Pre-Shower Detector andParticle Identification at sPHENIX

Kazuya Nagashima(M131852)
Quark Physics Laboratory
Department of Physics
Graduate School of Science
Hiroshima University

Supervisor： Associate Prof. Kenta Shigaki
Primary examiner ： Associate Prof. Kenta Shigaki
Examiner： Prof.
Yasushi Fukazawa

February 23, 2015

Abstract
A new state of matter called Quark Gluon Plasma (QGP) existed within 10 microseconds
after the big bang. QCD has the property of asymptotic freedom which is decreasing
running coupling constant (αs ) with increasing momentum transfer, and causes a phasetransition to QGP under conditions of extreme temperature and net baryon density. We
plan sPHENIX, the upgrade of PHENIX (the Pioneering High Energy Nuclear Interaction
eXpariment) for a perfect solution of physics properties of QGP. In this thesis, the designof the Pre-Shower detector and the particle identification at sPHENIX are studied.
(1) Design of the Pre-Shower detector
The Pre-Shower detector can detect the early stage of electromagnetic showers, and identify particles. The main motivation of the Pre-Shower is to separate direct photons produced in the initial hard scattering from background photons having very narrow opening
angles from decays of neutral mesons at high transverse momenta. At the leading order,
photons are produced back-to-back with the same transverse energy of associated partons(Jets). Therefore the energy loss of partons in the hot and dense medium can be measured via the transverse momentum ratio of direct photons and jets, because photons do
not strongly interact. In this thesis, the size of silicon pad and the thickness of the Pb
convertor were decided on the basis of signal-to-noise ratio of direct photons. In a single
particle simulation, the ratio of direct photons to neutral π meson can be improved be up
to a factor of 6 times.
(2) Particle Identification at sPHENIX
The yields of upsilon meson states are suppressed sequentially by QCD debye screening
in a hot and dense medium, because the eﬀect of QCD debye screening depends on the
distance between the two quarks. Therefore the relationship between the physical sizeof quarkonia and QCD debye screening can be solved via the measuremnt. The signalto-background ratio and the statistics are both critical for a successful measurement of
the upsilon meson states. In this thesis, the method of electron identification is established, and the charged hadron rejection is evaluated to be over 100. In this condition,
the signal-to-background of invariant mass spectram of upsilon meson states is above theunity.

1

Contents
1 Introduction
1.1 Modern Particle Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.1 Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.2 Quantum Electro-Weak Dynamics . . . . . . . . . . . . . . . . . . .
1.1.3 Quantum Chromo Dynamics . . . . . . . . . . . . . . . . . . . . . .
1.1.4 Quark Gluon Plasma . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.5 Relativistic Heavy-Ion Collision (RHIC) . . . . . . . . . . . . . . . .
1.1.6 Time Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Past Results at RHIC and LHC . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.1 High Transverse Momentum Suppression . . . . . . . . . . . . . . .
1.2.2 Jet Quenching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.3 Heavy Flavor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.4 Heavy quarkonia . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Motivation of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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2 sPHENIX Experiment
2.1 Physics Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 sPHENIX Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Silicon Vertex Trackers (VTX) . . . . . . . . . . . . . . . . . . . . .
2.2.2 Electromagnetic Calorimeter (EMCal) . . . . . . . . . . . . . . . . .
2.2.3 Hadron Calorimeter (HCal) . . . . . . . . . . . . . . . . . . . . . . .
2.2.4 Pre-Shower (PS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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3 Analysis Methods
3.1 Simulation and Framework . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 GEANT4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.2 sPHENIX Frame Work . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Energy Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Energy Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.2 Sampling Fraction . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Detected Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Single Photon Identification . . . . . . . . . . . . . . . . . . . . . . .
3.3.2 Multi-layers Pre-Shower . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.3 Electron Identification . . . . . . . . . . . . . . . . . . . . . . . . . .

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4 Results and Discussions
4.1 Design and Performance Study for the Pre-Shower Detector . . . . . . . . .
4.1.1 Design Optimization of the Pre-Shower . . . . . . . . . . . . . . . .
4.1.2 Energy Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.3 Occupancy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Particle Identification at sPHENIX . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 Photon Identification Fraction . . . . . . . . . . . . . . . . . . . . .
4.2.2 Enhancement Factor for Direct Photon . . . . . . . . . . . . . . . .
4.2.3 Multi-layers Pre-Shower . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.4 Electron Identification . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.5 Pion Rejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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5 Summary and Conclusions40

6 Acknowledgements

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7 Appendix
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7.1 Charged Particle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

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List of Figures
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Running coupling constant αs of strong interaction of a function of the
momentum transfer, Q [1] . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
QCD phase diagram [2] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Relativistic Heavy Ion Collider (RHIC) of the BNL [3] . . . . . . . . . . . . 9
The space time evolution in heavy ion collisions. [4] . . . . . . . . . . . . . 9
Neutral pi meson (π 0 ) (yellow), eta meson (η) (red) and direct γ (purple)
RAA as a function of transverse momentum for central Au + Au collisions.
[5] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Di-hadron correlations as measured by RHIC. The horizontal axis is theangle between the leading and the subleading particle. [6] . . . . . . . . . . 11
Comparison of the average radiative and elastic energy losses of light andheavy quarks passing through the medium produced in central AuAu collisions at RHIC energies [7] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
The mass spectrums measured with CMS are compared between in pp and
Pb+Pb. [8] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
NLO pQCD calculations of direct photons and π 0 for RHIC and LHC. The
counts per event in Au+Au or Pb+Pb collisions on the left plot. The direct
photon to π 0 ratio in p+p (Au+Au or Pb+Pb) on the right plot. [9] . . . . 13
(Left)The signal plus background in the Upsilon mass region for ten billion
0-10 % central Au+Au events, assuming a pion rejection factor of 90, withthe signal reduced by a pair identification eﬃciency of 49 %. The combined
backgrounds due to correlated bottom, correlated charm, and Drell-Yan are
shown as the red curve. The combined backgrounds due to fake electrons
combining with themselves, bottom, and charm are shown as the blue line.
(Right) The expected invariant mass distribution for ten billion 0-10 %central Au+Au events, after subtraction of combinatorial background using
the like-sign method. [9] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
The physics goals of sPHENX [9] . . . . . . . . . . . . . . . . . . . . . . . . 15
Calculasion results of dijet Aj . Central (green) and mid-central (blue) distributions are shown along with the initial PYTHIA(a widely used pQCD
event generator) distributions (red). [9] . . . . . . . . . . . . . . . . . . . . 15
Calculation results for the vacuum and medium modified distribution for
direct photon-reconstructed jet event at LHC collision energy (left) and
RHIC collision energy (right) [9] . . . . . . . . . . . . . . . . . . . . . . . . 16
The mass spectrum from reconstructed electron decay tracks for the three
Upsilon states. [9] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
sPHENIX detectors. [9] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Reconfiguration of the VTX inner two layers and additional tracking layers
as explained in the text. [9] . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
The transverse momentum resolution for single particle (pion). The fit
consists of a term that is constant in pT, and a term that is linear in pT. [9] 18
View of SPACAL Electro-magnetic Calorimeter. [9] . . . . . . . . . . . . . 19
Energy resolution achieved in beam tests of a prototype electromagnetic
calorimeter compared with GEANT4 Monte Calro simulation. [9] . . . . . . 19
View of Hadron Calorimeter (HCal). [9] . . . . . . . . . . . . . . . . . . . . 20

