Measurement of ω mesons
via radiative decay mode√in Au+Au collisions at sN N =200GeV
Misaki Ouchida(M052187)
Hiroshima University

Abstract
The modification of experimentally observable properties of vector mesons
such as mass and width, when embedded in a hot and dense medium created by the relativistic heavy-ion collisions, is one of the most fundamental
research issues in hadron physics. It could be linked to the chiral symmetry restoration, that is, the intricate key for searching the source of hadron
masses. The radiative decay mode of ω mesons (ω → π 0 γ) is a promising
approach for this study. Since the radiative reaction is likely to less interact in the medium than charged particle’s reation due to its electromagnetic
coupling, it is a clean way to investigate the properties. Furthermore, it has
a large branching ratio, about 9% and doesn’t have to concern the contamination of ρ mesons that all e+ e− experiments suffer from.
We measure ω mesons via radiative decay mode in Au+Au collisions at
C.M.S. collision energy per nucleon pair of 200GeV taken at the PHENIX
experiment using the Relativistic Heavy Ion Collider (RHIC). The RHIC
is proven to have an enough energy for researching the chiral phase transition leading to the expected mass modification. Since it is very challenging
to search specific particles in the high multiple collisions, the simulation iscarried out in advance to calculate an acceptance and to check a multiplicity dependence. The main issue of this analysis is the huge combinatorial
background inevitable for reconstructing particles from the three-body decay
mode. So we emphasis on doing the feasibility study using both simulation
and real data to search the best parameters such as momentum and energy
for selecting π 0 and γ before reconstructing√ ω. Finally, we find best values
for each parameter that can improve S/ B. After introducing these parameters, reconstructed ω invariant mass spectra as a function of ω transverse
momentum are shown and discussed. A further improvement of ω identification and how to approach the low momentum region where the in-medium
modification mainly dominate are considered.

Contents
1 Introduction
1
1.1 Chiral Symmetry Restoration . . . . . . . . . . . . . . . . . . 3
1.2 Low Mass Vector Mesons . . . . . . . . . . . . . . . . . . . . . 6
1.2.1 Medium Modification . . . . . . . . . . . . . . . . . . . 6
1.2.2 Current Status . . . . . . . . . . . . . . . . . . . . . . 9
1.3 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2 Experimental Setup
2.1 RHIC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 PHENIX Detector . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Global Detectors . . . . . . . . . . . . . . . . . . . . .
2.2.2 Muon Arm Detectors . . . . . . . . . . . . . . . . . . .
2.2.3 Central Arm Detectors . . . . . . . . . . . . . . . . . .
2.2.4 Electro Magnetic Calorimeter . . . . . . . . . . . . . .
2.3 Computing . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17
17
19
21
23
24
27
33

3 Analysis
3.1 Quest for ω mesons . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Data Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Event Generator . . . . . . . . . . . . . . . . . . . . .
3.3.2 Detector Simulation . . . . . . . . . . . . . . . . . . .
3.3.3 Multiplicity Dependence . . . . . . . . . . . . . . . . .
3.3.4 Cut Optimization . . . . . . . . . . . . . . . . . . . . .
3.3.5 Feasibility . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Signal Selection . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.1 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.2 Photon Identification . . . . . . . . . . . . . . . . . . .

36
36
38
39
39
40
42
47
53
60
60
62

i

3.4.3
3.4.4

Distribution of π 0 Invariant Mass . . . . . . . . . . . . 65
Best Cuts for Reconstructing ω . . . . . . . . . . . . . 67

4 Results and Discussion
4.1 Invariant Mass Spectra . . . . . . . . . . . . . . . . . . . . . .
4.2 Background Consideration . . . . . . . . . . . . . . . . . . . .
4.2.1 Combinatorial Background . . . . . . . . . . . . . . . .
4.2.2 Mixed Events Trail . . . . . . . . . . . . . . . . . . . .
4.3 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

68
68
72
72
74
80

5 Conclusion

81

A Kinematics

83

iiChapter 1
Introduction
The goal of the relativistic heavy ion physics is to explore nature’s most basic
ingredients and phenomena. Today, nuclear matter is said to be constructedby the most fundamental particle, quarks and leptons. Quarks themselves
can’t be ’liberated’ due to gluons that holds together them via the strong
force except in the extreme conditions.
The state of the nuclear matter is described by the Quantum Chromodynamics (QCD), the modern theory of the strong interaction. The QCD
exhibits a property called the asymptotic freedom[1], that is, the couplingstrength of gluons decreases with increasing energy and momentum. This is
the clue that the heavy ion physics stand for. As nuclear matter is heated andcompressed, hadrons occupy more and more of the available space. Eventually they start to overlap and the initially confined quarks and gluons begin to’percolate’ between the hadrons thus being ’liberated’ ! This state of matter,
the hot and dense fireball made of ’liberated’ quarks and gluons is commonly
called as the Quark Gluon Plasma (QGP).
This simple picture has originally provided the basis for models of thequark-hadron transition and has been essentially confirmed by numerical
QCD lattice calculations at finite temperature[2]. The Figure 1.1 shows asketch of the QCD phase diagram. Although the phase boundary between
the hadron matter and the QGP is not well known, lattice calculations gavean estimation of the critical temperature Tc and the baryon density needed
for the QGP creation. From there we can estimate that Tc is about up to
170 MeV and the density is approximately from 5 to 20 times of the normal
nuclear matter . However, the systematic error of the lattice result is notknown since it is unattainable using the reweighting method[2] to consider
1

