Particle Identi cation using Time of Flight in the International Large Detector ILD by

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.

Particle Identication using Time of Flight

in the International Large Detector ILD by

Sukeerthi Dharani

Fakultät für Physik und Geowissenschaften

August, 2018

This bachelor thesis has been carried out at Deutsches Elektronen-Synchrotron DESY

under the supervision of Prof. Dr. Thomas Naumann

Dr. Jenny List

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Abstract

The International Linear Collider ILC is a planned linear e⁺ e⁻ collider. With a well dened initial state, it would allow for high-precision measurements for various physics studies. In order to make high-precision measurements, the detector technology needs to ensure eective particle identication. Identifying known particles in a detector reduces the background and helps understand the physics process.

The objective of this thesis is to study the particle identication (PID) using time of ight at the International Large Detector (ILD). Dierent particles travel with dierent velocities and a particle can be identied using the time it takes to reach a detector. The time of ight (TOF) of particles from interaction point to the entry of electromagnetic calorimeter in the momentum range of 1 to 9 GeV is investigated. The particles that are studied in this thesis are protons, kaons and pions.

The separation of particles is done using various time resolutions to conclude which time resolution attains the expected particle identication. The particle identication using TOF complements dE/dx in the low momentum range.

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1. Introduction

Discoveries in the 19th and 20th century have given us remarkable insight into the fundamental structure of matter. The universe is made up of a few basic building blocks called fundamental particles or elementary particles.

Currently, the Standard Model (SM) classies all elementary particles. Elementary particles are categorized into quarks, leptons and bosons. Bosons are integer spin particles and are categorized into gauge bosons which are force carriers and scalar bosons whose spin is zero. Leptons are elementary particles with half-integer spin and grouped in three generations. Quarks are constituents of matter, combine to form hadrons. There are 6 quarks grouped in three generations.

Figure 1.1.: Particle content of the Standard Model [1].

Even-though the Standard Model predicts the behavior of particles accurately, it incorporates only three out of the four fundamental forces i.e. electromagnetism, strong and weak forces, omitting gravity. Furthermore, there are questions about dark matter, matter to antimatter ratio after the big bang, dierent mass scales of fermions, the origin of the Higgs boson and its mass etc., which are unanswered by the Standard Model.

High energy collision experiments help to learn about the elementary particles, their behavior and also to nd clues to the solutions for the questions above. In such experiments, a variety of particles will be created as a result of the collisions and so it is very

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important to identify known particles with precision.

This thesis will focus on the use of a time-of-ight (TOF) technique to identify particles emerging from high-energy particle interactions at the International Linear Collider (ILC), which is a proposal for a future electron-positron collider with an initial center- of-mass energy of 250 GeV, upgradable up to 1 TeV.

The path of the charged particles in a magnetic eld in a detector, depends on its momentum and charge. The momentum is the product of the mass and velocity. The velocity can be found by measuring the time taken by a particle to reach a known distance. This study uses natural units withc= 1 and ~= 1

The time of ight (TOF) i.e. the time taken by the particles to travel a specic distance, is used to identify the particles. In this thesis, the path travelled by particles from the interaction point to the entry of the electromagnetic calorimeter in the momentum range of 1 GeV to 9 GeV is investigated. The particle identication is not eective beyond this range since above 9 GeV the particles travel with almost the same velocity i.e. the speed of light. This study is done using ILCSoft version v02-00.

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2. The International Linear Collider (ILC)

International Linear Collider (ILC) is a planned 200-500 GeV e⁺ e⁻ linear collider and is upgradeable to reach energies up to 1 TeV. ILC is a e⁺ e⁻ linear collider so energy loss due to synchrotron radiation, which is inversely proportional to the fourth power of the mass of the colliding particles, is minimum. Since protons are collided in Large Hadron Collider (LHC), there is a large QCD background due to quark content and gluonic interactions. Collidinge⁺ e⁻ eliminates such background because electrons and positrons are elementary particles. Thus, we have a clean e⁺ e⁻ collision event with clear input.

In this chapter, the layout of ILC and its physics goals are discussed, based on [2, 3].

The gure below shows the layout of ILC. The subsystems are explained in section 2.2 and 2.3.

central region 5 km

2 km

positron main linac

11 km

electron main linac

11 km

2 km Damping Rings

e+ source

e source IR & detectors

e bunch compressor

e+ bunch compressor

Figure 2.1.: Schematic of ILC with subsystems [4]. Refer to section 2.2 and 2.3 for explanations.