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Concept diagram of the Pre-Shower. . . . . . . . . . . . . . . . . . . . . . .
GEANT4 simulation at sPHENIX . . . . . . . . . . . . . . . . . . . . . . .
The energy spectrum with GEANT4 and single particle simulation. It isfitted by the gauss function. . . . . . . . . . . . . . . . . . . . . . . . . . . .
Event display for decay two photons from π 0 at the Pre-Shower and the
SPACAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Number of hit cells with 10MeV threshold . . . . . . . . . . . . . . . . . . .
Ratio of max cell energy to sum cells energy with 10MeV threshold . . . . .
Position resolution as a function of weight parameter w0 . . . . . . . . . . .
Shower shape at the Pre-Shower . . . . . . . . . . . . . . . . . . . . . . . .
Number of hits each layers . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sum energy in each layer . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Correlations of hits between at 7 layer and at 10 layer . . . . . . . . . . . .
Electromagnetic shower development . . . . . . . . . . . . . . . . . . . . . .
Measured energy distribution . . . . . . . . . . . . . . . . . . . . . . . . . .
HCal scintillator energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Minimum opening angle of decay photons from π 0 as a function of thetransverse momentum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Opening angle of π 0 at pT = 40 GeV . . . . . . . . . . . . . . . . . . . . . .
Detection eﬃciency for perfect Pre-Shower as a function of dϕ under condition of constant area of cells. . . . . . . . . . . . . . . . . . . . . . . . . .
Detection eﬃciency as a function of transverse momentum in case of perfect
Pre-Shower . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Energy resolution as a function of transverse momentum. . . . . . . . . . .
Event display for HIJING most central Au+Au collisions . . . . . . . . . .
Photon ID fraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Enhancement Factor of a single photon to a single π 0 . . . . . . . . . . . . .
Enhancement factor for Multi-layer design . . . . . . . . . . . . . . . . . . .
Energy correlation between Pre-Shower and EMCal . . . . . . . . . . . . . .
Leaked energy distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Pion rejection in each calorimeter as a function of electron eﬃciency . . . .
Total pion rejection as a function of electron eﬃciency . . . . . . . . . . . .
Signal-to-noise ratio for direct photon measurement . . . . . . . . . . . . . .
Pion rejection for the measurement of upsilon meson . . . . . . . . . . . .
Stopping power for positive muons in cupper [1] . . . . . . . . . . . . . . . .
Most probable energy loss in silicon, scaled to the mean loss of a minimum
ionizing particle, 388 eV/µm. [1] . . . . . . . . . . . . . . . . . . . . . . . .

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1

Introduction

1.1

Modern Particle Physics

1.1.1

Standard Model

The Standard Model of particle physics is a theory concerning the electromagnetic, weak
and strong nuclear interactions which mediate the dynamics of the known subatomic
particles. At the Standard Model, seventeen elemental particles and three fundamental
interactions are assumed. twelve out of elemental particles are a matter particles called
quarks and leptons, the others are defined as force carriers that are called gauge particles
included Higgs particle which gives a mass to elemental particles, W and Z bosons.
1.1.2

Quantum Electro-Weak Dynamics

The electromagnetic interaction is described by Quantum Electro Dynamics (QED) as arelativistic quantum field theory. A photon of a gauge boson mediates the electromagnetic
interaction. Many theoretical values of QED agree with experimental values in a highaccuracy. The Lagrangian of QED is expressed by a following formula.

LQED =∑

ψ f (iγ µ ∂µ − mf )ψf + e

f∑1
Qf ψ f γ µ ψf Aµ − Fµν F µν
4
f

(1)

Here, ψf is the spinor which is wave function of spin, γ µ is Dirac matrix, Qf is elementarycharge, Aµ is electromagnetic vector potential, shows photon field, Fµν is electromagnetic
tensor. The second item of the Lagrangian shows interaction between charged particles
and electromagnetic field. That means the probability amplitude is in proportion toeQf . Also the weak interaction causes beta decay by mediating W and Z bosons. Todayelectromagnetic and weak interactions are unified by the Weinberg-Salam theory and called
the electro-weak interaction.
1.1.3

Quantum Chromo Dynamics

Quantum Chromo Dynamics (QCD) describes the strong interaction of quarks and gluons
with color charge exchange. Gluon of a gauge boson mediates the strong interaction.
The QCD was developed as an extension of QED via the imposition of a local SU(3)symmetry in color space and based on the gauge field theory. Its lagrangian is expressedby a following formula.

LQCD =∑

ψ q,a (iγ µ ∂µ − mq )ψq,a + gs

q∑

1 A AµνAψ f γ µ Tab
ψq,b GAµ − Gµν F
4q(2)

LQCD and LQED are in the same form. ψq,a is the quark field, gs is the coupling conA
stant of QCD, GAµ is the tensor of gluon field, T is the generator matrix of SU(3). LQCD
is remained invariable with gauge transformation. A feature of QCD is the momentum
transfer dependence of the strong coupling constant αs that is expressed in the following.
αs (µ2R ) ≃1
12π=
b0 log(µ2R /Λ2Q CD)(33 − 2nq )log(µ2R /Λ2Q CD)
6(3)

Here, ΛQCD is the scale parameter of the strong interaction (ΛQCD ≃ 200MeV) and
nf is the number of active quark flavors with quark mass less than Q. Figure 1 shows therunning coupling constant as a function of the momentum transfer. As shown in Figure 1,
in case of a large momentum transfer and equivalently at a short distance, the αs decreases
logarithmically, and quarks and gluons are freed from confined state. This phenomenon
is produced with asymptotic freedom caused by non-commutative gauge theory of QCD.

