Pseudo-rapidity Distribution of Charged
Particles in Relativistic Heavy Ion Collision
Kohta Haruna

Department of Physics Science
Graduate School of Science, Hiroshima University
February, 2006

Abstract
According to Quantum ChromoDynamics (QCD) theory, as the underlying
theory of strongly interacting system, quarks and gluons are deconﬁned andcan traverse freely out of the ordinary size of a nucleon under high temperature and/or dense condition. It is a hope that the relativistic heavy ion
collisions may create the high temperature condition. If the deconﬁnement
is interpreted as a state where the carriers of particle production are partonsand these partons interact each other having a longer mean free path thansize of a nucleon, it could be one of evidences of QCD deconﬁnement in aextreme condition.
A collision experiment of two gold nuclei at Relativistic Heavy Ion Collider(RHIC) at C.M.S. collision energy per nucleon pairs of 200GeV has been carried out at Brookhaven Notional Laboratory (BNL). The particles yieldedby collisions are measured by particle tracking detectors and charged particle
detectors using Cerenkov radiation. The multiplicity of primary charged particles is obtained as a function of pseudo-rapidity. The correction for detector
eﬃciency and geometrical acceptance and the estimation of background contributed by secondary particles which are radiated except in the collisionvertex is calculated by the simulation. Pseudo-rapidity is deﬁned as a function of polar angles between primary charged particles and beam axis andis deﬁned as η = −ln(tan(θ/2)). With an assumption that pseudo-rapidity
distribution is described by double Gaussian function, ﬁts are performed topseudo-rapidity distribution to interpolate and extrapolate the data points
and to integrate in the whole pseudo-rapidity region. The total multiplicity of primary charged particles normalized to the number of nucleon pairs
participating to a collision, compares with the results of e+ e− and pp/pp collisions as a function of collision centrality and collision energy.
From the results of comparisons, it was found that total multiplicity in central Au+Au collisions scales with e+ e− collisions rather than pp/pp collisions.
√
In addition to that, above sN N = 20GeV , it was found that there were noleading parton eﬀect in nucleus-nucleus collisions. In such collision energies,
particle production in e+ e− interaction is well described by a partonic picture. The scaling to e+ e− of multiplicity means that the degree of freedom ofpartons appears in the particle production in nucleus-nucleus collisions. Absence of leading eﬀect indicates the multiple interactions in nucleus-nucleus
collisions, therefore particle interactions in high energy nucleus collisions are
similar to the picture of deconﬁnement.

Contents
1 Introduction
1.1 Quark Gluon Plasma . . . . . . . . . . . . . . . . . . . . . . .
1.2 Particle Production . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Motivation of This Study . . . . . . . . . . . . . . . . . . . . .

5
5
6
9

2 Experimental Setup
2.1 Relativistic Heavy Ion Collider . . . . . . . . . . . . . . . . . .
2.2 PHENIX Detector . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Magnet . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Beam Beam Counter . . . . . . . . . . . . . . . . . . .
2.2.3 Zero Degree Calorimeters . . . . . . . . . . . . . . . .
2.2.4 Drift Chamber . . . . . . . . . . . . . . . . . . . . . .
2.2.5 Pad Chamber . . . . . . . . . . . . . . . . . . . . . . .
2.2.6 Ring Imaging Cerenkov Hodoscope . . . . . . . . . . .
2.2.7 Time Expansion Chamber . . . . . . . . . . . . . . . .
2.2.8 Time of Flight . . . . . . . . . . . . . . . . . . . . . . .
2.2.9 Electro Magnetic Calorimeters . . . . . . . . . . . . . .
2.2.10 Muon Spectrometers . . . . . . . . . . . . . . . . . . .
2.3 Trigger and Data Acquisition system . . . . . . . . . . . . . .

11
11
13
15
15
17
19
19
20
20
20
21
21
22

3 Data Analysis
3.1 Run Summary and Trigger Selection . . . . . . . . . . . . . .
3.2 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 FEM Calibration . . . . . . . . . . . . . . . . . . . . .
3.2.2 Gain Calibration . . . . . . . . . . . . . . . . . . . . .
3.2.3 Time Calibration . . . . . . . . . . . . . . . . . . . . .
3.3 Centrality Measurement . . . . . . . . . . . . . . . . . . . . .
3.4 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25
25
25
27
28
31
33
35

3

4

CONTENTS
3.4.1 Glauber Monte Carlo Simulation . . . . . . . . . . . .
3.4.2 Event Generator . . . . . . . . . . . . . . . . . . . . .
3.4.3 GEANT Simulation . . . . . . . . . . . . . . . . . . . .
3.5 Measurement of Charged Particle Multiplicity . . . . . . . . .
3.5.1 Pseudo-Rapidity Distribution . . . . . . . . . . . . . .
3.5.2 Total Multiplicity . . . . . . . . . . . . . . . . . . . . .

35
36
38
38
38
39

4 Results and Discussions
45
4.1 Collision Centrality Scaling . . . . . . . . . . . . . . . . . . . 45
4.2 Collision Energy Scaling . . . . . . . . . . . . . . . . . . . . . 45
5 Conclusion

49

Chapter 1
Introduction
1.1

Quark Gluon Plasma

A recurring theme in the history of physics is the desire to study nuclear matter under extreme conditions. There is considerable interest in the fate ofnuclear matter when subjected to density and temperature extremes [1, 2, 3].
According to Quantum ChromoDynamics (QCD) theory as the underlying
theory of storing interaction, quarks and anti-quarks, which are elementary
particles in the QCD frame, interact with one another exchanging gluons,namely strong force. In the normal condition, color-charged quarks are always conﬁned in neutral color (color-singlet) states, comprising baryons (3quark bound state) or mesons (2-quark bound state) by exchanging theircolor charges through gluons. Collins and Perry noted in 1975 [4] that the
reduction of the coupling constant at small distances indicated that the dense
nuclear matter at the center of neutron stars would consist of deconﬁned
quarks and gluons. Their treatment focused on the high density, low temperature regime of QCD, but they did note that similar arguments might
apply to the high temperatures present in the early universe. Just before thehadrons were formed, in a few µs after the big bang, the universe consistedof the melted soup of quarks and gluons. Under these extremely high density and/or temperature condition, the color force between quarks for long
distance is screened by dense gluons, allowing quarks to propagate for a long
distance. In such a medium, when the energy density ϵ exceeds some typical
hadronic value (∼ 1GeV /f m3 ), matter no longer consists of separate hadrons(protons, neutrons, etc.), but as their fundamental constituents, quarks and
5

6

CHAPTER 1. INTRODUCTION

gluons. Because of the apparent analogy with similar phenomena in atomic
physics, this phase of matter may be called the QCD (or quark gluon) plasma(QGP). At recent lattice QCD calculation [5] results in that the transition
temperature at zero baryon density is 170MeV.
High energy nuclear collisions would provide the unique opportunity to study
the nature of nuclear matter at such a high energy density, which could be the
QGP state, in the laboratory. Figure 1.1 shows a phase diagram of nuclear
matter as a function of baryon density and temperature, and how the QGP
state can be explored in high energy nuclear collisions. To study natureof the state of high baryon and/or energy density, enormous experimental
eﬀorts have been carried out in the ﬁxed target programs using Bevatron
at Lawrence Berkeley National Laboratory (LBNL), the Alternating Gradient Synchrotron (AGS) at Brookhaven National Laboratory (BNL), and theSuper Proton Synchrotron (SPS) at European Organization for Nuclear Research (CERN). Following the ﬁxed target experiments till 1999, the studyof high energy nuclear collisions has opened a new stage with the Relativistic Heavy Ion Collider (RHIC) at BNL, where the initial energy density incentral collision is expected to be suﬃcient for QGP formation.