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2.1. ILC Physics

The ILC is designed to investigate various open questions of particle physics like the mechanism of electroweak symmetry and search for physics beyond the Standard Model like supersymmetry, dark matter, extra dimensions etc. It will search for and explore new physics at energy scales up to 1 TeV.

The major aspects of the ILC physics program are given below [3].

• precision measurements of the properties of the Higgs boson.

• study of the top quark production at the mass threshold and at higher energies near the maximum of the cross section fore⁺ e⁻ → t¯t.

• searching for and potentially measuring the properties of new particles predicted by supersymmetry which are accessible at the energy range of the ILC.

• measurements on dark matter particles that might be present in the ILC mass range.

2.2. The Accelerator

The ILC uses 1.3 GHz superconducting radio-frequency (SCRF) accelerating technology.

The electrons are produced by 2 nanosecond laser light pulses targeted at a photo- cathode. The electrons are sent through damping rings with a circumference of 3.2 km to reduce the emittances. The beams from the damping rings are then injected into the main linacs to an energy of 5 GeV.

The high energy electrons are then passed through an undulator, producing synchrotron radiation. When the radiation is targeted at titanium alloy, it produces electron positron pairs. Then the positrons are collected and sent through damping rings before accelerated to 5 GeV in separate linac.

For a center-of-mass energy of 500 GeV, each of the linacs is about 11 km long. The two beam-delivery systems, each 2.2 km long, bring the beams into collision. More details can be found in [5].

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2.3. The Detectors

There are two detector concepts proposed for the ILC namely the Silicon Detector (SiD) [6] and International Large Detector (ILD)[7].

SiD is a compact detector with a 5 T magnetic eld, consisting of a silicon pixel vertex detector, silicon tracking, silicon tungsten electromagnetic calorimetry (ECAL) and highly segmented hadronic calorimetry (HCAL). SiD also incorporates a high-eld solenoid, iron ux return, and a muon identication system [8].

SiD enables time-stamping on single bunch crossings to provide robust performance with respect to beam backgrounds or beam loss. The use of silicon sensors in the vertex, tracking and calorimetry enables a unique integrated tracking system ideally suited for the particle ow.

The ILD is based on silicon vertex detectors, a time projection chamber as the central tracker, silicon tungsten electromagnetic calorimetry and steel scintillator hadron calorimetry. The ILD which this study is based, has an axial magnetic eld of 3.5 T.

The ILD is optimised for energy and momentum resolution, with exibility for op- eration at energies up to the TeV range. The time projection chamber (TPC) in ILD provides continuous tracking for pattern recognition and particle identication. The ILD is explained further in Chapter 3.

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3. The International Large Detector

All particles in an event, neutral or charged, have to be reconstructed individually in a detector. The International Large Detector (ILD) is a detector concept proposed for the ILC which is designed to perform high precision measurements using the particle ow concept to reconstruct multi-jet nal states. The software that is developed for this purpose is called Particle Flow Algorithm (PFA) [9].

.

Figure 3.1.: Octant view of the ILD with dimensions of each component.

The vertex detector (VTX) is a multi-layer pixel-vertex detector, having pure barrel geometry with an inner radius of 16mm which is the distance to the interaction point.

The silicon pixel detector that surrounds the vertex detector, is called Silicon Inner Tracker (SIT). It consists of two layer of silicon strip detectors positioned between VTX

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and Time projection chamber (TPC). In the forward region, a system of two silicon-pixel disks and ve silicon - strip disks (FTD) provides low angle tracking coverage. A time projection chamber (TPC) is a volume consisting of eld cage, which is usually lled with noble gas (90%) and quencher (10%), and end plates. It typically provides a robust tracking with over 200 space points per track. Outside the TPC system, there is a layer of silicon strip detectors called Silicon External Tracker (SET). The SET system enhances the tracking by providing high precision space points and also provides a possibility of time stamping. The ILD concept incorporates two dierent technology options for both highly segmented calorimeters ECAL and HCAL. The ECAL technologies are a Silicon- Tungsten (SiW) calorimeter and a scintillator-Tungsten calorimeter [7]. The ECAL with an inner radius of 1808 mm, provides up to 30 samples in depth and small transverse cell size, split into a barrel and an end-cap system. The two HCAL technologies under consideration are analogue steel-scintillator hadron calorimeter (AHCAL) [10] and semi- digital calorimeter (DHCAL) [11]. A large volume superconducting coil surrounds the calorimeters, creating an axial B eld of 3.5 Tesla. The return yoke acts as muon detector, a tail catcher and returns the magnetic ux of the coils.