Figure 1: Running coupling constant αs of strong interaction of a function of the momentum transfer, Q [1]1.1.4

Quark Gluon Plasma

A new state of matter called Quark Gluon Plasma (QGP) existed within 10 microseconds
after the big bang. QCD has the property of asymptotic freedom which express decreasing
the running coupling constant (αs ) with increasing momentum transfer, and causes a phasetransition to QGP under conditions of extreme temperature and net baryon density. That
is to say, quarks are released from confined state with increasing energy scale (> 200 MeV,
> 2 GeV/fm3 ). Figure 2 shows a theoretical phase diagram of nuclear matter as a functionof baryo-chemical potential μ and temperature T. QGP phase is created by high energy
heavy ion collisions. In recent years, QGP was measured as nearly perfect fluid which wascontrary to expectations by Relativistic Heavy-Ion Collision (RHIC).
1.1.5

Relativistic Heavy-Ion Collision (RHIC)

High energy heavy-ion collision is the only way to create QGP phase. It is performed
with Relativistic Heavy-Ion Collision (RHIC) at Brookhaven National Laboratory (BNL).
RHIC can accelerate a variety of nuclear beams from protons (p) to gold ions (Au) withmaximum energy up to 500 GeV for p and 200GeV per nucleon for Au. At first stageof acceleration, p and Au, are produced and accelerated by the Linac and the Tandem
7

Figure 2: QCD phase diagram [2]Van de Graaﬀ pre-accelerator. Secondly, the produced beam is more accelerated by theAlternating Gradient Synchrotron (AGS). AGS can accelerate the beam unto 28 GeV for
p and 10.8 GeV for Au per nucleon, and send into the RHIC rings. Finally, the beams areaccelerated up to its maximum energy and collided.
1.1.6

Time Evolution

At high energy heavy-ion collision, the ion is accelerated nearly to the speed of light. At
this time, it is disk shape by Lorentz contraction and the Color Glass Condense (CGC)that is saturation of gluon in atomic. At collision, part of partons scatter with large
momentum transfer in hard processes over very short time scales, τ (1/pT < 0.1fm/c). On
the other hands, most of the quarks pass through and interacted gluons create Glasma thatis gluon plasma. Quark pairs are created by gluon fusion in glasma. And then quarks andgluons become local equilibration that is occurring QGP phase transition. Temperatureof QGP decrease with quickly expansion, quarks and gluons are recombined and create
hadron gas phase. It is become final state with through chemical freeze-out and thermal
freeze-out.

1.2
1.2.1

Past Results at RHIC and LHCHigh Transverse Momentum Suppression

High pT particles are produced by heavy ion collisions and loss energy when pass throughthe matter created in the collision. The mechanism of energy loss in the dense matter isthought to be the gluon bremsstrahlung radiations and parton elastic scatterings. Thiseﬀect can be measured with the nuclear modification factor.

RAB =2 /dydp
dNAB
Tinel ) × d2 σ /dp(< Ncoll > /σpp
pp
T

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(4)

Figure 3: Relativistic Heavy Ion Collider (RHIC) of the BNL [3]Figure 4: The space time evolution in heavy ion collisions. [4]9where d2 NAA /dydpT is the invariant yield per unit rapidity, Ncoll is the number of binary
heavy-ion collision on the impact parameter range of corresponding centrality, σpp is the
cross section for inelastic proton-proton collisions. Figure 5 shows the nuclear modification
factor each particles. If medium eﬀect do not exit, π 0 and η RAA should be 1. But
practically yield of π 0 and η decrease greatly at high pT . On the other hands, direct γ
RAA is RAA = 1 because of not interacting strongly in a medium. So RAA describes theeﬀect of energy loss in a medium by strong interaction.

Figure 5: Neutral pi meson (π 0 ) (yellow), eta meson (η) (red) and direct γ (purple) RAA
as a function of transverse momentum for central Au + Au collisions. [5]1.2.2

Jet Quenching

The production time scale of high pT partons and photons in pQCD processes are very
short, τ < 1/pT < 0.1 fm/c. Thus their yields can be modified by interact on withmedium. The back-to-back dijets are produced by the pQCD process, which have sametransverse energy. So transverse momentum unbalance can be used as probes to study thestrongly interacting medium created, because these unbalances are occurred by diﬀerenceof medium pass length on the right plot in Figure 6. The left plot in Figure 6 show dihadron correlations as measured by RHIC. The horizontal axis is the angle between theleading and the subleading particle. The away side peak is clearly visible in p+p andd+Au collisions, but is absent in Au+Au collisions. This is jet quenching by interactionsin the medium.
1.2.3

Heavy Flavor

The mechanism of parton energy loss is gluon radiation and elastic scattering in QGP.
Quark dE/E depends on quarks mass. Especially bottom quark dE/E is extremely smaller
than others. Today, the energy loss of hadron including u, d and c quarks were measured,
but b did not. So B meson including bottom quark should be measured for eﬀect ofenergy loss in pp and AA collisions. Separating c/b quark is diﬃcult to achieve with semileptonic channel because of the single lepton spectrum contains both charm and bottom
contributions. So it is challenges for the future.
10Figure 6: Di-hadron correlations as measured by RHIC. The horizontal axis is the angle
between the leading and the subleading particle. [6]Figure 7: Comparison of the average radiative and elastic energy losses of light and heavy
quarks passing through the medium produced in central AuAu collisions at RHIC energies[7]11

1.2.4Heavy quarkonia

cc̄ and bb̄ vector masons are called the quarkonia (i.e. J/ψ, Υ and so on). These areproduced by only hard-scattering in nucleons-nucleons collisions, and aﬀected by the QCD
debye screening which is break bound state of quarks by color charged particles in the
hot and dense medium. Especially, the yields of upsilon meson states are suppressedsequentially by QCD debye screening in a hot and dense medium, because the eﬀect of
QCD debye screening depends on the distance between the two quarks. Therefore therelationship between the physical size of quarkonia and QCD debye screening can besolved via√the measuremnt. Figure 8 shows the mass distribution of upsilon three statesin PbPb SN N = 2.76 TeV.

Figure 8: The mass spectrums measured with CMS are compared between in pp and
Pb+Pb. [8]1.3

Motivation of this thesis

We plan sPHENIX, the upgrade of PHENIX (the Pioneering High Energy Nuclear Interaction eXpariment) for a perfect solution of physics properties of QGP. The sPHENIX
detector will be able to measure jets, b-tagged jets, photons, heavy flavors, quarkonia witha wide energy range. In this thesis, I focus on measurement of photons, heavy flavor andquarkonia.
Firstly, I studied the design of the Pre-Shower detector for separating direct photons fromdecay photons. Figure 9 show the count/event of direct photon and π 0 at RHIC and LHC,
and these ratio. In case of RHIC, the ratio of direct photons to π 0 is larger than three
in the region of 25 GeV ≤ pT . In the pT region from 10 to 25 GeV/c, however, direct
photons cannot be tagged or measured due to overwhelming decay photons as the electromagnetic calorimeter can identify photons from π 0 only up to 10 GeV/c. So we proposed
Pre-Shower detector which fills the gap of single photon measurement, and extends the12direct photon tagging to the lower transverse momentum. The performance goal is toimprove the signal-to-background ratio by a factor 3.
Secondly, I studied the identification of electron for measurements of upsilon 3 states,
where the signal-to-background ratio and the statistics are both critical for a successful
measurement. Figure 10 show the upsilon mass distribution before and after subtracting
background under condition of a pion rejection factor of 90% and a pair identification efficiency of 49 %. So I established the method of identifying electrons using the sPHENIX
detectors for the measurement and evaluated pion rejection which is the ratio of electroneﬃciency to charged pion eﬃciency.