1.2

Particle Production

In the relativistic heavy ion collisions, nuclei are contracted in the beam direction like pancakes due to the Lorentz boost. Figure 1.2 shows a schematic
drawing of a heavy ion collision. The number of nuclei participating in thecollision, called ”participants”, and the rest that do not participate in thecollision, called ”spectators”, could be geometrically determined by cut withthe straight line at the impact parameter b, namely the length of the overlap
region of colliding two nuclei.
The high multiplicities in heavy ion collision typically arise from the large
number of nucleon-nucleon collisions which occur, since many of the nucleons strike several times as they pass through the oncoming nucleus. Thus,
mechanism of particle production in heavy ion collision is complicated due
to its large number of nucleon-nucleon collisions and nuclear eﬀects which isoccurred in high energy acceleration.
On the other hand, both e+ e− collision and pp/pp collisions must ultimately
allow a description based on QCD, the theory of the strong interaction. The
large momentum transfer to the outgoing produced quark and anti-quark

1.2. PARTICLE PRODUCTION~200MeV

Early Universe
LHC
RHIC
SPS

T

er
ut
ar
ep
m
eT

7

HadronGas

Quark-Gluon
PlasmaAGS
SIS

Nuclear matter
Baryon density ρ

Neutron star
~5-20 nuclear

Figure 1.1: A phase diagram of nuclear matter as a function of baryon density
ρ and temperature T. Hadronic phase is shown at low density and temperature, and the QGP phase is shown at high density and/or temperature,
separated by mixed phase shown by the black band [13].

8

CHAPTER 1. INTRODUCTION

in e+ e− reactions allows the use of perturbative QCD to describe the spectrum of quarks and gluons radiated as the system fragments [6] . pp/pp
collisions are not generally thought to be amenable to such a perturbativedescription, since the transverse momentum exchanges involved are typicallyless than 1GeV/c. Instead, phenomenological approaches (e.g. PYTHIA [7])are used to describe the spectrum of particles. The crucial diﬀerence between e+ e− collision and pp/pp collisions is existence of leading partons in
pp collisions. Due to it, available center of mass energy for particle production is reduced in pp/pp collisions. However available multiplicity of primarycharged particles (⟨Nch ⟩) in pp collision is similar to that for e+ e− collision√√√
with se+ e− = sef f , where sef f is the pp center of mass energy minus
the energy taken away by the leading parton. This is interpreted as a universal mechanism of particle production controlled dominantly by the available
center of mass energy [8, 9] .

Before collision

After collisionbSpectators

Participants

y=0
rapidity
Figure 1.2: A schematic drawing of a heavy ion collision. Nuclei are geometrically separated into participants and spectators for the impact parameterb [13].

1.3. MOTIVATION OF THIS STUDY

1.3

9

Motivation of This Study

Studies of hadron nucleus interaction demonstrated that the average multiplicity of primary charged particles (⟨Nch ⟩) did not scale proportionally tothe number of binary collisions (Ncoll ) in the reaction, but rather was foundto scale with the number of wounded nuclei participating inelastically in thecollision (Npart ) [10, 11] . Thus, by scaling the particle yields measured inheavy ion collisions by Npart /2, the data from heavy ion collisions may bedirectly compared with similar yields in elementary pp, pp, or even the annihilation of e+ e− into hadrons. Comparisons with e+ e− collision and pp/pp
collisions are made to investigate whether conﬁnement of quarks and gluons
is broken in high energy heavy ion collisions or not. The naive view is that
Nch in heavy ion collision scales to the pp/pp collisions if there are not something special. However, if it scales to e+ e− collision, then, it may be quite
remarkable issue. In this paper, I report the results of the measurement ofmultiplicity of primary charged particles per pseudo-rapidity (dNch /dη) and
Nch as a function of collision centrality for high energy Au+Au collisions at√√
sN N = 200GeV , where sN N is the center of mass collision energy per
nucleon pair.
In Chapter 2, the accelerator facilities and experimental setup of detectors
are introduced. In particular, subsystem, which is utilized to detect charged
particles in forward rapidity region, is explained in detail.
In Chapter 3, the method for calibration for subsystem, simulation tools,
and measurement of dNch /dη especially in forward rapidity region, are introduced. For central rapidity region (|η| < 0.35), dNch /dη has been alreadymeasured by using the central detectors in PHENIX [12]. Thus, in this paper, I focus to the measurement for forward rapidity region.
In Chapter 4, the results of my analysis are reported. Then the Nch which is
obtained in Au+Au collisions is discussed by comparison with e+ e− collisionand pp/pp collisions, where Nch is scaled by Npart /2.
Finally, I give the conclusion of this analysis in Chapter 5.

Chapter 2
Experimental Setup
2.1

Relativistic Heavy Ion Collider

The Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory (BNL) has a capability to accelerate and collide several types ofparticle species, e.g. gold-gold (Au+Au), deuteron-gold (d+Au) and polarized proton-proton (p+p) collisions. A schematic diagram of the RHIC
facility is shown in Figure 2.1. In Au+Au collisions, bunches of Au ions areprovided from the Tandem-Van-de-Graaﬀ and accelerated up to 1A MeV,
then injected into the Booster Synchrotron to accelerate up to 192A MeV,
and then injected in the Alternating Gradient Synchrotron (AGS) ring. The
AGS accelerator, which has been used for many ﬁxed target experiments inheavy ion collisions at the center of mass energies from 2.5 to 4.5GeV, isused as a pre-accelerator for the RHIC ring. The bunches of Au ions, accelerated up to 10.8GeV by the AGS ring, are send to the AGS-To-RHIC
transfer line, where a switching magnet sends the ion bunches down one oftwo beam lines. The two Au beams are injected into the right and left ringsof RHIC, labeled yellow and blue ring, respectively. The injected two Au
beams are accelerated up to 100GeV per nucleon in the RHIC ring, and collide at six beam interaction points. RHIC has the total length of 3.8km ringand number of bunches per ring is 60 and each bunch consists of ∼ 1 × 109√
Au ions. In Au+Au collisions at sN N = 200GeV , designed luminosity is
2 × 1026 cm−2 s−1 . Four experiments are located at four of the six interaction
points, i.e. PHENIX, STAR, PHOBOS and BRAHMS as shown by Figure
2.1.
11

12

CHAPTER 2. EXPERIMENTAL SETUP

Figure 2.1: A schematic diagram of the AGS and RHIC facilities [13].