2

Figure 1.1: Sketch of the QCD phase diagramthe volume V → ∞ when calculating the nuclear density going to 0.
Some relativistic heavy ion collisions were conducted already and some√ arestill in operation or in preparation. The Heavy Ion Synchrotron (SIS)( s '2A√ GeV) at GSI in Darmstadt, the Alternating Gradient Synchrotron (AGS)( s ' 5A GeV) at the Brookhaven National√Laboratory (BNL) in New
York and the Super Proton Synchrotron (SPS)( s ' 20A GeV) at CERN
√ in
Geneva began in mid 80’s. The Relativistic Heavy Ion Collider (RHIC)( s =200A GeV) at the√ BNL has been ongoing since 2000 and the Large Hadron
Collider (LHC)( s ∼ 1.5A TeV) at CERN is planed to operate from 2007.
According to the model predictions[3], RHIC and SPS energy are indeed lying
on the phase boundary. AGS is below the boundary line, however, it is not
excluded that the fireball in the initial state appears in the deconfined phasesince the initial energy density expected at AGS is of the order of 1 GeV/fm3
thus, it is larger than the critical energy density along the boundary. The
LHC is hoped for crossing the boundary in the near future.

3

1.1

Chiral Symmetry Restoration

There are two fundamental properties of the QGP. The one is the deconfinement explained previously, the other is Chiral Symmetry Restoration.
Chirality, coming from the Greek word ”χ²ιρ” has the meaning of ”hand”[4].
An object or a system has chirality if it differs from its mirror image. Such
objects then come in two forms, L (left-handed) and R (right-handed), which
are mirror images of each other. The Figure 1.2 shows a image of an object
having both L and R. If a particle has mass, both L and R components must
exist. The reason is that massive particles travel slower than the speed oflight and a particle that appears L in a particular reference frame will look R
from a reference frame moving faster than the particle (a bird in the Figure1.2). That means, chirality is not conserved; in a massless world chirality isconserved, but this is sufficient but not necessary condition.

Lmirrorleft-handedRright-handed

Figure 1.2: Image of the Chiral Symmetry

4
In QCD, it can be encoded in following Lagrangian[5]XX
1 (a) (a)µν
LQCD = − FµνF+iψ̄qi γ µ (Dµ )ij ψqj −mq ψ̄qj ψqi ,
4
q
q
(a)
= ∂µ Aaν − ∂ν Aaµ − gs fabc Abµ Acν ,Fµν(Dµ )ij = δij ∂µ + igs

X λai,j
a

2

Aaµ ,

(1.1)
(1.2)
(1.3)

where gs is the QCD coupling constant, and the fabc are the structure constants of the SU(3) algebra. The ψqi (x) are the 4-compoment Dirac spinors
associated with each quark field of 3 color i and flavor q, and the Aaµ (x) are
the 8 gluon fields.
(a) (a)µν
Let us explain roughly the Equation (1.1). The first term, 14 Fµν
F
,
P i µ
j
corresponds to the free gluon field, the second term, i q ψ̄q γ (Dµ )ij ψq , corresponds to the interaction of quark in the gluon field and the last term,Pjq mq ψ̄q ψqi , corresponds to the free quarks of mass mq in a rest state. mq
represents the diagonal matrix of current quark masses,
mq = 





mu
md
ms

...



,



(1.4)

which are parameters of the Standard Model. With mu , md , ms ' 4, 7, 150
MeV and mc , mb , mt ' 1.5, 4.5, 175 GeV. There is an obvious separation
into sectors of ’light’ and ’heavy’ quarks.
Chiral symmetry of QCD means that all states have a chiral partner with
opposite parity and equal mass. But in the real world, the mass term is
not 0 as above so then a mass of a chiral parter is not equal to an associateparticle. For instance, ρ (J P = 1− ) m=770 MeV has a chiral partner as a1(J P = 1+ ) m=1250 MeV and N(1/2+ ) m=940 MeV has a chiral parter as
N? (1/2− ) m=1535 MeV. The difference is too large to be explained by thesmall current quark masses. It can be concluded that the chiral symmetryis spontaneously broken and taking it conversely, constituent quark masses
can be generated by the spontaneous breaking ot the chiral symmetry. It issaid that the structure of the lowest-mass hadrons (involved the light-quark
sector comprised of u, d, s quarks) is largely determined by chiral symmetry

5and its dynamical breaking in the physical vacuum. And many models link
the hadron masses to the quark condensate.
In the physical vacuum, quarks and gluons condense giving rise to nonvanishing vacuum expectation values hψ̄ψi[7], also called condensate, that istheir average, mathematical expectation value in the vacuum. Let us consider
the one of such condensate for quarks, the quark condensate hq̄qi. The Figure
1.3 is a three dimension picture showing the correlation between the quark
condensate and QCD phase diagram (see the Figure 1.1).