[1] count[2] ratio

Figure 9: NLO pQCD calculations of direct photons and π 0 for RHIC and LHC. The
counts per event in Au+Au or Pb+Pb collisions on the left plot. The direct photon to π 0ratio in p+p (Au+Au or Pb+Pb) on the right plot. [9]13Figure 10: (Left)The signal plus background in the Upsilon mass region for ten billion 0-10
% central Au+Au events, assuming a pion rejection factor of 90, with the signal reduced
by a pair identification eﬃciency of 49 %. The combined backgrounds due to correlatedbottom, correlated charm, and Drell-Yan are shown as the red curve. The combined
backgrounds due to fake electrons combining with themselves, bottom, and charm areshown as the blue line. (Right) The expected invariant mass distribution for ten billion
0-10 % central Au+Au events, after subtraction of combinatorial background using thelike-sign method. [9]2sPHENIX Experiment

The sPHENIX is a major upgrade to the PHENIX detector at the Relativistic Heavy
Ion Collider. The physics programs of sPHENIX primarily aim at jets and heavy flavors
addressing fundamental questions about the nature of the strongly coupled quark-gluon
plasma. We have a run plan for 2021-2022 including of 22 weeks of Au+Au, and extended
periods of p+p and p(d)+Au running with the high luminosity available at RHIC andthe high data acquisitions bandwidth at sPHENIX.
√ sPHENIX will record 100 billion andsample over 2/3 of a trillion Au+Au collision at SN N = 200 GeV.

2.1

Physics Motivation

The physics cases for sPHENIX are in the following.
1. Jets, Heavy Quark jets
The energy loss of a parton and the parton shower evolving in medium are understood
via the measurement of jets. Theoretical calculations attempting to describe the wealth of
new data from RHIC and the LHC have not yet reconciled some of the basic features, withsome models including large energy transfer to the medium as heat and others with mostly
radiative energy loss. Figure 12 shows the produceted diet asymmetry (Aj ) at RHIC for
mid-central and central Au+Au collisions for leading jets ET1 > 20 GeV and jet radiusparameter R = 0.4 and R = 0.2 in the left and right histograms. The diet asymmetry isexpressed Aj = (E1 -E2 )/(E1 +E2 ).
2. Direct Photons and Fragmentation Functions
14

Figure 11: The physics goals of sPHENX [9]Figure 12: Calculasion results of dijet Aj . Central (green) and mid-central (blue) distributions are shown along with the initial PYTHIA(a widely used pQCD event generator)
distributions (red). [9]15Figure 13: Calculation results for the vacuum and medium modified distribution for direct
photon-reconstructed jet event at LHC collision energy (left) and RHIC collision energy(right) [9]At leading order (LO), photons are produced with the same transverse energy of associated partons. Therefore the energy loss of partons in the hot and dense medium can bemeasured with the transverse momentum ratio of direct photons and jets, because photons do not strongly interact. In other wards, photon + jet productions are the golden
channel to investigate energy loss of partons in the medium. Figure 13 shows the ratioof the reconstructed jet energy with R = 0.3 relateve to the direct photon energy. Here,zj γ is expressed zj γ = pTjet /pTγ .
3. Beauty Quarkonia in the QGP
The yields of upsilon meson states are suppressed sequentially by QCD debye screening in a
hot and dense medium, because the eﬀect of QCD debye screening depends on the distance
between the two quarks. Therefore the relationship between the physical size of quarkonia
and QCD debye screening can be solved via the measurements. And the temperaturedependency of QCD debye screening can be measured with comparison between RHIC
and LHC. Figure 14 shows the reconstructed mass spectrum for dielectric decays withsimulation at sPHENIX.

2.2

sPHENIX Detectors

The sPHENIX detectors include the silicon tracking, electromagnetic and hadronic calorimeters, magnetic solenoid and readout electronics. The sPHENIX is large acceptance (ϕ=2π,η=± 1.1) and 15k Hz data acquisition. Detectors performance are studied using a full
GEANT4 simulation of the detector. The sPHENIX detectors will be able to measure
jets, b-tagged jets, photons, quarkonia, charged hadron with a wide energy range.

16Figure 14: The mass spectrum from reconstructed electron decay tracks for the three
Upsilon states. [9]Figure 15: sPHENIX detectors. [9]172.2.1

Silicon Vertex Trackers (VTX)The silicon vertex tracker is working in current PHENIX and two inner pixels layers at
radii 2.5 and 5 cm from vertex point and two outer strip-pixels layers at radii 11.8 and 16.7
cm. In case of the sPHENIX, the silicon vertex tracker includes two inner pixels layers
and five outer strip-pixels layers in Figure 16. The pT resolution for single pions is shown
as a function of pT in Figure 17.

Figure 16: Reconfiguration of the VTX inner two layers and additional tracking layers as
explained in the text. [9]Figure 17: The transverse momentum resolution for single particle (pion). The fit consistsof a term that is constant in pT, and a term that is linear in pT. [9]182.2.2

Electromagnetic Calorimeter (EMCal)

The sPHENIX electromagnetic calorimeter has scintillation√ fiber in tungsten epoxy as
shown in Figure 18, 18 radiation length (X0 ) and 12 %/ E energy resolution as shownin Figure 19 and segmentation of δη × δϕ = 0.024×0.024, and covers a pseudo rapidity
range of |η| < 1.1. It is called SPACAL EMCal.

[1]
Prototype built and tested at FNAL (Fermi
National Accelerator Laboratory)[2]
Scintillation fiber in tungsten epoxy

Figure 18: View of SPACAL Electro-magnetic Calorimeter. [9]Figure 19: Energy resolution achieved in beam tests of a prototype electromagnetic
calorimeter compared with GEANT4 Monte Calro simulation. [9]2.2.3

Hadron Calorimeter (HCal)

The sPHENIX hadron calorimeterhas two longitudinal segments, 5 interaction lengths as√shown in Figure34, 100%/ E energy resolution and segmentation of δη × δϕ = 0.1 × 0.1.
Inner HCal is stainless steel and outer HCal is magnet steel.

19[1] View of sPHENIX barrel[2] Two longitudinal segments. Inner HCalis stainless and outer HCal is magnet steel.
Figure 20: View of Hadron Calorimeter (HCal). [9]2.2.4

Pre-Shower (PS)The Pre-Shower detector is to identify particles and installed in front of the Electromagnetic Calorimeter. Figure 21 shows the concept diagram of the Pre-Shower. The photon
identification requires no hit near the surface layer. On the other hands, a charged pion isvetoed by requiring large energy deposited at deep layer. Also separating a single photon
from decay two photons requires one hit at deep layer, if the Pre-Shower has good segmentation.
At sPHENIX, the Pre-Shower detector aims at enhancing the physics capabilities ofsPHENIX in the following three aspects. Firstly, identification of direct photons in transverse momentum range above 10 GeV/c, where the sPHENIX electromagnetic calorimeter
is not capable of discriminating single photons from hadron (mostly π 0 ) decay, as well asa measurement of direct photons themselves, to a much border kinetic range. Secondly,
identification of π 0 via two photon decay channel in the transverse momentum range up
to 40 GeV/c. Thirdly, Identification of electron via measurements of upsilon 3 states,
where the signal-to-background ratio and the statistics are both critical for a successful
measurement. In this thesis, the baseline design of the Pre-Shower is 2.4 X0 tungsten
converter, 0.5 cm×0.5 cm single silicon mini-pad.