2.2. PHENIX DETECTOR

2.2

13

PHENIX Detector

The Pioneering High Energy Nuclear Interaction eXperiment (PHENIX) isan exploratory experiment for the investigation of high energy collisions ofheavy ions. The purpose of the PHENIX is to provide powerful particle identiﬁcation capabilities for hadrons, leptons, and photons over a wide momentum range. The PHENIX consists of a collection of detectors, each which perform a speciﬁc role in the measurement of the results of a heavy ion collision.
The detectors are grouped into two central arms, which have pseudo-rapidity
coverage of |η| < 0.35 and 90 degree azimuthal angle for each arm and arecapable of measuring a variety of particles, and two muon arms which havepseudo-rapidity coverage of 1.2 < |η| < 2.4 and focus on the measurementof muon particles. There are also additional event characterization detectorsthat are specialized to make triggers and to measure the luminosity and thecentrality in heavy ion collisions, and a set of three huge magnets that bend
the trajectories of the charged particles. Figure 2.2 shows the bird view of
PHENIX detector. And detector setup for second year is shown in Figure
2.3 .

Figure 2.2: Overview of PHENIX detectors [14].

14

CHAPTER 2. EXPERIMENTAL SETUP

PHENIX Detector - Second Year Physics Run
PC3
PC2

PbSc

PC3
TEC

CentralMagnetInstalled
Active

PbSc

PbSc

PbSc
DC

DC
RICH

RICH
BB

PbSc

PbGl
MVD

PC1

PbSc

PC1

PbGl

TOF

Beam View

West
So

uth

M

East

Central Magnet

uo

nM

ag
n

nM

r
No

et

M
th

n
ag

et

uo

BB
ZDC SouthZDC North

MuID

MuID
MVD
MuTr

South

Side View

North

Figure 2.3: Schematic drawings of the PHENIX detector setup for second
year running, viewed in a cut through the collision vertex (top ﬁgure), parallelto the beam axis (bottom ﬁgure) [15].

2.2. PHENIX DETECTOR

2.2.1

15

Magnet

The central magnet (CM) consists of inner coil, outer coil and return yoke.
They provide cylindrical magnetic ﬁeld optimized to the diﬀerent physics
programs for central arms because of the two independent coils. The Muon
Magnet (MM) uses two solenoidal coils to produce a radial magnetic ﬁeld.
The coils are wound around a tapered piston and the ﬂux propagates out tothe lampshade. Figure 2.4 illustrates a vertical cutaway view of the PHENIX
magnets with the magnetic ﬁeld lines. Due to the magnetic ﬁeld, the charged
particles with the momentum of less than 0.2GeV/c are trapped in the ﬁeld.
During the run for this work, both coils are not activated because multiplicity
of charged particles is measured in this paper and I do not need to know the
momentum information in this case.

2.2.2

Beam Beam Counter

The Beam Beam Counters (BBC) are placed at 144.35cm along to beam
pipe from the nominal collision vertex point and covers the pseudo-rapidityof 3 < |η| < 4 and 2π in azimuthal angle surround the beam pipe (see Figure2.2). Each of BBC consists of 64 Cerenkov counters, each of which consists ofa quartz Cerenkov radiator and a mesh-dynode photo multiplier tube (PMT)
readout. Since the magnetic ﬁeld around BBC is expected to be about 3kG,these PMTs are designed to work in such a high magnetic ﬁeld environment.
Quartz has the 3cm thickness and refractive index of 1.47. Therefore, theBBC detects charged particles, of which beta is more than 0.68. Figure 2.5
shows the one side of BBC and the one of elememts of BBC is shown in
Figure 2.6. The BBC is designed to measure the number of charged particles
produced by the collisions and to measure the collision vertex, collision timeand collision centrality. Collision timing is evaluated from the average of thearrival times as:(T1 + T2 −tT 0 =

2

2L
)
c

(2.1)

where T1 and T2 are the observed values of arrival time at each side and L
is the length from the collision point to the surface of BBC. The c is velocity
of light. Collision vertex is evaluated from the diﬀerence of the arrival times

16

CHAPTER 2. EXPERIMENTAL SETUPPH ENIX

-4.0

-2.0

0.0

2.0

4.0

Z (m)

Magnetic field lines for the two Central Magnet coils in combined (++) mode

Figure 2.4: A simulation of the magnetic ﬁeld lines inside the three PHENIX
magnets. The arrows on the inner ﬁeld lines represent the ﬁeld direction [15].

2.2. PHENIX DETECTOR

17

as:
Zvertex =(T1 − T2 ) × c
2

(2.2)

The collision timing is served as a start time for the time of ﬂight measurement. The time resolution of each BBC is evaluated to be around 524ps.
The vertex position accuracy is estimated to be better than 1 cm.

Figure 2.5: A picture of BBC array comprising 64 BBC elements [16].

2.2.3

Zero Degree Calorimeters

The Zero Degree Calorimeters (ZDC) is placed at 18.25m along to beam
pipe from the nominal collision vertex point (see Figure 2.2). Each of themconsists of alternating tiles of plates of tungsten and layers of optical ﬁbers.
The direction of the plates and layers are tilted by 45 degree relative to theincident neutron direction to collect the Cerenkov light as shown in Figure
2.7. The ZDC are designed to measure spectator neutron which do notparticipate in the collision and to determine the collision vertex and collisioncentrality. Thus both north and south ZDC sit at just upstream of the last
bending magnet on the RHIC ring which is shown by Figure 2.8.

18

CHAPTER 2. EXPERIMENTAL SETUP

Figure 2.6: A picture of elements of BBC, which is consists of quartz andPMT [16].

Figure 2.7: A picture of ZDC of one side [17].

2.2. PHENIX DETECTOR

19

Figure 2.8: A schematic drawings of ZDC. Bottom ﬁgure shows a top view ofthe beam geometry and ZDC location. Top ﬁgure shows a beam’s eye viewof the ZDC location [17].