Figure 1.3: The quark condensate and QCD phase diagram [8]In the case of QCD, if the chiral symmetry is spontaneously broken, thequark condensate is non-zero and said to be: hq̄qi ≈ 250 MeV3 . At hightemperatures or high densities (the blue field in the Figure 1.3), numerical
QCD calculations predict that the quark condensate vanishes: hq̄qi → 0, i.e.
chiral symmetry is restored in this region. This means, there is a transitionof the system that constitute mass when it’s going to the extreme condition.
We will discuss the probe of the Chiral Symmetry Restoration in the next
section.

6

1.2

Low Mass Vector Mesons

Low-mass vector mesons are considered the most sensitive probe of chiral symmetry restoration. The key is their lifetimes (see the Figure 1.4).
The typical fireball, the hot and dense matter called QGP discussed previously, is said to㨪10 fm/c
have ∼ 10 fm/c lifetime [9]. While some lowfireballmass vector mesons, φ, ω and ρ have lifetimes
NKHGVKOGas
46 fm/c, 23fm/c and 1.3 fm/c respectively.
OCUU
This means, a lot of vector mesons (most of the fm/c
ρ mesons) have a chance of decaying inside the fm/c/G8
medium. They should provide an unique tool/G8phi(Ǟ)
 fm/crho(ǹ)
to observe in-medium modifications of its prop/G8
omega(ȁ)
erties (e.g. mass and/or width) which could belinked to the Chiral Symmetry Restoration. In
this section, we’re going to describe how the
Figure 1.4: Lifetimes
matter effects vector mesons’ properties by atheoritical calculation first and going to report
the current experimental status next.

1.2.1

Medium Modification

The most common approach to evaluate medium effects on vector mesons
properties consists of evaluating effective interactions with surrounding hadrons
from the heat bath[14][10], leading to in-medium insertions which are resummed in the propagator as (here for the ρ),2−1Dρ (M, q; µB , T ) = [M 2 − (m(0)
p ) − Σρππ − ΣρB − ΣρM ] ,(1.5)

where M , m(0)p :mass and bare mass, q:momentum, µB :baryon density andT :temperature. The different contributions may be classified as; modifications of the pions in the ππ decay (Σρππ ), direct ρ-baryon couplings (ΣρB )and direct ρ-meson couplings (ΣρM ).
The imaginary part of the propagator (ImDρ ) is coincides with the spectral function up to a factor of (-2). The Figure 1.5 and The Figure 1.6 show
its value for rho and omega mesons. They agree in that the main effect is a
substantial broading, accompanied by a small upward mass shift.

7

Figure 1.5: ρ meson spectral function, ImDρ (M ,q = 0), in hadronic matter
under approximate conditions (µB = 330MeV)[11].

Figure 1.6: ρ meson and ω meson spectral function in nuclear matter atρ = ρ0 and ρ = 2ρ0 , compared to those in the vacuum[12].

8
How is the degeneracy of chiral partners realized? Do the masses drop to
zero? Do the widths increase? The fact is that there is no good answer toany of these questions so far. The one theory which has just shown was doneby Ralf.Rap et al. It expected that the mean of vector meson’s mass would
barely shift to upward and width would get brouder, however, the othercalculations based on different models result in different way. The Figure 1.7
is such one result done by T.Hatsuda and S.H.Lee using QCD sum rules[13].
It shows that the mass shift inversely downward.

1/2

Figure 1.7: (a) The ρ-ω meson mass m and the continuum threshold S0
as a function of ρ/ρ0 . (b) The same figure for the φ-meson mass with two
typical values of y (the strangeness content in the nucleon). Dashed lines
indicate the K 0 K 0 and K + K − threshold at ρ = 0 which are the main decay
modes of φ.
Since there’s no clear consistent results for the theoritical approach tosearch for the effect of Chiral Symmetry Restoration, we couldn’t estimate
how the vector meson’s mass exactly change in advance. Therefore, it can besaid that this is the example where experiments has the potential to guidethe theory. Next, we compare the current experimental results.

9

1.2.2

Current Status

A lot of experimental challenges for searching the in-medium modifications ofvector mesons had been executed and some experiments are still in advance.
We are going to introduce following five major experiments producing interesting results. KEK (Japan), Jlab (U.S.) and CBELSA/TAPS (Germany)
are the experiments using elementary reactions using fixed targets for creating high density. CERES and NA60 (Both in CERN at Geneva) are theheavy ion experiments for creating high temperature. The merit of the elementary reactions is that those are well controlled conditions since there’s notime dependence of baryon density. The demerit is the small medium effects
because the reaction temperature is low. On the other hand, the merit of
the heavy ion collisions is the sizable effects due to high densities and temperatures. The demerit is that any signal represents an integration over thefull space-time history of the heavy-ion collision with strong variations in
densities and temperatures[15].
The Figure 1.8 shows a comparison of the five experiments’ results foreach vector meson. Let us see them one by one.