20

Figure 21: Concept diagram of the Pre-Shower.

3

Analysis Methods

3.1

Simulation and Framework

3.1.1

GEANT4

GEANT4 (GEometry And Tracking) is a computing platform for the simulation of thepassage of particles (proton, neutron, electron, and so on) through matter, using Monte
Carlo methods. It has many tools of physics process, geometry of detector, visualization,etc. The significance of GEANT4 is expecting a result before experiment. Therefore it isessential for high energy physics, astro physics, nuclear physics.
3.1.2

sPHENIX Frame Work

The sPHENIX simulations has employed the GEANT4 for full detector simulations. It
have been integrated with the PHENIX software framework, used analysis tools. The
detectors and read out electronics are highly configurable in GEANT4 frame work, making
it easy to test various geometries and detector concepts. Magnetic field maps for BaBar
magnet have been imported from Opera calculation. We keep every energy deposition andtrack of each particle, to trace back to the original particle from the event generator.

3.2

Energy Calibration

3.2.1

Energy Resolution

The energy resolution is calculated by the energy spectrum which is obtained by the
GEANT4 simulation. It is expressed in the following formula.
σp0= √ + p1
(5)
E
E
21

Figure 22: GEANT4 simulation at sPHENIXAt the left side of a formula, σ is a variance of distribution and E is a measured energy.
The right side of a formula show a fitting function as a function of the measured energy.
Where p0 and p1 are the fitting parameters. At low momentum region, the p0 is dominantand determines the resolution curve. On the other hands, the p1 is dominant at highmomentum region. Figure 23 shows the energy distributions measured by the Pre-Swoer
and the EMCal. It is fitted by the Gauss function.
3.2.2

Sampling Fraction

A sampling fraction is inverse of a calibration constant and used to reconstruct energy. It
is expressed in the following:
SamplingFraction =Evis
Einvis + Evis

(6)

Where Evis is a deposited energy in the detector, Einvis is the deposited energy in theconverter. In other words, a sampling fraction is a ratio of the detectable energy to total
deposited energy in the detector. The sampling fraction of detectors depends on ratio of
amount of substance between a converter and a detector, and is related with the energy
resolution. At the sPHENIX, sampling fraction of the EMCal is 2.6 %. So we should
optimize the design of the Pre-Shower with little eﬀect on EMCal resolution. Table1
shows sampling fractions each radiationn length (X0 ) of the Pre-Shower.
Where the silicon is same thickness of 0.006 cm. As shown in table, if the converter
thickness of the Pre-Shower is less than 1.6X0 , its sampling fraction is less than the EMCal.
However the identification of electrons and photons need enough amount of substance,
because probability of electromagnetic shower caused depend on it. So we should haveseveral candidates of the Pre-Shower which are 1.6X0 , 2.0X0 and 2.4X0 .

22

Figure 23: The energy spectrum with GEANT4 and single particle simulation. It is fitted
by the gauss function.

3.3
3.3.1

Detected Procedures
Single Photon Identification

Main motivation of the Pre-Shower detector is to separate direct photon from decay photons from high transverse momentum π 0 . Opening angle of decay 2 photons from hightransverse momentum π 0 is very narrow. Therefore their causing electromagnetic showers
are merged and they are identified as single photon at the EMCal. So an early developing electromagnetic shower should be measured using very thin and good segmentation
Pre-Shower detector. In this thesis, the methods of single photon identification are in thefollowing.
1, Number of hits.
In case of ideal condition, single photon hit one cell in the Pre-Shower. On the otherhands, π 0 decay 2 photons hit two cells as the Figure 24. So identification of direct photon requires one hit on the Pre-Shower with the appropriate threshold and the region cut
which is the size of the EMCal cluster. Figure 25 shows the number of hit cells with
10MeV threshold in case of single photons and single π 0 . As shown in figure, the direct
photon identification becomes possible by requiring only one hit. Also a case of no hits at
the Pre-Shower is identified as a single photon.
2, Ratio of the max cell energy to the sum cells energy.
In case of single photon, the ratio of the highest cell energy to the sum cells energy shouldbe almost one, because the electromagnetic shower from the single photon goes in one cell.
On the other hands, ratio of π 0 decay photons should be about 50%, because two photons
occur electromagnetic shower. As shown in figure 26, the distribution is diﬀerent between
single photon and π 0 and the peak at one shows only one hit at the Pre-Shower.
3, Shower Shape.
23

Figure 24: Event display for decay two photons from π 0 at the Pre-Shower and the
SPACAL[2] single π 0[1] single photon

Figure 25: Number of hit cells with 10MeV threshold24

Table 1: Sampling Fraction
Tungsten Radiation Length
2.4X0
2.0X0
1.8X0
1.6X0
1.2X0
1.0X0
0.6X0

MatterTungsten
SilliconTungsten
SilliconTungsten
SilliconTungsten
SilliconTungsten
SilliconTungsten
SilliconTungsten
Sillicon

Mean Energy
57.5 MeV
1.1 MeV37.1 MeV
0.9 MeV29.0 MeV
0.7 MeV22.3 MeV
0.6 MeV12.4 MeV
0.4 MeV
8.8 MeV
0.3 MeV
3.9 MeV
0.2 MeV

Stat. Err.
32.3 MeV
0.8 MeV21.8 MeV
0.7 MeV17.4 MeV
0.6 MeV13.7 MeV
0.5 MeV
7.6 MeV
0.4 MeV
5.3 MeV
0.3 MeV
2.1 MeV
0.2 MeVSampling Fraction
1.9%
2.3%
2.5%
2.7%
3.3%
3.7%
5.1%

In case of developing EM shower, hit distribution of π 0 decay photons is formed as ellipse.
So its covariant matrix of ϕ and η become larger than that in the case of single photon.
Shower shape is defined as following equation.