2.2.4Drift Chamber

The Drift Chamber (DC) is placed between 2.02m and 2.46m in the radial
distance from the nominal interaction point and consists of 3 diﬀerent direction of the wire: same directions as the beam pipe which is namely X
module, and ±6 degree tiled angled relative to the beam pipe direction. The
detector consists of 2 modules for each direction which are namely U andV module, respectively. Diﬀerence in the design of X and U, V module isconditioned by the fact that X module should provide wire to run along z
axis. On the contrary, U, V module should provide some slope of wires withrespect to z axis. A module consists of 4 or 12 anode wires depending on
the wire direction. In total, 40 drift cells are located in diﬀerent radii. Eachsector is ﬁlled with 50-50% Argon-Ethane gas mixture. The designed position
resolution in a single wire is 0.15mm and the two track resolution is 1.5mm.

2.2.5

Pad Chamber

The Pad Chamber (PC) consists of 3 layers; PC1 at 2.5m, PC2 at 4.1m andPC3 at 5.0m apart from the beam pipe and each layer consists of 8 sectors.
The PC is designed as a multi wire proportional chamber with readout of the20

CHAPTER 2. EXPERIMENTAL SETUP

cathode pads. Each pad has either 8.2 × 1.5mm2 or 8.2 × 2.7mm2 dimension.
A single pixel is small copper rectangle which is connected to 8 other small
copper rectangles. All 9 pixels are read out by a single discriminator. The
object which is composed of 9 connected pixels is called a ”pad”. Whenever a charged track passes through the pad chamber, there should be threeneighboring pads which all receive an induced signal large enough to trigger
their three separate discriminators. The 9 fold ambiguity of which pixel is
hit is resolved by looking at which set of three pads has hits. The structureof three neighboring pixels which gets uniquely identiﬁed as the location of
the track is called a ”cell”. The designed position resolution for the cell is±4mm. The purpose of the detector is to measure the charged multiplicity
and to reduce the background in the sample of charged particles.

2.2.6

Ring Imaging Cerenkov Hodoscope

The Ring Imaging Cerenkov Hodoscope (RICH) is designed to identify theelectron, positron and high pT charged particle. Each of the detectors in theeast and west arms has a volume of roughly 40m3 and minimum thicknessof 87cm of the gas at atmosphere pressure, which is CO2 gas is used. The
Cerenkov photons produced in the gas are reﬂected on the mirror and are
detected by the PMT. The average radius of Cerenkov ring is 8cm and theaverage number of the Cerenkov photons produced by electron is 11 on theplane where the PMT are sitting.

2.2.7

Time Expansion Chamber

The Time Expansion Chamber (TEC) is sitting only in the east arm at the
distance between 4.2 and 4.9m apart from the beam pipe. It consists of 6
cells with 3cm drift length in diﬀerent radii. The drift time, position andthe pulse height are measured by the anode wires. This detector is designed
to improve the momentum resolution at the higher pT than 4GeV/c and to
identify electron and positron using the energy loss information.

2.2.8

Time of Flight

The Time Of Flight detector (TOF) consists of 960 scintillator slats whichhas 1.5cm width and 1.5cm length. It covers 45 degree in the azimuthal

2.2. PHENIX DETECTOR

21

angle. The designed time resolution is 100 ps. the TOF has capability toidentify the charged pion and kaon at pT up to 2.5GeV/c.

2.2.9

Electro Magnetic Calorimeters

The Electro Magnetic Calorimeters (EMCal) is the primary tool for measuring photons. There are two kind of calorimeter in the PHENIX. One is a
shashlik type lead scintillator sampling calorimeter (PbSc) and another is alead grass calorimeter (PbGl). The PbSc sectors fully cover the acceptance of
the west arm, half cover the which of the east arm and each of them consistsof 18 (3 × 6) super modules. Each of super module consists of 36 (6 × 6)
modules. Each of module consists of 4 (2 × 2) towers. Then, each of towers
consists of sampling cells made of alternating 65 lead tiles and 66 scintillators
tiles whose thickness are 4.0mm and 1.5mm, respectively. Therefore, Eachsector consists of 2592 (36 × 72) individual towers. The surface area of each
tower is 5.52 × 5.52cm2 and the active depth is 37.5cm with 18 radiation
lengths. The sampling cells are optically connected by 32 longitudinally penetrating wavelength shifting ﬁbers and collected light signals are read out by
a PMT at the back of the tower. The PbGl is a Cerenkov type calorimeter. A lead grass has 4.0 × 4.0 cross section and 40cm length. The entire
array comprises 9216 tower previously, which are individually wrapped withaluminized mylar foil and shrink tube and are isolated optically.

2.2.10

Muon Spectrometers

The muon spectrometers are located at the pseudo-rapidity ranges of −2.25 <η < −1.15 (the south muon arm) and 1.15 < η < 2.44 (the north muon arm)with the full azimuthal coverage. Each muon arm is composed of the Muon
Tracker (MuTr) with the Muon Magnet ant the Muon Identiﬁer (MuID). It
is designed to measure vector mesons. Each MuTr provides trajectories ofcharged particles and is composed of three stations of cathode-strip readout
tracking chambers. The MuID is comprised of six walls of steel absorbers
interleaved with ﬁve layers of plastic proportional Iarocci tubes.

22

2.3

CHAPTER 2. EXPERIMENTAL SETUP

Trigger and Data Acquisition system

The PHENIX detector consists of several subsystems and each has hundreds
to thousands readout channels. The interaction rate at designed luminosity
is a few kHz for Au+Au central collisions. To handle a high rate and a large
amount of data, the PHENIX Data Acquisition (DAQ) system is designed byusing the pipeline processing technique which is performed by simultaneous
triggering and readout as shown in Figure 2.9. This is accomplished throughthe features of detector front ends and the ability to accommodate higher
level triggers. In order to preserve the high interaction rate capability, aﬂexible triggering system that permits tagging of events is constructed. The
PHENIX DAQ system has two types of triggering levels, denoted as level
1 (LVL1) and level 2 (LVL2). The LVL1 trigger system is composed of
the Local Level 1 (LL1) systems which communicate with some participant
detectors, and the Global Level 1 (GL1) system which provides a trigger
decision according to the LL1 algorithm.