Figure 1.8: Current status of in-medium modifications of vector mesons[15].

10
KEK
The invariant mass spectra of e+ e− pairs produced in 12 GeV p + A interactions are mesured at the KEK Proton Synchrotron [16][17]. Copper andcarbon targets are used to study the nuclear-size dependence of e+ e− invariant mass distributions (see the Figure 1.9). On the low-mass side of the ω
meson peak, a significant enhancement over the known hadroninc sources
has been observed. Also a significant excess on√the low-mass side of the phimeson peak is observed in the low βγ(= β/ 1 − β 2 ) region of φ mesons(βγ < 1.25) with copper targets.
Jlab
While KEK measured vector mesons, the CEBAF Large Angle Spectrometer(CLAS) detector located in the Jefferson Laboratory (Jlab) collected data
in 2002[18]. The experiment had the conditions with an intense photon
source, and 2 D, 12 C, 48 Ti, 56 Fe and 208 Pb targets. The method is same as
KEK, however, it tuned out the results is inconsistent. The results are compatible with no mass shift at all and have a normal width broadening.
CBELSA/TAPS
The photoproduction of ω mesons on nuclei has been investigated using
the Crystal Barrel/TAPS experiment at the ELSA tagged photon facility
in Bonn[19]. Results obtained for Nb are compared to a reference measurement on a LH2 target. While for recoiling, long-lived mesons (π 0 ,η and η0),which decay outside of the nucleus, a difference in the line shape for the twodata samples is not observed. They find a significant enhancement towards
lower masses for ω mesons produced on the Nb target (see the right plot in
the Figure 1.11). For momenta less than 500 MeV/c an in-medium ω meson+35
2mass of Mmedium = [772+4−4 (stat)35 (syst)] MeV/c has been deduced at an
estimated average nuclear density of 0.6ρ0 .

11Figure 1.9: Invariant mass spectra of e+ e− measured in KEK E-325
experiment[16]. The result of the model calculation considering the in-media
modification for the (a)C and (b)Cu targets, together with (c) the fit resultwith the ρ − ω interference for the Cu target. In (a) and (b), the shapesof ω → e+ e− (dotted line) and ρ → e+ e− (dash-dotted line) were modified
according to the model using the formula m(ρ)/m(0) = 1 − k(ρ/ρ0 ) withk = 0.092.

Figure 1.10: Invariant mass spectra of e+ e− measured in Jlab[18] with acalculation plot of with and without modification. χ2 fit are used to assess
the mass shift.

12Figure 1.11: Left plot: π 0 γ invariant mass for the Nb data (solid histogram)and LH2 data (dashed histogram) after background subtraction[19]. Right
plot: Mean value of the π 0 γ invariant mass as a function of the ω momentum
at an estimated average density of 0.6ρ0 for the Nb data (circles) and theLH2 (crosses) along with a fit.
CERES
The measurement of e+ e− pair production in central Pb-Au collisions at 158A
GeV/c were produced in the CERN-Super-Proton-Synchrotron(SPS) by the
CERES experiment[20]. A significant excess of the e+ e− pair yield over the
expectation from hadron decays is observed (the enhancement is pronounced
in the mass region 0.2 < mee < 0.6 GeV/c2 in the Figure 1.12). The dataclearly favor a substantial in-medium broadening of the ρ pole mass.
NA60
Low-mass muon pairs in 158AGeV indium-indium collisions were mesured
at the CERN SPS[21]. A significant excess of pairs is observed above theyield expected from neutral meson decays (see the Figure 1.13). The unprecedented sample size of 360’000 dimuons and the good mass resolution of
about 2% could isolate the excess by subtraction of the decay sources. The
shape of the resulting mass spectrum is consistent with a dominant contribution from π + π − → ρ → µ+ µ− annihilation. The associated space-time
averaged ρ spectral function shows a strong broadening, but essentially noshift in mass.

13

Figure 1.12: Invariant e+ e− mass spectrum compared to the expectationfrom hadronic decays at the CERES experiment[20].

Figure 1.13: Excess mass spectra of dimuons at the NA60 experiment[21].
The cocktail ρ (red lines) and the level of uncorrelated charm decays (dashedlines) are shown for comparison.

14
Despite of enormous progress in the experiments, there is no fully consistent picture as yet. It is needless to say that further experiments andanalysis are in demand. For now on, HADES at GSI in German and RHIC
at BNL (Here, we are involved. The detail will be described in the next
chapter.) are still working and lots of analysis are good in advance. In the
future, the Large Hadron Collider (LHC) at CERN in Geneva is planned forthe heavy ion collisions and Compressed Baryonic Matter (CBM) at GSI isplanned for the elementary reaction using heavy ion beams. We put thosemajor experiments according to the time scale and the energy scale in the
Figure 1.14. Presently, RHIC is positioned at the highest energy experimentand producing intriguing results of vector meson’s analysis.