2
σϕ,η
=

Σi wi (ϕi − ϕ̄)(ηi − η̄)Σ i wi(7)where ϕi and ηi are position of the each cell, ϕ̄ and η̄ are the center of the energy cluster,wi is the weight parameter described as follow:
wi = max(0, w0 + ln

Ei
)
E

(8)

where Ei is energy in each cell, E is the sum energy in the cluster, w0 is called thefree weight parameter is determined by position resolution. Figure 27 shows the position
resolution of the Pre-Shower as a function of w0 . As a result, the position resolution isthe best at w0 of 6.0.
Figure 28 shows the distribution of shower shape for each particle and threshold. The
blue histogram shows a single photon, and the red histogram shows a single π 0 for eachthreshold. As shown from these results, there are almost no diﬀerence in the shower shape.
So the shower shape is not useful for the direct photon identification.
3.3.2

Multi-layers Pre-Shower

We should study the multi-layers Pre-Shower for good separation of direct photon fromdecay photons. It was assumed total radiation length of 2.4 X0 included 10 layers (i.e.
(0.24 X0 + silicon detector) × 10). Figure 31 shows the number of hits in each layer at pT
25

[2] single π 0[1] single photon

Figure 26: Ratio of max cell energy to sum cells energy with 10MeV threshold

Figure 27: Position resolution as a function of weight parameter w026

[1] 0MeV threshold[2] 10MeV thereshold

Figure 28: Shower shape at the Pre-Shower= 15 GeV. The red histograms show a single photon at 15 GeV and the blue histograms
show a single π 0 at 15 GeV. The diﬀerence in distributions at hits = 0 become conspicuouswith each layer of depth, because the probability of electron pair creation vary from thenumber of photons. So we should require no hit on layer of the Pre-Shower for identifying
a single photon.
Figure 30 show the sum energy deposited in each layer. The red histograms show asingle photon and the blue histograms show a single π 0 and the green histograms show asingle π − of pT = 15 GeV. The diﬀerence in distributions between the single photon and thesingle π 0 become conspicuous with each layer of depth as the number of hits. On the otherhands, the distribution of the single π − are same, because these are minimum-ionization
particles. In other words, almost all of single π − deposit energy at the silicon detector with
the ionization loss. So separating a single photon from charged hadron requires no energy
deposit near the surface, or large energy deposit at deep areas of the Pre-Shower. However
charged hadrons are vetoed with the tracking and the ratio of momentum to energy at thesPHENIX. So the design of the Pre-Shower is based on to separate photons from decay
photons. If we read out double layers, we should select deep areas of the Pre-Shower. In
this thesis, the design of double layers Pre-Shower is to read out 7 and 10 layers. Figure
31 show the correlation of the number of hits at 7 and 10 layers. The left plot shows the
single photons and the right plot shows the single π 0 . As show from this, the single π 0 are
vetoed by requiring hits = 0 in each layer.
3.3.3

Electron Identification

In this section, the identification (ID) of electrons is described. Leptons are the primary
signature of electro-weak processes. They are used in a lot of physics analysis. Electron
ID, separating electrons from charged hadrons background. Electrons are identified by ratio of momentum to deposited energy, hit cells and shower shape. At the electromagnetic
calorimeter, electrons can deposit large energy, hit many cells with developing electromagnetic shower. On the other hands, charged hadrons can hardly cause electromagnetic
shower, because its mass is very much lager than electron mass (i.e these are minimum
ionization particles).
Figure 32 show diﬀerence of developing shower between electrons and charged pions.
27

Figure 29: Number of hits each layers

28

Figure 30: Sum energy in each layer

Figure 31: Correlations of hits between at 7 layer and at 10 layer29[2] Number of hits as a function of radiation
length[1] Deposited energy as a function ofradiation length

Figure 32: Electromagnetic shower development

It plots energy deposit in each layer as a function of radiation length with the single
particle simulation using the GEANT4. In this simulation, the total radiation lengthis 31X0 , including the Pre-Shower of 1 layer (1X0 ), and the sampling electromagnetic
calorimeter of 50 layers (0.6X0 × 50). The first point shows energy deposit or hit cells in
the Pre-Shower, other points show energy deposit or hit cells in each layer in the sampling
electromagnetic calorimeter. As shown in figure 32, the identification of electrons become
possible with diﬀerence of developing shower. But practically we cannot read out alllayers of sampling calorimeter in cost. So we should read out three places that are the
Pre-Shower, the EMCal and the HCal.

[1] preshower[2] EMCal

Figure 33: Measured energy distribution

Figure 33 shows the distribution of cluster energy at the Pre-Shower and the EMCal.
As shown in Figure 33 on the left plot, many charged pions hardly deposit energy in the
Pre-Shower. On the other hands, electrons deposit large energy. Also some charged pions
deposit large energy because of causing hadronic interactions. At the EMCal, electrons
deposit almost all energy. Thus the distribution of cluster energy deposited by electrons
become a gaussian distribution. The cause of tail at low energy is due to magnetic field30

by BaBar magnet, that is say, the electromagnetic shower is deformed. On the otherhands, the distribution of charged hadrons have two components. The peak at 0.3 GeV is
produced by minimum ionization particles. Another component is produced by hadronicinteractions.

Figure 34: HCal scintillator energy

Figure 34 shows the distribution of the energy deposited at scintillator of HCal. As
shown in the figure, electrons hardly deposit energy in the HCal, because these deposit
almost all energy in the EMCal. On the other hands, Almost all charged pions depositedlarge energy by hadronic interactions. As shown from these results, we can separate
electrons from charged hadrons by the energy cut for each calorimeter.

31

4Results and Discussions

In this thesis, 2 topics of the Pre-Shower detector and particle identification are discussed.

4.1

Design and Performance Study for the Pre-Shower Detector

At the beginning of this section, the design of the Pre-Shower is decided by Monte Calroand GEANT4 simulations. Next the occupancy and energy resolution were evaluated incase of that design. Furthermore the method of separating direct photon from π 0 decay
photons is described, and the fraction of direct photon identification to π 0 decay photons
miss identification is evaluated.
4.1.1

Design Optimization of the Pre-Shower

I and Ueda made the simulator including generator of π 0 and decay process based on theMonte Calro simulation for deciding segmentation of the Pre-Shower. Figure 35 shows
the minimum opening angle of decay 2 photons from π 0 as a function of the transverse
momentum. At least the Pre-Shower segmentation should be less than 0.01 rad for identifying decay 2 photons from 40 GeV/c π 0 . Figure 36 shows the distribution of the opening
angle at pT 40 GeV/c. The opening angle becomes minimum in case of decaying verticallyto direction of π 0 on rest frame of π 0 . The right plot shows the correlation between ϕ andη of opening angle.

Figure 35: Minimum opening angle of decay photons from π 0 as a function of the transverse
momentum.
Figure 37 shows detection eﬃciency of 40 GeV π 0 as a function of shape of cell undercondition of constant area, that is to say, dϕ × dη = 0.01. This simulation assumed theperfect Pre-Shower detector, i.e, it is evaluated by only geometry. In the case of square or
thin rectangular, detection eﬃciency is high.

32[1] Opening angle of decay photons from π 0 .
[2] Correlation of ϕ and η.
Figure 36: Opening angle of π 0 at pT = 40 GeV

Figure 37: Detection eﬃciency for perfect Pre-Shower as a function of dϕ under conditionof constant area of cells.

33

Figure 38 shows the detection eﬃciency of π 0 for each size of cell and pT . The detectionof π 0 is defined as that cells hit by π 0 decay photons are separated by two cells or more.
The red and the blue closed circles show shape of square, and the red and the blue filled
opened circle show shape of oblong. At pT ≤ 35 GeV, the segmentation of 5 × 5 mm is thebest detection eﬃciency. Also the Pre-Shower segmentation should be less than EMCal
segmentation (24 × 24 mm), because the position resolution of the Pre-Shower should belower than the EMCal. In light of these, the segmentation of 5 × 5 mm is good. So its
segmentation was defined as a base design.