2.3. TRIGGER AND DATA ACQUISITION SYSTEM

GL1
Busy

GTM

RHIC clocks

End
User

DCM

Data Packets
over Parallel
FIFO Interface

SEB
SEB
SEB
SEB

Linux Farm
~600 CPU's

en

So
ut
C
ZD

Data packets
over fiber~350000 ch
Shield Wall

Missing:• ARCNET Serial Interface to FEMs
• High and Low Voltage Control andassociated control systems• Alarm system

MTM

D
ov atapa er Pa
ss NE ck
in V etg
Bu IS ss To
kPartitioner
DCB

FEM

Clock

RHIC
Computing
Facility

Busy

Clock, Trigger,
Mode bits
over fiberhA(e S u.g bs.E y
as ste
tD m
C
)

ZD

C

N

L1

or
th

TriggerCountingrooma few miles later'trigger' is a placeholder
for a much more complex'Local Level 1' trigger system

Interaction region

23

GL1 Global Level 1 Trigger
GTM Granual Timing Module
MTM Master Timing Module
DCB Data Collection Board
DCM Data Collection Module
FEM Front End Module
SEB Sub Event Buffer
ATP Assembly Trigger Processor

OnlineMonitoring

ATM Switch
ATP

tape
storage
1.2PB

20MB/s
250TB/yr

Figure 2.9: Illustrates the block diagram of the DAQ system in detail. Signals
from the various PHENIX subsystems are processed by Front End Module(FEM) that convert the analog signals into digital signals. If the LVL1 trigger
accepts a collision event, the LVL1 trigger sends a signal to the GranuleTiming Module (GTM) in conjunction with the RHIC clock provided by
the Master Timing Module (MTM). The GTM requires the FEM to send
its digitized data to the Data Correction Module (DCM). Many parallel
data stream from the DCM are sent to the Event Builder (EvB). The EvB
performs the ﬁnal stage of event assembly, which is named as PHENIX Raw
Data File (PRDF), and provides an environment for the LVL2 trigger [15].

Chapter 3
Data Analysis
3.1

Run Summary and Trigger Selection

In the Year 2 Au+Au running at RHIC (2001∼2002), the PHENIX took theminimum bias events which have been taken by the LVL1 trigger determinedby the two LL1 trigger requirements for BBC and ZDC as:• At least two PMT are ﬁred in each BBC (north side and south side,
respectively). And the collision vertex measured by BBC is within
75cm.
• At least one forward neutron has to be registered in each ZDC.
The minimum bias events include collision events from central to peripheral
in 92% of the interaction cross section and. The LVL2 trigger is used to takeonly interesting
physics events. The PHENIX accumulated the integrated∫
luminosity Ldt ∼ 24mb−1 . Figure 3.1 shows a summary plot of luminosity
measured by 4 experiments at RHIC.

3.2

Calibration

In this section, the calibration method for PMT which is component of BBC,and Front End Modules (FEM) read out modules. PMT calibration is basedon event data in Au+Au collisions, on the other hand, FEM calibration isbased on special data taken by using internal test pulse or external injected
pulse.
25

26

CHAPTER 3. DATA ANALYSIS

Figure 3.1: Luminosities estimated by PHENIX (blue), STAR (red), PHOBOS (green) and BRAHMS (black) for Year2 Au+Au running [15].

3.2. CALIBRATION

3.2.1

27

FEM Calibration

Pedestal measurement: Usually pedestal values can be measured as Analog to Digital Converter (ADC) channels when zero charge is injected. But
this general method cannot be used, because our ADC is self gated ADC,
that is, the ADC gate does not open until the injected charge exceed a certain threshold. Thus pedestal values can be measured based on scanned databy changing Digital to Analog Converter (DAC) values. After slope between
DAC values and ADC values is obtained, the pedestal values are determinedby extrapolating the slope at the zero DAC values as shown in Figure 3.2.

Figure 3.2: Measured ADC channels as a function of DAC value. Pedestal
was obtained by extrapolating the ﬁt line at the zero DAC value.
ADC conversion factor measurement: Conversion factors from ADC
values to charge values of PMT output are estimated by external charge injections. The external charge is created by function generator and that values
are determined by charge integrated by using digital oscilloscope. After slope
between injected charge value and ADC value is obtained, conversion factors
are determined by slope parameters of linear function ﬁt as shown in Figure
3.3.
TDC conversion factor measurement: Conversion factor from TDC
values to time values can be measured based on scanned data by changing
delay setting for the test pulse injection. In the case of PHENIX DAQ system,
the timing of stop pulse injection is ﬁxed relative to GTM. The delay values
indicate the time between GTM timing and start timing pulse injection.

28

CHAPTER 3. DATA ANALYSIS

Figure 3.3: Measured ADC channels as a function of injected charge. Conversion factors were determined by inverse slope parameter ﬁt with linear
function.

When the delay values increase, TDC values decrease. After slope between
TDC values and delay values is obtained, conversion factors are determinedby slope parameter of linear function ﬁt as shown in Figure 3.4.
TDC overﬂow measurement: The overﬂow values in TDC channel are
important parameters, since they deﬁne whether hit are valid or not. Whenstop timing is not injected until TDC gate is closed, the overﬂow values are
output. Typical overﬂow distribution is Gaussian so that the distribution isﬁt by its function. The overﬂow values are determined by mean and sigma
of function as shown in Figure 3.5.

3.2.2

Gain Calibration

Determination of operational high voltage: Expected PMT gains are
estimated based on values of ADC channel which are obtained when one
charged particle is injected to BBC, denoted by ”MIP”, together with gain
curve of each PMT obtained by laser pulse injection. The gain curve will be
ﬁt with an empirical function;f (HV ) = exp(p0 + p1 × HV + p2 × HV 2 )(3.1)

where p0, p1, and p2 are parameters. In order to get absolute scale which
provides us optimal operational high voltage values, the gain curve is scaled3.2. CALIBRATION

29

Figure 3.4: Measured TDC channels as a function of delay setting of test
pulses. Conversion factors were determined by inverse slope parameter ﬁtwith linear function.

Tdc0 overflow of PMT0

Entries1183937194 ± 45.6

8000

Constant
Mean

3009 ± 0.0

7000

Sigma

2.196 ± 0.009

6000
5000
4000
3000
2000
1000
0

3000

3005

3010

3015

3020

TDC [ch]Figure 3.5: TDC overﬂow distribution as a function of TDC channel. Fitted
Gaussian is shown by red line on the distribution and parameters of resultof ﬁt are shown in the right box on the ﬁgure.

30

CHAPTER 3. DATA ANALYSIS

with MIP values. Based on the curve, the operational voltage values which
would produce 40pC for one MIP are determined. Once operational values
are obtained for each PMT, we take an average high voltage values over typically eight PMTs in a HV group. Figure 3.6 shows the result of determinationof HV.

Figure 3.6: The gain curve of a PMT by laser (black line). Data points oflaser peak with diﬀerent HV values are shown as blue points on the black line.
Red line shows the scaled gain curve to the MIP peak at the pre-conditionof HV setting, which is indicated as red point on the red line. Blue pointon the red line is the target HV values for each PMT, which is set by 40pC
for output charge of PMT. The operational voltage of each PMT is shown as
green star, which is calculated by the average values of belonging HV group[18].