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4. Particle Identication Techniques

Particle Identication (PID) plays a crucial part in particle physics experiments. In this chapter, we will see various particle identication techniques used in high energy physics and specically in the ILD.

4.1. Motivation for PID

Particle identication helps to understand the underlying physics process and enhance- ment of the signal from the background. The goal of PID techniques is to identify as many particles as possible such that the track reconstruction and jet energy resolution are improved.

The particle identication techniques are used in a variety of physics studies such as avor physics, hadron spectroscopy, rare decays, CP violation in B meson decays, exotic hadronic decays, exotic states of matter like quark-gluon plasma. For example, identication and reconstruction of b quark and c quark jets is used to study Higgs and top physics studies.

4.2. General PID Techniques

In a typical high energy experiment, we aim to reconstruct particles and their tracks as fully as possible i.e. identify particles from the interaction points. There are various techniques used to identify particles.

A particle can be identied using its measured mass and charge. Mass can be obtained by measuring momentum p and velocity β.

Mass: m = p

βγ (4.1)

where Lorentz factor γ is calculated from γ = √¹

1−β²

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• dE/dx

Charged particles lose energy when passing through matter by ionization. Particles are identied by the energy loss per unit distance i.e. dE/dx. For this method, momentum has to be known.

−dE

dx ∝ z²

β² lnaβ²γ² (4.2)

wherez is the charge, β is the velocity, a is a constant,γ is the Lorentz factor.

• Time of Flight (TOF)

Time required by a particle to reach certain distance depends on the mass. Based on the time that a particle takes to reach the TOF detector or between two detectors, the particle can be identied. Using the time information and the distance, one can calculate the velocityβ.

τ ∝ 1

β (4.3)

The ability to distinguish particle types diminishes as the particle velocity ap- proaches its maximum allowed value i.e. the speed of light, and thus is ecient only for particles with a small Lorentz factor.

Since the time of ight of particles is in the order of nanoseconds, the time resolution that is needed is in the order of nanoseconds to picoseconds. The current electronics of the prototypes yield time resolutions in the order of 10 ns.

• Cherenkov radiation: A charged particle, when it travels faster than light in a medium, emits Cherenkov radiation. The angle of the emitted photons to the angle of the propagation of the particle depends on its velocity.

β >1/n (4.4)

Cherenkov angle cosθ= 1/βn (4.5)

A cherenkov detector is not foreseen for ILD because the particle ow requires minimum material before calorimeters.

• Transition radiation: Particles with Lorentz factorγ ≥1000 emit high energy (X- ray) photons when crossing dierent medium. Fast electrons and positrons can be identied using this method.

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• Identifying Neutrinos

The presence of neutrinos can be found in the nal states of a decay or a reaction by missing momenta and missing energy.

• Identifying long lived particles

Long lived particles such as particles containing a c or b quark, or a τ lepton can be identied by reconstructing secondary vertices [7]

4.3. Particle Identication Techniques for p, π , K in ILD

In this section, various PID techniques that is used to identify p,π, K at the International Large Detector are discussed.

• dE/dx:

TPC yields particle identication based on energy loss per unit distance i.e. dE/dx.

• TOF:

The ECAL and SET provide the possibility of time stamping. The option of having an extra timing layer at the entry of the ECAL is also considered.

Using the TOF method, the charged particles such as protons, kaons, pions are separated at low momentum range.

This thesis is an investigation of how well these particles are identied in terms of the separation power and what time resolution is required to achieve it.

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5. Time of Flight Analysis

In this chapter, the kinematics of a particle in a magnetic eld and how dierent particles take dierent time to reach certain distance, as well as the time resolution required for the particle identication using the time of ight information are discussed.