Figure 38: Detection eﬃciency as a function of transverse momentum in case of perfect
Pre-Shower

4.1.2

Energy Resolution

The Pre-Shower detector will be installed in front of the electromagnetic calorimeter.
So the eﬀect on the EMCal energy resolution should be evaluated in the case with andwithout the Pre-Shower. Also the energy resolution depends on thickness of convertor.
Figure 39 shows the energy resolution as a function of transverse momentum, evaluatedby simulation of single electrons and the GEANT4 simulation. The blue points show thecase with PS (2.4X0 ) and the green show the case with PS (1.6X0 ) and the read show thecase without PS. The diﬀerence of resolution between with and without the Pre-Shower
is less than 1 %. As a result, there is little eﬀect of the additional detector on the energy
resolution of sPHENIX for electromagnetic particles.
4.1.3

Occupancy

In case of high energy nucleon collisions, occupancy needs to be evaluated firstly. Because
the number of hit cells aﬀect strongly identification of single particle under condition ofhigh multiplicity. The occupancy of the Pre-Shower was calculated using HIJING (event
generator for heavy ion collision) and GEANT4 simulation. There were 894 hit cells out of34

Figure 39: Energy resolution as a function of transverse momentum.

35k in average of 100 events. And the average number of cells in clusters was factor of 1.3.
dNch /dη was 614 in range of η = ± 0.275. As a result, the occupancy of the Pre-Shower
was 2.5 % in HIJING Au + Au at b = 0 fm and it can be accepted.

Figure 40: Event display for HIJING most central Au+Au collisions

4.2

Particle Identification at sPHENIX

In this section, the results of performance of particle identification at sPHENIX are shown.
Firstly, the photon identification fraction is evaluated. It is the fraction of identificationof photon and misidentification of decay photons. The enhancement factor is evaluated35

by using these results. Secondly, the eﬃciency of identification of electrons and charged
pions are evaluated with full GEANT4 simulation. The pion rejection is evaluated byusing these results.
4.2.1

Photon Identification Fraction

Figure 41 show the photon identification fraction which is the probability of identifying
a single photon or mis-identifying a single π 0 as a single photon. The blue points show
fraction using the EMCal, the red filled and open points show the fraction using the PreShower. In case of using the EMCal, a single photon is identified by that a reconstructedmass of π 0 is out of 3 sigma from its mean. As a result, the EMCal can not separate asingle photon from a single π 0 above 5 GeV in pT , because two electromagnetic showerfrom π 0 are merged. On the other hands, the Pre-Shower can separate a single photon
from a single π 0 at wider transverse momentum. At next section, the ratio of identificationof a single photon to misidentification of a single π 0 will be discussed.

[1] No thereshold[2] 10 MeV threshold

Figure 41: Photon ID fraction

Table 2: Cut variables for identifying a single photon
Variables
Required cuts
Number of hit cells with Pre-Shower
Nhit ≤ 1
Ratio of max deposited energy to sum energy 0.8 ≤ Emax /Esum

4.2.2

Enhancement Factor for Direct Photon

Figure 42 show enhancement factor of signal-to-background ratio of direct photon for eachthreshold as a function of transverse momentum. The red points show case of using the
Pre-Shower of 5×5 mm segmentations and 10×10 mm segmentations, and the blue points
show case of using the EMCal. At the good case (i.e. no threshold), the enhancement
factor for the case the Pre-Shower is in the range from 4 to 7 at 5 GeV ≤ pt ≤ 40 GeV.
On the other hand, the enhancement factor for the case the EMCal are around 1.0 at 10
GeV ≤ pt ≤ 40 GeV. As shown from this result, the signal-to-noise ratio of direct photon36

is enhanced by a factor from 4 to 6 by using the Pre-Shower. Also in case of the bad case(i.e. 10 MeV threshold), its factor are from 3 to 4.

[1] 10MeV threshold[2] Zero threshold

Figure 42: Enhancement Factor of a single photon to a single π 0

4.2.3

Multi-layers Pre-Shower

The design of the multi-layers Pre-Shower was studied for improvement of the direct
photon purity. In this simulation, the multi-layers Pre-Shower has ten layers. The layer 7
and layer 10 are read out for evaluating the two layers Pre-Shower. The left plot in Figure
43 shows the enhancement factors as a function of transverse momentum. The red points
show enhancement factor for no hit on both layer 7 and layer 10 at Pre-Shower and theblue points show the enhancement factor for no hit on layer 10 at Pre-Shower. In case ofno hit. the enhancement factors of using both layers are less than that of using layer 10.
Therefore, the enhancement factor do not improve by reading out multi layers in the caserequiring no hit is in each layer.

Figure 43: Enhancement factor for Multi-layer design37

4.2.4

Electron Identification

For electron identification, some variables were measured and calculated from the PreShower, the EMCal and the HCal. In this section, the electron identification is describedusing each calorimeter. First of all, the case of using the Pre-Shower and the EMCal is
discussed. Figure 44 show the correlation of energy measured by the Pre-Shower and the
EMCal. The right figure shows correlation after applying cut. The required cut values forelectron ID are in the following table. As a result, the pion rejection was the factor of 1160
at 70 % electron eﬃciency by applying these cuts. Also in case of using only the EMCal, it
is the factor of 166 at 70 % electron eﬃciency. That is say, the pion rejection is improvedby one order of magnitude by using the Pre-Shower. Secondly, the electron ID with theinner HCal is discussed. The left histogram on the Figure 45 shows the leaked energy
from the EMCal in the inner HCal, and the right histogram show the leaked energy after
electron identification with the Pre-Shower and the EMCal. As shown in figure, the leakedenergy in the inner HCal is good tool for the electron ID. The pion rejection is about 100
at 90 % electron eﬃciency with only inner HCal. Incidentally, the measurement of upsilonmeson requires 100 pion rejection at 90 % electron eﬃciency. So the pion rejection with 3
calorimeters is discussed in the next section.