Figure 1.14: Major experiments in the time scale (upper) and the energy
scale (lower). Red letter represents the heavy ion collisions and blue letter
represents the elementary reactions.

15

1.3

Motivation

The modification of experimentally observable properties of vector mesons
such as mass and width, when embedded in a hot and dense medium, is
one of the most fundamental research issues in hadron physics. It could
be linked to the Chiral Symmetry Restoration associated with the sourceof hadron masses. We pick ω mesons since they have relatively short life
times, 23 fm/c (a half of φ mesons’, 46 fm/c) leading to the high possibilityof decaying in the medium. The Table 1.1 shows the details of the ω mesons’
status.

Mass
Full width

Decay modesω (782) mesons
m = 782.65 ± 0.12MeV
Γ = 8.49 ± 0.08MeV+ − 0
π π π (BR: 89.1±0.7%)π0γ(BR: 8.90+0.27-0.23%)
..
.
e+ e−
..
.

(BR: 7.18±0.12×10−5 )Table 1.1: The status of ω mesons [5]Lots of theories and simulations[22][23][24] pointed out that a promising
approach to investigate in-medium modifications of the ω meson is to study
the radiative decay mode, ω → π 0 γ. We chose this decay mode being blessedwith following essential advantages.
• clean way to investigate the properties (due to its electromagnetic coupling to the nucleons, the reaction probability of the photon is almost
the same for all nucleons inside the nucleus)• large branching ratio (about 3 orders of magnitude larger than e+ e− )• no ρ-contribution (since the ρ → π 0 γ branching ratio(BR) is only 7 ×
10−4 and therefore suppressed by 2 orders of magnitude relative to theω BR into this channel)

16
The disadvantage of this decay mode is that there is possible π 0 -rescattering
within the nuclear medium, which would distort the deduced ω invariant mass
distribution. However, the distorted events are predicted to accumulate at∼500 MeV/c2 which is far below the nominal ω invariant mass. This leads
to a small contributions of only about 3% in the mass range of interest,
0.6GeV/c2 <Mπ0 γ <0.8GeV/c2 [22].
The mass modification should persist at RHIC’s high energies and thatPHENIX (the experiment we involved; explained in the next Chapter) with
its excellent mass resolution has an unique opportunity to measure photons
and reconstruct particles. In the collisions of d+Au and p+p at the PHENIX,
ω mesons could be measured and the cross-section has shown[48]. However,
the enough temperature for the phase transition leading to the mass modification would be occurred in the collisions of both heavy ions such as Au+Au.
It is challenging to search specific particles in such collisions due to it’s highmultiplicity, but worth study to do it. That’s why we started this analysis.
In this Chapter, we introduced the heavy ion physics, Chiral Symmetry
Restoration, theoritical and experimental status of low mass vector mesons.
In the Chapter 2, the accelerator facilities and the experimental setup of
detectors are discussed. In the Chapter 3, the method for this analysis,
simulation studies and data selections are shown. In the Chapter 4, we report
our latest results. The plots of invariant mass are shown and we discuss theway to subtract the background. We give the conclusion in the Chapter 5.

Chapter 2
Experimental Setup
The Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory is a world-class scientific research facility that began operation in 2000,
following 10 years of development and construction[25].

2.1

RHIC

The process of accelerating an ion involves several accelerators that make up
the RHIC complex. The Figure 2.1 shows the RHIC complex.
The ion beam starts its journey in the Tandem Van de Graaff. It consistsof two electrostatic accelerators which is capable of producing voltage up to
15 million volts, sending them on their way towards the Booster. From theTandem, the bunches of ions enter the Tandem-to-Booster beamline, which
carries them through a vacuum via a magnetic field to the Booster. At thispoint, they’re traveling at about 5% the speed of light. Then the ions areprovided with more energy at the Booster Accelerator with electromagnetic
waves and they reach a speed of 37% that of light. As they whirl aroundthe Alternating Gradient Synchrotron (AGS) and are accelerated as in the
Booster, the ions get even more energy – until they are traveling at 99.7% the
speed of light. When the ion beam is traveling at top speed in the AGS, it istaken down another beam line called the AGS-To-RHIC (ATR) transfer line.
Once they reach the end of the ATR transfer line, the ions are divided into 2
bunches, traveling either clockwise or counterclockwise in the so-called blue
and yellow lines. From here on, the counter-rotating beams are accelerated,
as in the Booster and AGS, and then circulate in RHIC.
17

CHAPTER 2. EXPERIMENTAL SETUP

18

Figure 2.1: The RHIC complex
The RHIC ring has a circumference of 3.8km with the maximum bunchof 120 and the designed luminosity is 2×1026 cm−2 s−2 for Au ion. The ringhas six intersection points where its two rings of accelerating magnets cross,allowing the particle beams to collide. The Figure 2.2 shows it’s interaction
points. If RHIC’s ring is thought of a clock face, the four current experiments
are at 6 o’clock (STAR), 8 o’clock (PHENIX), 10 o’clock (PHOBOS) and 2
o’clock (BREAMS). There are two additional intersection points at 12 and4 o’ clock where future experiments may be placed.
PHENIX, the Pioneering High Energy Nuclear Interaction eXperiment, isthe largest of the four experiments where our analysis data is taken. PHENIX
is designed specifically to measure direct probes of the collisions such as electrons, muons, and photons by its multi purpose detectors. In the subsequent
sections we describe the PHENIX detector and its various detector components.