5.1. Motion of Charged Particles in Magnetic eld

The general motion of a charged particle in a uniform magnetic eldB~ in vacuum has a constant velocity parallel to B~ and experiences the Lorentz force which acts perpendic- ular to the velocity of the particle and to the magnetic eld. Thus the particle travels in a circular motion at right angles toB~ i.e. in three dimensional space, the trajectory of the particle is a helix. The radius of the trajectory is calculated in this section.

Figure 5.1.: Motion of a charged particle in a magnetic eld.

The force exerted by a magnetic eld B~ on a charge q moving at a velocity~v is

F~B =q~v×B~ (5.1)

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Considering the transverse (X-Y) plane such that the angles are 90^◦. Then, the centripetal force that acts on the charged particle is given by

F = mv²

r (5.2)

The radiusr of the particle path can be calculated using FB=qvB = mv²

r (5.3)

⇒r= mv

qB (5.4)

r = p

qB (5.5)

where p is the transverse momentum of the particle.

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5.2. Formalism

The gure below shows the path of a particle originating from interaction point IP and travelling the path length L. The distance l is the inner radius of ECAL which is considered for this study as an example.

Figure 5.2.: Particle travelling from interaction point IP hits the calorimeter.

The time taken for a particle to travel distance L is T = L

β (5.6)

The momentum of the particle is given by (Equation: 5.5)

p=rqB (5.7)

As mentioned in Chapter 2, the magnetic eld strength is 3.5 T and the inner radius of the ECAL is 1808mm. The minimum momentum required for the particle to reach the ECAL inner radius from the interaction point, is

p= 0.904[m]·1.602·10⁻¹⁹[C]·3.5[T] (5.8) p= 0.9485GeV (5.9)

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p≃0.95GeV (5.10) Particles with momentum less than 0.95 GeV would spiral inside the TPC and will not reach the barrel calorimeter. Instead, they will reach the endcaps, which are not included in this study.

Figure 5.3.: Particle travelling from interaction point IP in a schematic octant view of the detector.

Using Pythagorean trigonometric identity, one can determine that the particles that start with θ > 37.57^◦ will hit the barrel ECAL. In order to gather the particles that starts in the right direction (i.e. θ >37.57^◦ ), the following formula is used.

cosθ= pz

pt (5.11)

wherepzis the longitudinal momentum andpt=p

p²_x+p²_y is the transverse momentum.

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5.3. Software Framework

In this section, a general overview of software framework that is used in this study and how the particle identication is done using the time of ight information are explained.

5.3.1. Monte Carlo and Reconstructed Particles

A Monte Carlo (MC) event generator, based on a theoretical model, simulates particle physics events. Particle reconstruction is the process in which basic signals recorded by the detector are reconstructed to tracks and clusters which then is merged to particles produced in the collision. The particles which are reconstructed from the detector signals are called reconstructed particles.

This study is done using standard tools of ILCSoft version v02-00 [12]. The event class used in this study is e⁺e⁻→tt¯with a centre-of-mass energy of 500 GeV. The top quarktdecays to a bottom quark and a W⁺ boson which in turn decays to a quark and an antiquark along with a lepton and a neutrino: t→ bqq¯. The top antiquark t¯decays to a bottom antiquark and aW⁻ boson which decays to a quark and an antiquark along with a lepton and a neutrino: ¯t → ¯bqq¯. Pair production of top quarks is suitable for studying this detector performance because it is an event with output of 6 quarks and so there will be large number of particles in the detector.

In order to study individual particles, dedicated single particle samples are used. Since there are many particles in a physics event le like t¯t, it is dicult to study individual particles. A single particle only le contains particles from one particle type sent into the detector with various momenta in dierent directions. Various parameters like energy, momentum, time of ight of Monte-Carlo and reconstructed particles are written into an Ntuple le called LCTuple. The data is accessed by writing appropriate root macros [13].

5.3.2. The TOF Processor

In this thesis, the time of arrival of particles at the entry of ECal is investigated.

The time information is based on the true hit time from GEANT4. GEANT4 is a toolkit for simulating the passage of particles through matter which includes a complete range of functionality including tracking, geometry, physics models and hits [14].

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The time of ight of every reconstructed particle is calculated using a Marlin processor [15]. The processor creates TOF in two ways namely "First hit" and "Closest hits".

First hit calculates time of the arrival of a particle when it rst hits the calorimeter.

The closest hits takes the rst N closest hits to the ECAL entry and the entry point is found by extrapolating the hits. This thesis is based on TOF using the "Closest hits"

approximation.