PMT gain measurement: PMT gains are estimated based on one
MIP values. In order to select one MIP event, certain condition is attached,which is a constraint of no hit in surround the certain PMT. MIP peak will

3.2. CALIBRATION

31

be clariﬁed so that ADC distribution is ﬁt by empirical function as shown in
Figure 3.7;
p2
2 × exp(p0 + p1 × ADC + ADC)
f (ADC) =1 + exp(exp(− ADC−p3))3(ADC − p5)2
+p4 × exp(−)
2 × p62(3.2)

where from p0 to p6 are parameters. ADC distribution can be separated to
MIP distribution and background distribution. Background distribution isestimated by empirical function;f (ADC) =p2
2 × exp(p0 + p1 × ADC + ADC)
ADC−p3
1 + exp(exp(− 3 ))(3.3)

and MIP distribution is declared by Gaussian function. After ﬁtting to ADC
distribution, background is subtracted with background function. Then MIP
values are estimated by Gaussian function ﬁt to MIP distribution which is
ADC distribution after the background distribution is subtracted as shownin Figure 3.8.

3.2.3

Time Calibration

The slewing eﬀect represents the timing diﬀerence as the signal height output
from PMT, traverses the threshold values of discriminator in FEM which
deﬁnes whether it is hit event or not. If pulse height is large, slewing eﬀect
is small. On the other hand, if pulse height is small, slewing eﬀect becomessigniﬁcant. In order to correct the slewing eﬀect, new parameterization of
slewing correction is implemented. At ﬁrst, reference hit time in each side
is calculated by taking an average of non slewing corrected hit time of PMTwith valid hit. Its valid hit is deﬁned by that TDC values are less than its
overﬂow minus its sigma of overﬂow times four. Given a reference hit time
per event, the time diﬀerence between the reference hit time and hit timeof each PMT is measured. The time diﬀerence is plotted with respect tomeasured charge for each. This is named by slewing curve. Once the slewing
curve is obtained, the curve is ﬁt with the empirical function;f (ADC) = p0 +p3
p1
+ p2 × log(ADC) +
ADC
ADC 2

(3.4)

32

CHAPTER 3. DATA ANALYSIS

350
300
250
200
150
100
50
0
0

50

100

150

200

250
ADC [ch]Figure 3.7: ADC distribution subtracted threshold values. Blue line shows
ﬁtted function of background plus MIP distribution which is Gaussian. Redline shows background function.

200

85.11 ch/MIP

150

100

50

0

-50
0

50

100

150

200

250
ADC [ch]Figure 3.8: ADC distribution subtracted background. Red line shows Gaussian ﬁt. PMT gain is determined by mean values of ﬁt parameter divided by
ADC gain constants.

3.3. CENTRALITY MEASUREMENT

33

Time Difference [ns]where p0, p1, p2, and p3 is parameters. Given slewing corrected hit time foreach PMT, reference hit time is recalculated by using corrected hit time. The
time diﬀerence between corrected reference hit time and non corrected hit
time of each PMT is also measured. This iteration is repeated ﬁve times, since
it is necessary to improve time resolution as shown in Figure 3.9. Finally,corrected reference hit time in each side is named by ”arm hit time” and thisis used for calculation of collision vertex and collision time. Figure 3.10 shows
the corrected slewing curve using ﬁtted function and Figure 3.11 shows the
projectile of corrected slewing curve along the x axis.
3
2.5
2
1.5
1
0.5
0
-0.5
-1
-1.5
2

10

3

10

ADC [ch]Figure 3.9: Typical slewing curve overlaid with ﬁt slewing function.

3.3

Centrality Measurement

Collision centrality is the value which is related to impact parameter. Zeropercentile of centrality indicates the collision between the two nuclei occurredwith having zero impact parameter. When they collide with non zero impact
parameter, charged particles emitted from interactive region are detected by
BBC and spectator neutrons which is not participating with interaction aredetected by ZDC. Schematic scenario is shown by Figure 3.12. After theboomerang plot of BBC versus ZDC is obtained, centrality is estimated bywhat is called by ”clock method”. The angle ϕ of a given event in the BBC

CHAPTER 3. DATA ANALYSISTime Difference [ns]

34

1
0.8
0.6
0.4
0.2
-0
-0.2
-0.4
-0.6
-0.8
-1

2

3

10

10

ADC [ch]Figure 3.10: Corrected slewing curve.

9000

Entries
Constant

8000
7000

57178
7834 ± 49.4

Mean

0.014 ± 0.000

Sigma

0.05146 ± 0.00026

6000
5000
4000
3000
2000
1000
0

-0.4

-0.3

-0.2

-0.1

-0

0.1

0.2
0.3
0.4
Time Difference [ns]Figure 3.11: The timing diﬀerence between reference time and corrected
timing of a PMT. The sigma of ﬁt function is deﬁned as the timing resolution.

3.4. SIMULATION35

ZDC plane is calculated with respect to the point (0.2×BBC/BBCmax , 0) in
the BBC ZDC plane. From Monte Carlo simulation (MC simulation) result,the angle ϕ is converted to percentiles of centrality.

Figure 3.12: Scatter plot between BBC charge sum and ZDC energy sum.
Color coding shows centrality class in 5 percent. BBC and ZDC is normalizedby maximum values, respectively.

3.4

Simulation

3.4.1

Glauber Monte Carlo Simulation

The Glauber model is based on a simple geometrical picture of a nucleusnucleus collision. Nucleons are assumed to travel on straight line trajectories, independent of whether they collide with other nucleons or not. Aftera nucleon is struck by another nucleon, one deﬁnitely has a highly excited

36

CHAPTER 3. DATA ANALYSIS

baryonic object. It is assumed in the Glauber model that the cross section
for the interaction of this excited object with other ground state or excitednucleons is identical to the ordinary inelastic nucleon-nucleon cross section
σN N . In the MC framework, the nucleons of the two Au nuclei are distributedin space according to the nucleon density proﬁle. Then an impact parameterof the nucleus-nucleus collision is chosen randomly. A participant is deﬁned
as a nucleon that has suﬀered at least one inelastic nucleon-nucleon collision. The number of participants Npart is frequently used to characterize thecentrality of a nucleus-nucleus collision, especially when reactions of nuclei
with diﬀerent mass number A are compared. Another quantity that can becalculated in the Glauber model is the average impact parameter ⟨b⟩ of acentrality class. The coordinate system is chosen such that the centers of
the two nuclei are at (-b/2, 0) and (b/2, 0), respectively, where b denotes
the impact parameter as shown in Figure 3.13. The nuclear density proﬁleis parameterized by a Woods-Saxon function;
ρ(r) = ρ0 ·1
1 + exp( r−R
)
a

(3.5)

For gold nuclei the parameters
R = 6.38f m and a = 0.54f m

(3.6)

√
are used. For a center of mass energy of sN N = 200GeV an inelastic
nucleon-nucleon cross section of σN N = 42mb was used in the Glauber calculations.

3.4.2

Event Generator

Heavy Ion Jet INteraction Generator (HIJING) Monte Carlo model is used inorder to simulate the primary multiplicity in Au collision. HIJING basicallyis designed to simulate multiple jets and particle production in Au collision.
PYTHIA subroutines and Lund jet fragmentation scheme are used. Detailed
systematic comparison of HIJING results with a very wide range of data
demonstrates that a quantitative understanding of the interplay between soft
string dynamics and hard QCD interaction has been achieved. In particular,
HIJING reproduces many inclusive spectra and two particle correlations,and explains the observed ﬂavor and multiplicity dependence of the averagetransverse momentum.