CHAPTER 2. EXPERIMENTAL SETUP

19

Figure 2.2: RHIC Beam Interaction Points.

2.2

PHENIX Detector

The PHENIX Experiment consists of a collection of detectors, each of which
perform a specific role in the measurement of the results of a heavy ion
collision. The setup of the PHENIX experiment[26][27] as shown in the Figure 4.12 can be grouped into three categories; global detectors[28] closed tothe beam pipe and the four spectrometer arm, 2 muon arms[29] which has
pseudo-rapidity(refer to the Introduction) coverage of ±(1.2-2.4), and 2 central arms[30] which has pseudo-rapidity coverage of ±0.35 and 180azimuthal
angle in total.
Two beams coming from the beam pipe will be made to collide at thecenter of the detector. Then global detectors measure the start time, vertex
and multiplicity of the interactions. As shown in the name, muon arms
focus on the measurement of muon particles. Central arms are capable ofmeasureing a variety of particles including pions, protons, kaons, deutrons,
electron and photons. Electro Magnetic Calorimeter, the one of a detector
in the central arm which is the key for measuring photons, is explained in
the last of this section separately since this analysis deeply depends on thisdetector.

CHAPTER 2. EXPERIMENTAL SETUP

20

PHENIX Detector
PC3
PC2

PbSc

PbSc

PbSc

RICH

BB

PbSc

PbSc

DC

DC
RICH

PC3
TEC

CentralMagnet

PbGl
MVD

PC1

PbSc

PC1

PbGl

aerogelTOF

Beam View

uthCentral Magnet

So

West
Mu

on

Ma

gn

East

rth
No

et

t

ne

o
Mu

ag
nM

BB
ZDC SouthZDC North

MuID

MuID

MVD
MuTr

South

Side View

North

Figure 2.3: The PHENIX Detector configuration (2004)

CHAPTER 2. EXPERIMENTAL SETUP

2.2.1

21

Global Detectors

In order to charcteraze the nature of an event following a heavy ion collision, three global detectors[28] were employed. They consist of Beam Beam
Counters (BBC), Zero Degree Calorimeters (ZDC) and Multiplicity Vertex
Detector (MVD).
Beam Beam Counters (BBC)Our analysis group contributes to this detector and has a responsibility for it
every year. The Beam Beam Counters (BBC)[28][31] have four major tasks,
to measure the collision vertex, to produce a signal for the PHENIX trigger
and to determine three important variables ;the centrality, the time of beambeam collisions for the TOF(will be explained later) measurements and thereaction plane. The determination of the centrality and the reaction plane
are discussed in the Section 1.3.

vertex position

BBC north

Beam

Beam

144.35cm

144.35cm

North

South

BBC south

Figure 2.4: The position of BBC. The BBC’s are placed 144 cm from thecenter of the ineraction diamond and surround the beam pipe. Assume thearrival times of leading charged particles from beam collisions to each BBC
south and north as TS and TN . So then the vertex position = (TS − TN )/2 × c, the vertex time = (TS − TN − 144.35 × 2/c)/2.

CHAPTER 2. EXPERIMENTAL SETUP

22

The BBC consists of two identical sets of counters installed on both sidesof the collision point along the beam axis, one on the North side and theother on the South side of the PHENIX coordinate system. The Figure 2.4
shows the position of BBC and the way to measure the vertex position andthe vertex time. The single BBC consisting of one-inch mesh dynode photomultiplier tubes mounted on a 3 cm quartz radiator. And it is comprising
64 BBC elements. The ineraction position along the beam axis is calculated
from individual time measurements of fast leading particles hitting BBC on
the both sides of the interaction point. With an intrinsic timing resolutionof 70 ps, BBC determines the interaction position with a precision of 0.6 cm.
Zero Degree Calorimeters (ZDC)
The Zero Degree Calorimeters (ZDC)[32] are hadron calorimeter standard to
all four experiments at RHIC. The two ZDCs are located at 18m north andsouth from the nominal collision point. Since both north and south ZDC sit
at just the upstream of the last bending magnet on the RHIC ring, most of
the charged particles are swept out from the acceptance. So then the ZDC
measures the beam energy neutrons emitted in the breakup of the nuclear
remnant that misses the interaction zone. The calorimeters are also theprinciple device to monitor the beam luminosity during the run and serves
as an event trigger for all four RHIC experiments.
Multiplicity Vertex Detector (MVD)
The Multiplicity Vertex Detector (MVD)[28] provides a more precise determination of event position and multiplicity and measures fluctuations of thecharged particle distributions. It is composed of concentric barrels of siliconstrip detectors around the beampipe and two disk-shaped endcaps of silicon
pad detectors at z ∼= ±35 cm, where z refers to the beam axis. The length of
the active part of the silicon strip barrels is approximately 64 cm. The design
criteria included large rapidity and good azimuthal coverage and granularity
while also minimizing costs and material in the electron arm acceptance.