ŶƚƌǇ ƉŽŝŶƚ ŝŶƚŽƚŚĞ>

ĂůŽƌŝŵĞƚĞƌŚŝƚƐ

>

y z

dƌĂĐŬŽĨ ƚŚĞƉĂƌƚŝĐůĞ

/W

Figure 5.4.: Graphical representation of the extrapolation of the calorimeter hits to nd the entry point into the calorimeter (ECAL).

In the "Closest hits" method, the rst 10 hits in the calorimeter are tted to a trajectory in the calorimeter and the trajectory is extrapolated to nd the entry point of the particle into the calorimeter.

The processors also create dierent time resolutions by Gaussian smearing of the true time from GEANT4. This enables one to study the resolution required for the particle identication. The gaussian smearing is done by drawing a random number from a normal gaussian with mean 0 and width 1. The number is multiplied with resolution and added to the true time. The smearing is done for each hit and then combined. The time resolutions that are used in this study are 10, 50, 100 ps.

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5.3.3. β vs Momentum

Consider a particle traveling from the interaction point, enters the ECAL at time T with a path length of L. From equation: 5.6, the relativistic speed of the particle, is given by

β = L

T (5.12)

The relativistic speed β obtained from the equation above is plotted against the momentum for all reconstructed particles. The following cuts are applied to the plot such that the particles reaching the barrel ECAL is selected.

1. In order to lter particles that travel in the right direction i.e. θ >37.57^◦ in Fig. 5.3, a cut to thecosθ in Equation: 5.11 is applied.

2. Particles with transverse momentum pt > 0.95 GeV (refer to Equation: 5.10) are chosen such that particles which spiral in the TPC are rejected.

Figure 5.5.:β vs momentum for all reconstructed particles in a t¯t sample before and after cuts.

Particles with dierent mass and momenta travel at dierent velocitiesβ. Thus, particles can be identied from theβvs momentum plot using the known mass of the particles.

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Particle Mass

Proton 938.272 MeV Kaon 493.677 MeV Pion 139.571 MeV Muon 105. 658 MeV Electron 510.999 keV

Table 5.1.: Masses of relevant particles.

A particle with mass m and momentum p has velocity

β = p

pp²+m². (5.13)

Figure 5.6.:β vs momentum with the expected (theory) beta calculated from equation (5.13) in solid lines.

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To dierentiate between particles for a specic momenta, slices of momentum (in β vs momentum plot) is projected on to the vertical axis of Fig. 5.5 i.e. β.

The gure 5.7 shows the dierent particles (peaks) at a momentum of 2 GeV for the true arrival time, without considering a nite time resolution. The width of the momentum slice is 50 MeV.

Figure 5.7.:β distribution at 2 GeV with verticle lines representing the theoretical values of β. The width of the momentum slice is 50 MeV

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6. Particle Identication using TOF

The PID performance can be quantied in terms of a separation power. The separation power is a quantitative measure of how well two particles can be dierentiated.

6.1. Separation Power

The separation power is the dierence between the mean of two distributions expressed in multiples of the width (resolution). It determines the quality of the PID technique and the signicance of the detector response.

Figure 6.1.: Two gaussian peaks with means µ1, µ2 and resolutions σ1,σ2 respectively.

Consider two gaussian distributions with means µ1 and µ2 and widths (i.e. standard deviation)σ1 and σ2 respectively. The resolution in the separation power, is expressed

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either as the average of the individual resolutions or the root mean square of the individual resolutions.

The separation power is given by S = |µ1 −µ2|

qσ²₁+σ²₂ 2

or S = |µ1−µ2|

σ₁+σ₂ 2

(6.1) In this study, the rst denition has been chosen, thus the separation between two particles A and B is given by

S_A/B = |β_A−β_B| qσ_βA² +σ²_βB

2

. (6.2)

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6.1.1. Gaussian t

The individual particle peaks inβvs momentum are to be tted with a Gaussian function such that the separation can be found. For doing a Gaussian t on each particle, the reconstruction is done with a dedicated single particle only sample. This removes the contamination that a physics event le like t¯thas, such that the individual particles can be studied. Fromβvs momentum plots of single particle les with a 50 MeV momentum bin width, the following plots are drawn.