3.4. SIMULATION

37

Figure 3.13: Sketch of the coordinate system used for the calculation. The
big circles indicate the two Au nuclei in the transverse plane. The impact
parameter is parallel to the x axis. The participating nucleons are depicted
as ﬁlled disks [19].

38

3.4.3

CHAPTER 3. DATA ANALYSIS

GEANT Simulation

The PHENIX Integrated Simulation Application (PISA) is a GEANT3-based
simulation code. The main inputs to PISA are the event selection, the detector geometry setup for the active and passive volumes, and the tracking
criteria. The PISA input ﬁle also speciﬁes the various options for the interaction types, energy thresholds, and active detector elements, etc. The
GEANT software is then used to track the primary particles and their secondaries within an event. When these particles pass through the selected active
detector subsystem, speciﬁc hit output data structures are ﬁlled during theevent. When all particles and secondaries in the event have been tracked
until they are stopped or escape the detector volume, then the stored hits
are written to an output ﬁle called by ”PISA hit ﬁle”. From PISA hit ﬁle,the PRDF ﬁle is output by using event reconstructing code. Since PISA hit
ﬁle has the information of tracking for all primary and secondary particles, it
can be calculated the total length of track passing through detector element.
In the case of BBC, element is the Quarts and interaction type is Cerenkov
radiation. Using calibration constants obtained from real data, ADC andTDC output values are calculated by length of track and timing of ﬁst incident particles, respectively. Then their values are output to PRDF ﬁle. FromPISA hit ﬁle, primary ancestry ﬁle is also generated. Ancestry ﬁle is used for
estimation of number primary charged particles per pseudo-rapidity. PRDF
ﬁle is used for obtaining the number of detected charged particles.

3.5

Measurement of Charged Particle Multiplicity

3.5.1

Pseudo-Rapidity Distribution

From simulation data, the conversion factor, which can convert from numberof detected charged particles to multiplicity of primary charged particles, isobtained. BBC has six groups of radius from beam pipe to each PMT center
position in each side. Rapidity coverage changes with collision vertex point.
Thus, conversion factors are obtained for each radii groups and each vertex
region. When collision vertex is zero, the diﬀerence of rapidity coverage between the radii groups is about 0.2, and when collision vertex shift 2.5cm,
the diﬀerence of coverage for one radii group is 0.043. 3.14 shows the shift3.5. MEASUREMENT OF CHARGED PARTICLE MULTIPLICITY

39

of each 32 PMTs rapidity coverage when vertex shift ±2.5cm. As seen in
3.14, 7 PMT groups are completely separated about its rapidity coverage.
3.15 indicates the 7 PMT groups identiﬁed by color, which is consists thecolor in 3.14 and also has same radius from center of PMT to beam pipe.
Therefore, the collision vertex will be separated in 5cm, thus 7 groups of avertex region, and radii group of PMT will be separated by 14 groups, northand south PMT is separated by 7 groups, respectively. Using the ancestry
ﬁle, I count the number of primary charged particles for each group. For eachgroup, number of detected charged particles is counted by summing whole
PMT included same group. After two dimensional histograms between number of detected charged particles and primary charged particles are obtained,
liner function is ﬁtted to histogram under assumption that its scatter plot isliner as shown in Figure 3.16. Using event data, number of detected charged
particles is obtained in same way written in above, which is separated bycollision centrality as shown in Figure 3.17, then, using ﬁtted liner function,
number of detected charged particles is corrected to dNch /dη. The distribution of number of detected charged particles separated by collision centrality
is known by negative binomial distribution (NBD). The mean value of NBD
is simple average of distribution, so that the number of detected charged
particles indicates simple mean values. Standard error of the mean (SEM)
is estimated by root mean square (RMS) of distribution divided by squareroot of number of entries of distribution. As statistical error, error propagation of SDM and ﬁtting error is calculated. Finally, dNch /dη is obtainedfor eight rapidity regions by taking an average, which has bin width of 0.2.
As systematic error, deviation between average value and each mean value
is applied.

3.5.2

Total Multiplicity

In [20], the rapidity distribution of multiplicity of charged particles has been
explained using a stochastic approach based on the Ornstein-Uhlenbeck (OU)
process with the evolution parameter t, the frictional coeﬃcient γ and thevariance σ 2 , described by the partial diﬀerential equation;∂P (y, t)∂1 σ2 ∂ 2= γ{ y +}P (y, t)
(3.7)
∂t
∂y
2 γ ∂y 2√
Introducing two sources at ymax = ln( sN N /mN ) at t = 0 and setting
P (y, 0) = 0.5{δ(y + ymax ) + δ(y − ymax )}, we obtain the distribution func-

40

CHAPTER 3. DATA ANALYSIS

Figure 3.14: The demonstrated histogram of pseudo-rapidity coverage foreach PMT. The vertex position is shift ±2.5cm around the zero. The groupof having same color belongs the group of having same radius.

Figure 3.15: The drawings of color separated PMT groups having same radius. These colors correspond to which is shown in 3.14.

41

dNch

3.5. MEASUREMENT OF CHARGED PARTICLE MULTIPLICITY

25
102
20

15
10
10

5
1
0
0

20

40

60

80
100
charge sum [MIP]

Figure 3.16: Scatter plot between multiplicity of primary charged particle
and number of charged particles detected by BBC. Black line shows ﬁt linear function. Conversion factors are determined by ﬁt parameter of linear
function.

42

CHAPTER 3. DATA ANALYSIS

0% ~ 5%
10% ~ 15%3

1020% ~ 25%
102

10

1
0

20

40

60

80

100

120
140
charge sum [MIP]

Figure 3.17: Charge sum distribution of BBC. NBD separated by color shows
charge sum distribution selected by using centrality class. Simple mean and
RMS is applied for data point after correction.

tion for dN/dη, which derives the symmetric double Gaussian distributionat η = 0:dNch(x − p1)2(−x − p1)2
= p0 × exp(−
)
+
p0
×
exp(−
)
dη
2 × p222 × p22(3.8)

where p0, p1, and p2 is parameters. Double Gaussian distribution is ﬁtted to rapidity distribution in order to interpolate and extrapolate the data
point. Then integration over whole rapidity region is carried out so that total multiplicity of primary charged particles as shown in Figure 3.18. Fitting
ambiguity is applied as systematic errors of total multiplicity as a functionof collision centrality.

dNch/dη

3.5. MEASUREMENT OF CHARGED PARTICLE MULTIPLICITY

700

600

0-5

30 - 35

10 - 1540 - 45

20 - 25

50 - 55

43

500

400

300

200

100

0

dNch/dη

-6

700

600

-4

-2

0

2

4

5 - 1035 - 40

15 - 2045 - 50

25 - 30

55 - 60

6
η

500

400

300

200

100

0

-6

-4

-2

0

2

4

6
η

Figure 3.18: Pseudo-rapidity distribution of primary multiplicity of charged
particles. Red line shows double Gaussian function ﬁt to the data point.
Twelve centrality classes are separated, which is shown by diﬀerence ofmarker style.

