare efficiencies at truth and reconstructed level, and the simplified requirement is enough for this purpose.

Tab. 5 and 6 indicate that the fraction of photons incident on the same EMC cell does not change much in η-direction of the first and second layer as m

is increased. The third layer is the first to show a decrease. Comparing with Fig. 4 and 5, this is not surprising.

The distribution in Fig. 5 show the evolution of a clear dip in number of events for small

values of ∆φ as m

is increased which is not seen in Fig. 4. These tendencies exist on both

truth and reconstructed level. For this reason, second layer discriminating variables R

and

R

is of interest as a further development of the project. Because the pair of photons hit

the same EMC cell in η-direction for around 50% of the totalt number of events consistently

with varied m

, the deposited energy should be concentrated to a small amount of the cells

leading to a large ratio on R

. For the same reason, the lateral shower width w

should be

an interesting variable to study. In the opposite direction of thought it should be interesting to see how R

is affected because of the decreasing fraction of photons hitting the same EMC cell in φ-direction as m

is increased. First layer discriminating variables of interest is, without clear justification from simulation results, E

and E

. If two maxima can be found in the same cluster from reconstruction, then E

should be small for a diphoton as the identical particles in principle deposit the same amount of energy in the first layer of the EMC. E

is the discriminating variable that shows the least promise. However, it gives information about the minimum deposited energy in the region between the two maxima that potentially originates from a diphoton. It is a thought rather than a convincing argu- ment that if a local minimum exist between two large peaks of energy deposit, this could in combination with E

be used to identify the signature as a diphoton candidate. For the definition of R

, R

, w

, E

and E

, see Section. 2.2.2.

A last note must be added on the fast-simulation of the ATLAS detector using Delphes.

The detector simulator is a realistic model of the geometry of the ATLAS detector but it does not simulate interactions between particle and detector material that produces electro- magnetic showers in the detector. However, to understand the limitations of reconstruction of collimated photons, Delphes produce perfectly fine results. At a later stage where identi- fication algorithms are to be taken into consideration, the detector simulation will need to be more realistic.

6 Conclusion and further developments

Today, searches of explanations to the limitations of the Standard Model is preferred at

particle accelerators such as the Large Hadron Collider because of their ability to accelerate

particles to energies where interesting new particles might be produced and found. However,

many theories that go beyond the Standard Model show collimated photons in the final state

and conventional methods to reconstruct the particles fail. Therefore it is of high interest to

study these signatures and understand the limitations of conventional reconstruction meth-

ods in order to formulate methods to reconstruct and identify collimated particles. This

project focused on a model based on the Composite Higgs Model where pair production of

vector like tops are allowed in pp-collisions. Events of these collisions and of their decay into

an exotic (pseudo) scalar S, followed by the decay into a pair of photons, were generated

using Madgraph. Pythia was used for showering and hadronization and Delphes was used

for fast-simulation of the ATLAS detector. Using the simulation outputs, the angular sep-

aration (∆R

) and the rectangular separation (∆η, ∆φ) between the pair of photons was

calculated. The angular separation was used to compute the efficiency of photons that likely

will fail isolation requirements. The rectangular separation was compared with the granu-

larity of the cells in the electromagnetic calorimeter in order to further collect information

about what discriminating variables might be interesting to study in future developments of

this project. It was found that ∆η did not change much over the granularity of the cells as

the mass of S was increased. It was also found that ∆φ decreased over the granularity of

the cells as the mass of S was increased. Comparing these results with the writer’s current

knowledge in discriminating variables used for identification, R

, R

, w

, E

and E

was

regarded as interesting variables to study in further work.

As a next step in a future development in this project it is recommended to simulate and implement code to study also the possible decay of S into Zγ. Z can decay into e

e

which, like the photon, are experimentally very clean in the detector. The code is a little bit more complicated as one have to deal with photons and electrons. However, it is interesting to know how conventional methods deal also with collimated electrons in the final state. After this suggested implementation, the discriminating variables can be studied with the goal to more efficiently count collimated particles.

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7 Appendix

7.1 Invariant mass for simulation m

=2000GeV

50 60 70 80 90 100 110 120 130 140 150 γ) γ M ( 0

500 1000 1500 2000 2500 3000

Events

(a) m

= 100GeV.

100 120 140 160 180 200 220 240 260 280 300 γ) γ M ( 0

500 1000 1500 2000 2500 3000 3500

Events

(b) m

= 200GeV.

300 320 340 360 380 400 420 440 460 480 500 γ) γ M ( 0

500 1000 1500 2000 2500 3000 3500 4000

Events

(c) m

= 400GeV.

500 520 540 560 580 600 620 640 660 680 700 γ) γ M ( 0

500 1000 1500 2000 2500 3000 3500 4000

Events

(d) m

= 600GeV.

Figure 6: Simulation at truth level for m

= 2000GeV. The figure show the invariant mass of the

diphotons.

50 60 70 80 90 100 110 120 130 140 150 γ) γ M ( 0

200 400 600 800 1000

Events

(a) m

= 100GeV.

100 120 140 160 180 200 220 240 260 280 300 γ) γ M ( 0

200 400 600 800 1000 1200 1400 1600 1800

Events

(b) m

= 200GeV.

300 320 340 360 380 400 420 440 460 480 500 γ) γ M ( 0

200 400 600 800 1000 1200 1400 1600

Events

(c) m

= 400GeV.

500 520 540 560 580 600 620 640 660 680 700 γ) γ M ( 0

200 400 600 800 1000 1200 Events 1400

(d) m

= 600GeV.

Figure 7: Simulation at reconstructed level for m

= 2000GeV. The figure show the invariant mass

of the best candidate diphotons.