Figure 6.2.: Gaussian t applied to a proton peak in the β distribution at 2 GeV momentum using a single particle only sample at dierent time resolutions.

Figure 6.3.: Gaussian t applied to a proton peak in the β distribution at 8 GeV momentum using a single particle only sample at dierent time resolutions.

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Figure 6.4.: Gaussian t applied to a kaon peak in theβdistribution at 2 GeV momentum using a single particle only sample at dierent time resolutions.

Figure 6.5.: Gaussian t applied to a kaon peak in theβdistribution at 8 GeV momentum using a single particle only sample at dierent time resolutions.

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Figure 6.6.: Gaussian t applied to a pion peak in theβdistribution at 2 GeV momentum using a single particle only sample at dierent time resolutions.

Figure 6.7.: Gaussian t applied to a pion peak in theβdistribution at 8 GeV momentum using a single particle only sample at dierent time resolutions.

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6.1.2. Gaussian Error Propagation

Due to limited number of MC events, there is uncertainty in determining the separation power. The uncertainity of separation power S is given by

∆S = s

∂S

∂µ1

∆µ²1+ ∂S

∂µ2

∆µ²2+ ∂S

∂σ1

∆σ²1+ ∂S

∂σ2

∆σ2² (6.3) Inserting derivatives

∂S

∂µ1

,

∂S

∂µ2

,

∂S

∂σ1

,

∂S

∂σ2

in the above equation, the uncertainty on separation Power is

∆S = v u u t

∆µ²1

σ²₁+σ₂² 2

+ ∆µ²2

σ₁²+σ₂² 2

+ ∆σ²1 (µ1−µ2)²σ1²

4_σ₂

1+σ²₂ 2

³ + ∆σ²2 (µ1−µ2)²σ2²

4_σ₂

1+σ²₂ 2

³ (6.4)

∆S = v u u t

∆µ²1 + ∆µ²2

σ₁²+σ₂² 2

+ (µ1−µ2)² (σ1²∆σ²1 +σ2²∆σ2²) 4

σ₁²+σ²₂ 2

³ (6.5)

The standard deviation (Equation: 6.5) of the individual Gaussian peaks are then written into the root macro using TGraph to create separation power plots.

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6.2. Particle separation using Time of Flight

In this section, separation power of protons/kaons and kaons/pions are investigated. The separation power depends on momentum range. From this section, one could conclude, until which momentum the separation power is eective i.e. 2σ separation between the gaussian t to the particle peaks.

6.2.1. p/K separation

Figure 6.8.: Separation power between protons and kaon as a function of momentum assuming dierent time resolutions.

The p/K separation is eective up to 7.9 GeV using 50 ps time resolution and up to 5.8 GeV using 100 ps time resolution. The 10 ps time resolution which is similar to the 0 ps i.e. the true arrival time, can separate protons from kaons above 9 GeV.

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6.2.2. K/ π separation

Figure 6.9.: Seperation power between kaons and pions as a function of momentum assuming dierent time resolutions.

From this gure one can see that particle identication for p/K can be performed up to 4.3 GeV and 3.4 GeV using 50 ps resolution and 100 ps resolution respectively. The 10 ps time resolution is similar to the 0 ps which is the true arrival time. The 10 ps resolution detector can separate protons from kaons up to 5.5 GeV.

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6.3. Particle Separation using Time of Flight and dE/dx

In this section, particle separation using TOF is compared with dE/dx [16]. From this section, one could see how well the two particle identication techniques work together in low momentum region.

6.3.1. p/K separation

Figure 6.10.: Separation power between protons and kaons as a function of momentum using TOF anddE/dx [16].

The particle identication by a TOF detector operating at 50 ps and 100 ps time resolution complements the dE/dx by covering low momentum region up to 8 GeV and 6 GeV respectively.

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The low momentum particles, which spirals inside the TPC and reaches the end cap, can be identied using dE/dx.

Thus these two particle identication techniques work well together.

6.3.2. K/ π separation

Figure 6.11.: Seperation power between kaons and pions as a function of momentum using TOF anddE/dx [16].

p/K separation using dE/dxis eective from 1 GeV until 45 GeV. Whereas TOF separates Kaons from Pions better thandE/dx up to 3.5 GeV with 50 ps time resolution and until 2.6 GeV with 100 ps time resolution.