CHAPTER 2. EXPERIMENTAL SETUP

2.2.2

23

Muon Arm Detectors

A pair of forward spectrometers were set for the purpose of measuring muons.
Each muon spectrometer has a large geometric acceptance of about one
seteradian and excellent momentum resolution and muon identification.
Muon Tracker
The Muon Tracker (MuTr)[29] consists of three stations of multi-plane drift
chambers that provide precision tracking. Each of the three stations of cathode strip chambers presented unique design requirements. All are in the
shape of octants built with a 3.175 mm half gap, 5 mm cathode strips andwith alternate strips readout. The above design sepecifications led√to the relative mass resolution, approximately given by σ(M )/M = 6%/ M , where
M is in GeV. This mass resolution enables a clear separation of the ρ/ω peakfrom the φ, J/ψ and ψ0, with an acceptable separation of Υ and Υ0.
Muon Identifier
The Muon Identifier (MuID)[29] consists of alternating layers of steel absorbers and low resolution tracking layers of streamer tubes. There are six
such panels per gap arranged around the square hole left for the beam pipe
to pass through. The Figure 2.5 shows the panels as installed in the south
arm of PHENIX. The MuID design and the algorithms are used to reject thelarge hadron background from muon. The design goal of a pion rejection rate
is about 2.0 × 10−4 and it is consistent with the result from a simulation[29].

Figure 2.5: The south Muon Identifier

CHAPTER 2. EXPERIMENTAL SETUP

2.2.3

24

Central Arm Detectors

The central arm is equipped with detectors for electron, hadron and photon
measurements. The separation of negative and positive tracks are done by
applying a magnetic field from Central Magnet. The tracking system uses
three sets of Pad Chamber to provide precise three-dimensional space points
neede for pattern recognization. The precise projective tracking of Drift
Chamber is the basis of the excellent momentum reslution. Time Expansion
Chamber in the east arm provides additional tracking and particle identification. Time-of-Flight and Ring Imaging Cherenkov detectors also provide
particle identification. Aerogel Cerenkov Counter was introduced in 2003 toenhance the particle identification capability. Electro Magnetic Calorimeter
described in the subsequent section is the outermost subsystem on the central
arms and provides measurements of both photons and energetic electrons.
Central Magnet
The Central Magnet[33] is energized by two pairs of concentric coils, which
can be run separately, together, or in opposition. The Figure 2.6 shows
the field lines when both coils are turned on. It provides a field aroundthe interaction vertex that is parallel to the beam. This allows momentum
analysis of charged particles in the polar angle range from 70to 110.
Pad Chamber
The Pad Chambers(PC)[34] are multiwire proportional chambers that form
three separate layers of the PHENIX central tracking system. Each detector contains a single plane of wires inside a gas volume bounded by two
cathode planes. One cathode is finely segmented into an array of pixels.
The charge induced on a number of pixels when a charged particle starts anavalanche on an anode wire, is read out through specially designed readout
electronics. There are three sets of Pad Chambers instrumented in PHENIX,
called PC1, PC2 and PC3. The PC1 is located immediately behind theDrift Chambers(DC). The PC2 in the west arm is behind the Ring Imaging
Cherenkov(RICH) and the PC3 in both arms are in front of the Electromagnetic Calorimeter(EMCal). The Figure 4.12 shows the location.
The PCs are the only non-projective detectors in the central tracking
system and thus are critical elements of the pattern recognition. It’s information is also essential for particle identification, particularly for critical

CHAPTER 2. EXPERIMENTAL SETUP

25

PH 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 2.6: PHENIX Central Magnet Field Lines
electron identification which has to have a hadron rejection factor of 104 .
The DC and PC1 information gives direction vectors through the RICH,
while PC2 and PC3 are needed to resolve ambiguities in the outer detectors
where about 30 % of the particle striking the EMCal are produced by either
secondary interactions and particle decays outside the aperture of the DC.
Drift Chamber
The Drift Chambers (DC)[34] are cylinderically shaped and located in theregion from 2 to 2.4m from the beam axis and 2m along the beam direction
shown in the Figure 4.12. Each DC measures charged particle trajectories todetermine pT of each particle and ultimately, the invariant mass of particle
pairs. The DC also participates in the pattern recognition at high particle
track densities by providing position information that is used to link tracks
through the various PHENIX detector sub-systems.