Chapter 4
Results and Discussions
4.1

Collision Centrality Scaling

In Figure 4.1, Nch /(Npart /2) is shown for this work as a function of Npart .
It was found that Nch /(Npart /2) in Au+Au central collision scales to whichin e+ e− collision. Also it was found that in peripheral Au+Au collision,
Nch /(Npart /2) does not scale to both which in pp/pp collisions and e+ e−
collision. The decreasing of Nch /(Npart /2) can be naively understood thatthe ”leading” parton eﬀect comes to appear toward the peripheral collision.
This may be not surprising because peripheral collision becomes more closely
to the pp collision rather than e+ e− collision. No ”leading” parton eﬀect incentral collision suggests that there is no energy dissipation, thus, collisionenergies carried into the interaction region are exhaustively used for particle
production. And this is occurred by results of multiple scattering between
incoming nucleons.

4.2

Collision Energy Scaling

In Figure 4.2a, the data on Nch from pp/pp, e+ e− and central heavy ion collisions scaled by Npart /2 are plotted as a function of collision energy. pp/pp,
e+ e− data and errors are taken from a compilation [21]. The errors are thequadratically combined statistical and systematic errors. Heavy ion data are√shown for central Au+Au collision at RHIC ( sN N = 200GeV , this work),√
Au+Au collision from PHOBOS at the RHIC ( sN N = 130, 56 and 19.6GeV ),√Au+Au collision from E895 at the AGS ( sN N = 2.6 ∼ 4.3GeV ) and Pb+Pb
45

〈Nch〉 / 〈Npart / 2〉

46

CHAPTER 4. RESULTS AND DISCUSSIONS

34
32
30
28
26
24

e+ePHENIX
pp(pp)

22
20
18
16
-50

0

50

100

150

200

250

300

350

400
Npart

Figure 4.1: The total charged multiplicity scaled by number of participants√
pair as a function of number of participants for Au+Au collision at sN N =200GeV . The green box shows pp data at sqrtsN N = 200GeV . The dottedline shows the values from the e+ e− .

4.2. COLLISION ENERGY SCALING

47√
collision from NA49 at the SPS ( sN N = 8.6, 12.2, 17.3GeV ). All of theerrors shown for the heavy ion data are systematic. Perturbative QCD calculations are able to predict the dependence of averaged multiplicity in e+ e−√
collisions as a function of sN N [23]. A ﬁt to the e+ e− data has been used
to Figure 4.2b to see how the various systems compare with e+ e− data by√
scaling all of the data at a given sN N . Figure 4.2b shows that the average
multiplicity in pp/pp collisions is below which in e+ e− data but having thesame slope between e+ e− data and pp/pp data. From the results in mea√
surements of leading partons in pp collisions, dN/dxF where xF = 2pz / sin the collider reference frame√ is approximately constant for non diﬀractive
eventsover a large range of s [22] and xF ∼ 0.5. Therefore, rescaling the√s of each point by a factor of 0.5, brings the data into agreement with thee+ e− data. Diﬀerently from pp data, heavy ion data are reasonable agreement with the e+ e− data above top SPS energy in no correction of ”leading”
eﬀect.

48

CHAPTER 4. RESULTS AND DISCUSSIONS

40
35〈Nch〉 ( / 〈Npart / 2〉 )

30
25
20
15

e+e- Data
Fit to e+epp(pp) Datapp(pp) (@ s / 2)
AA Data
PHENIX

10
5
0
1

10

s [GeV]

10

2

10

3

2

10

1

+

〈Nch〉 ( / 〈Npart / 2〉 ) / e e- Fit

1.2

0.8

0.6

0.4

0.2
1

10

s [GeV]

103

Figure 4.2: (a) The total multiplicity of charged particles for pp, pp, e+ e− ,and central nucleus-nucleus collisions scaled by number of participants pair
as a function of collision energy. The dotted line is a perturbative QCD
expression ﬁt to the e+ e− data. The pink box shows the pp/pp data correctedof ”leading” parton eﬀect. (b) The data in (a) ﬁgure divided by pQCD ﬁt.

Chapter 5
Conclusion
The pseudo-rapidity distribution of multiplicity of primary charged particles√
as a function of collision centrality in Au+Au collisions at sN N = 200GeV
was obtained. The total multiplicity per number of nucleon pairs participating to a collision (Nch /(Npart /2)) was obtained as a function of Npart .
√+ −Nch /(Npart√ /2) in sN N = 200GeV was compared with e e and pp/pp datain same s as a function of Npart . It is found that in peripheral collisions,
Nch /(Npart /2) corresponds to neither e+ e− nor pp/pp collisions. However, incentral collisions it is found that Nch /(Npart /2) corresponds in the same wayof e+ e− data. This indicates that there are no leading parton eﬀect in central
collisions which is observed in pp/pp collisions. This leads to the interpretations that all collision energies carried into interactions are consumed for particle productions without dissipations. This implies that multiple scattering
is occurring in high energy heavy ion collisions. In addition to Nch /(Npart /2)√
in central Au+Au collision at sN N = 200GeV , other experimental data in+ −central nuclear-nuclear collisions are compared√ with e e and pp/pp data inwide center of mass energy range. Above s = 20GeV , average multiplicity in e+ e− collision can be well described by pQCD and this shows thatthe freedom of parton appears in such energy regions. The comparison as afunction of collision energy elucidate that Nch /(Npart /2) in heavy ion colli√sion above sN N = 20GeV scales to e+ e− data with no correction of leading
parton eﬀect. This leads to a picture that in high energy heavy ion collision,√
especially above sN N = 20GeV , carriers of particle production is believed
to be partons.
In summary, high energy nuclear-nuclear interaction looks like the partonsare freely interact each other having longer mean free path than the ordinary49

50

CHAPTER 5. CONCLUSION

nucleon size. This is not contradictory with a picture of the deconﬁnement.

Acknowledgement
I ﬁrst would like to express my great gratitude to Prof. T. Sugitate of Hiroshima University. I would like to express my great gratitude to Prof. K.
Shigaki and Dr. K. Homma for their educaional suggestions. I also would liketo express my great gratitude to T. Nakamura, Y. Tsuchimoto, K. Hosokawa,
H. Harada, Y. Nakamiya and H. Sakata

Bibliography[1] G. F. Chapline, M. H. Johnson, E. Teller, and M. S. Weiss. Highly
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