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7. Conclusion

The primary goal of particle identication is to enhance the reconstruction by taking into account the correct mass of the particles. An ecient PID technique can separate particles from one another and can contribute to reconstruction signicantly.

The particle identication using the time of ight (TOF) in the International Large Detector (ILD) was investigated in this thesis. Until now, the particle identication in the ILD is carried out by the Time Projection Chamber (TPC) using dE/dx. This study represents the possibility of improving the PID by adding TOF. The momentum range in which the particle identication using TOF is eective, depends on the time resolution. The time of ight of particles from the interaction point to the calorimeter, ranges in the order of nanoseconds so the time resolutions that were investigated in this study are are 10 ps, 50 ps and 100 ps.

From the analysis part, it is evident that a TOF detector with 10 ps and 50 ps time resolution is ecient in the momentum range of 1 to 9 GeV than 100 ps. A detector with 10 ps time resolution, if feasible in the ILD, can extend the capability to separate protons from koans above 9 GeV and kaons from pions up to 5.5 GeV. Particle

identication using a TOF detector working with 50 ps time resolution, can separate kaons from pions up to a momentum of 4.3 GeV and protons from kaons till 8 GeV. A 100 ps TOF detector can separate kaons from pions till 3.4 GeV and protons from kaons up to 5.8 GeV. The current TOF detector technologies that can have ps time resolution are scintillators, Multi-gap Resistive Plate Chambers (MRPC), SiPMs etc.

Default in ILD is the ECAL which is made of tungsten as absorber and silicon as sensitive material whose alternative would be scintillator with SiPM readout.

The particle identication using TOF compliments dE/dx method by covering the low momentum range. The separation power between pions and kaons is over 3σ up to 10 GeV using TOF and dE/dx. Thus, having a TOF detector will complement the other particle identication techniques in ILD to improve the overall reconstruction.

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Part I.

Appendix

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List of Figures

1.1. Particle content of the Standard Model [1]. . . 9

2.1. Schematic of ILC with subsystems [4]. Refer to section 2.2 and 2.3 for explanations. . . 11

3.1. Octant view of the ILD with dimensions of each component. . . 14

5.1. Motion of a charged particle in a magnetic eld. . . 19

5.2. Particle travelling from interaction point IP hits the calorimeter. . . 21

5.3. Particle travelling from interaction point IP in a schematic octant view of the detector. . . 22

5.4. Graphical representation of the extrapolation of the calorimeter hits to nd the entry point into the calorimeter (ECAL). . . 24

5.5. β vs momentum for all reconstructed particles in a t¯t sample before and after cuts. . . 25

5.6. β vs momentum with the expected (theory) beta calculated from equation (5.13) in solid lines. . . 26

5.7. β distribution at 2 GeV with verticle lines representing the theoretical values of β. The width of the momentum slice is 50 MeV . . . 27 6.1. Two gaussian peaks with means µ1,µ2 and resolutions σ1,σ2 respectively. 28 6.2. Gaussian t applied to a proton peak in the β distribution at 2 GeV

momentum using a single particle only sample at dierent time resolutions. 30 6.3. Gaussian t applied to a proton peak in the β distribution at 8 GeV

momentum using a single particle only sample at dierent time resolutions. 30 6.4. Gaussian t applied to a kaon peak in the β distribution at 2 GeV mo-

mentum using a single particle only sample at dierent time resolutions. 31 6.5. Gaussian t applied to a kaon peak in the β distribution at 8 GeV mo-

mentum using a single particle only sample at dierent time resolutions. 31

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6.6. Gaussian t applied to a pion peak in the β distribution at 2 GeV momentum using a single particle only sample at dierent time resolutions. 32 6.7. Gaussian t applied to a pion peak in the β distribution at 8 GeV mo-

mentum using a single particle only sample at dierent time resolutions. 32 6.8. Separation power between protons and kaon as a function of momentum

assuming dierent time resolutions. . . 34 6.9. Seperation power between kaons and pions as a function of momentum

assuming dierent time resolutions. . . 35 6.10. Separation power between protons and kaons as a function of momentum

using TOF and dE/dx [16]. . . 36 6.11. Seperation power between kaons and pions as a function of momentum

using TOF and dE/dx [16]. . . 37

List of Tables

5.1. Masses of relevant particles. . . 26

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Particle Identi cation using Time of Flight in the International Large Detector ILD by