[2] After applying cut[1] Before applying cut

Figure 44: Energy correlation between Pre-Shower and EMCal

Table 3: Cut variables for identifying a electron
Variables
Required cuts
Energy measured with Pre-Shower
0.002 GeV ≤ E ≥ 0.026 GeV
Energy momentum matching
3.8/5 ≤ E /pT ≥ 5.4/5
Number of hit cells with Pre-Shower
2 ≤ Nhit
Number of hit cells with EMCal
8 ≤ Nhit ≥ 20
Diﬀerence of mean position
0.004 ≤ σϕ ≤ 0.01

4.2.5

Pion Rejection

In this section, the total pion rejection with the sPHENIX calorimeters are discussed.
Figure 46 show the pion rejection in each calorimeter as a function of the electron eﬃciency.
38

[2] Leaked energy distribution after applying
cut with the Pre-Shower and the EMCal[1] Leaked energy distribution

Figure 45: Leaked energy distribution

In this figures, only the cut of measured energy in each calorimeter is used. As shownin this figure, the pion rejection with the HCal was the most highest in calorimeters at
90 % electron eﬃciency. So the total pion rejection should be evaluated, based on the
cut variables of the inner HCal. That is say that the cut variables of the inner HCal ischanged from 100 % to 80 %, and the cut variables of the Pre-Shower and the EMCal areconstant which are 98 % eﬃciency at the Pre-Shower and 99 % eﬃciency at the EMCal.
Figure 47 shows the total pion rejection as a function of the electron eﬃciency with tree
calorimeters. The red points are with three calorimeters, and the blue points with the
EMCal and the inner HCal. As shown from the Figure 47, the total pion rejection was
improved by a factor of two using the Pre-Shower. In case of using three calorimeters,
the total pion rejection is 200 at 90 % electron eﬃciency. It is suﬃcient for the upsilon
measurements.

Figure 46: Pion rejection in each calorimeter as a function of electron eﬃciency

39

Figure 47: Total pion rejection as a function of electron eﬃciency

5

Summary and Conclusions

We have studied the design of the Pre-Shower detector and the particle identification at
sPHENIX. Firstly, we have decided the design of Pre-Shower detector that is the segmentation of 5×5 mm, the converter radiation length of 2.4 X0 . In this conditions, theenhancement factor of direct photons to decay photons from π 0 ratio is 6, that is to say, thesignal-to-noise ratio becames 10 times at pT range from 5.0 GeV to 40 GeV in the Figure
48. Especially, it is over 3 at above pT of 15 GeV. These results show the measurementof direct photons is enabled. Furthermore, we have evaluated the design of multi-layers
Pre-Shower for improving the direct photon to π 0 ratio. However the enhancement factor
did not improv in case of reading out 2 layers Pre-Shower. This is considered that thedirect photon to π 0 ratio depend on converter thickness but not number of read out. So
we should thicken converter of the Pre-Shower, if we want to further improve it.

[1] Enhancement factor of direct photon to [2] Count per event of direct photon and π 0
decay photons ratio[9]
Figure 48: Signal-to-noise ratio for direct photon measurement

Secondly, we have established the method of the electron identification at sPHENIX.
The total pion rejection is 200 at 90 % electron eﬃciency by using 3 calorimeters in the40

left plot on Figure 49. The right plot show the upsilon mass spectrum in case of pion
rejection = 90 and electron eﬃciency = 90 %. In this condition, the signal-to-noise ratioof the upsilon measurement is above the unity. As a result, the measurement of upsilonmeson with three states is measurable.

[1] Total pion rejection as a function of aelectron eﬃciency[2] Upsilon mass spectrum for ten billion
0-10 % central Au+Au events [9]Figure 49: Pion rejection for the measurement of upsilon meson

In this thesis, the enhancement factor of direct photons to decay photons, and thetotal pion rejection are evaluated by using a single particle simulation, but practicallythese shouldd be evaluated under condition of high multiplicity in heavy ion collisions.
Therefore it is challenges for the future.

41

6

Acknowledgements

I would like to thank my supervisor Prof. K.Shigaki. He gave me the thesis topics andvaluable advises. I could not have done this work without his support. I would liketo greatly appreciate Assistant Prof. K.Homma for his guidance and encouragement in
PHENIX BBC subsystem group. Not only so, but he showed a good example as scientist.
I would like to express my gratitude to Dr. Y.Akiba for his valuable advises. Not only
so, but he gave me the next topic and interest of heavy ion collisions experiment. I am
grateful to Prof. T.Sugitate and Assistant Prof. T.Miyoshi for their useful comments.
I would like to express my appreciation to whom I worked together in the Hiroshimagroup. Dr. Y. Nakamiya, Mr. S. Yano, Mr. T. Hoshino, Mr. T. Hasebe and Mr. T.
Okubo taught me detail of analysis methods and PHENIX BBC work. I had an enjoyable
thesis work with Mr. D. Sekihata, Ms. R. Tanizaki, Mr. Y. Nakazato and Mr. T. Yuasa
and other Hiroshima group members. Especially, I had an enjoyable thanks to R.Tanizaki,
both in my public and my private life.
I would like to express my thank to the PHENIX collaboration and the PHENIX-J group.
They supported my life at BNL and advised in my thesis work.

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7

Appendix

7.1

Charged Particle

A charged particle loses kinetic energy, and is deflected the direction when it passes throughthe material. It mainly interact atoms or electrons in the material. Its process is expressedwith Beth-Bloch.

−

dE
dx

= nZz 24πα2 (hc)22me c2 β 2 γ 2
(ln
− β2)
me c2 β 2I(9)where n is density of atom in the material, Ze is charge of atoms, me is mass of electrons,
ze is charge of the particle, I is parameter of average exiting potential (I ≃ 16Z 0.9 eV). As
known from this Eq, the energy loss independent mass of the particle, but depend on the
speed (β −2 ) and the charge (z 2 ). In addition, if particle have same charge, the energy loss
is same value in case of increasing the speed (β ≥ 0.96), it is called minimum ionization
particles.

Figure 50: Stopping power for positive muons in cupper [1]Also low mass particles as electrons and positrons cause bremsstrahlung radiation
easily. Bremsstrahlung is electromagnetic radiation produced by deceleration of a charged
particle when deflected by another charged particle. A photon is converted when themoving charged particle loses kinetic energy by it, i.e, a photon have the loss energy. It is
expressed as Eq.
σbrem ∝

Z 2 α3m2 c 4The σbrem is a cross section of bremsstrahlung.
dE
dx of bremsstrahlung can be written as
43

(10)

Figure 51: Most probable energy loss in silicon, scaled to the mean loss of a minimum
ionizing particle, 388 eV/µm. [1]

−

4r2
183
dE
= − 0 Z 2 E0 N log 1/3
dx r
137
Z

44

(11)

References[1] Particle Data Group, Phys.Rev .D86 ,010001 (2012) (//peg.lbl.gov)[2] K. Yagi etal ., Part.Phys.Nucl .Phys.Cosmol . 23, 1 (2005) [Quark-Gluon
Plasma].
[3] www.bnl.gov/rhic[4] P. F. Kolb, HeavyIonPhys. 21, 234 (2004).
[5] https://www.phenix.bnl.gov/WWW/info/figs/055/[6] https://www.star.bnl.gov/central/focus/highPt/[7] David d Enterria etal ., High-pT Hadron Suppression and Jet Quenching, ThephysicsoftheQuark − Gluon − PlasmaLectureNotesinPhysics 785,
pp 285-339.
[8] S. Chatrchyan etal ., Phys.Rev .Lett 109, 222301 (2012) [CMS Collaboration].
[9] http://www.phenix.bnl.gov/plans.html

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