CHAPTER 2. EXPERIMENTAL SETUP

26

Time Expansion Chamber
The Time Expansion Chamber (TEC)[34] is composed of a set of 24 large
multi-wire tracking chambers and it risides in the East arm. The TEC measures all charged particles passing through its active area, providing direction
vectors that are matched to additional track information from the DC’s andPC’s. It also enhances the momentum reslution at pT ≥ 4 GeV/c by combining with the DC to provide a long lever arm for improved track-angle
resolution.
Time-of-Flight
The Time-of-Flight (ToF)[35] system serves as a primary particle identification device for charged hadrons in PHENIX. It is designed to have about
100 ps timing resolution in order to achieve clear particle separation in thehigh momentum region, i.e. π/K separation up to 2.4 GeV/c and K/proton
separation up to 4.0 GeV/c. The ToF detector is placed at a distance of
5.1 m from the collision vertex, in between the PC3 and the EMCal in the
East arm. It consists of 10 panels of ToF walls. One ToF wall consists of 96
segments, each equipped with a plastic scintillator slat and photomultipliertubes which are read out at both ends.
Ring Imaging Cherenkov
The Ring Imaging Cherenkov (RHIC)[35](the photo shown in the Figure 2.7)
is one of the primary devices for separation of electrons from the large num-

Figure 2.7: The Ring Imaging Cherenkov detector (before an installation)

CHAPTER 2. EXPERIMENTAL SETUP

27

bers of the more copiously produced pions, that provides e/π discrimination
below the π Cherenkov threshold which is set at about 4 GeV/c. In combination with the EMCal in each arm and the TEC in one arm, the goal is tolimit the false identification of hadrons as e+ and e− to less than 1 per 104 ,for momenta below the Cherenkov threshold.
The RICH is located between the inner and outer tracking units. The
location can be seen in the Figure 4.12. Each RICH detector has a volumeof 40 m3 and contains 48 composite mirror panels forming two intersecting
spherical surfaces, with a total reflecting area of 20 m2 . The spherical mirrors
focus Cherenkov light onto two arrays of 1280 UV photomultipier tubes.
Aerogel Cerenkov Counter
The Aerogel Cerenkov Counter (AEROGEL) [36] is the additional particle
identification installed in 2003 since there were some gaps in the particle
identification if it is only done by TOF and RICH. Thanks to that, hadron
particle identification can be achieved seamlessly up to pT ∼ 8 GeV/c. Also,
the AEROGEL system has excellent trigger capability for high pT particles.
The detector is located between the PC2 and PC3 in the West arm (shownin the Figure 4.12). It consists of 160 boxes and each box has aerogel with arefactive index of n =1.0114, the best index for a combination with RICH.

2.2.4

Electro Magnetic Calorimeter

The Electro Magnetic Calorimeter (EMCal)[37] is used to measure the spatial position and energy of electrons and photons produced in heavy ion collisions. It covers the full central spectrometer acceptance of 70≤ θ ≤110with
two walls, each subtending 90in azimuth. One wall comprises four sectors of a
Lead Scintillator Calorimeter (PbSc) and the other has two sectors of a Lead
Glass Calorimeter (PbGl). The Figure 4.12 shows the location. Both detectors have very good energy, spatial and timing resolution, while the PbSc
excels in timing and the PbGl in energy measurements. We will describe
them separately since their design and the properties are quite different. After that, the Cluster Algorithm which is the key for the particle identification
will be explained.

CHAPTER 2. EXPERIMENTAL SETUP

28

Wavelength
shifting fibers

Layers oflead andscintillator tiles
TowersFigure 2.8: Interior view of PbSc module
Lead Scintillator Calorimeter (PbSc)
The Lead Scintillator Calorimeter (PbSc) is a shashlik type sampling calorimeter made of alternating tiles of Pb and scintillator consisting of 15552 individual towers and convering an area of approximately 48 m2 . The basic building
block is a module consisting of four (optically isolated) towers which are readout individually. Four towers are mechanically grouped together into a single
structural entity called a ”module” as shown in the Figure 2.8. 36 modules
are attached to a backbone and held together by welded stainless steel skinson the outside to form a rigid structure called a ”supermodule”. 18 supermodules make a ”sector”, a 2×4 m2 plane with its own regid steel frame.
The PbSc has a nomical energy resolution as,
8.1%

σE /E = 2.1% ⊕ q

E(GeV ),

where ⊕ denotes a root of the quadratic sum, α ⊕ β =position resolution as[38],√ 2
α + β 2 , and a

5.9(mm).
σx (E) = 1.4(mm) + q
E(GeV )
Intrinsic timing resolution is better than 200 ps for electromagnetic showers.

CHAPTER 2. EXPERIMENTAL SETUP

29

lead glass matrix withcarbon fibre/epoxy

photomultiplierwith housing

mirror foil
LED board
photodiode withpreamplifierreflective cover

Figure 2.9: Exploded view of a PbGl supermodule(SM)Lead Glass Calorimeter (PbGl)
The Lead Glass Calorimeter (PbGl) is a Cherenkov type calorimeter, which
occupies the two lower sectors of the East arm. Each PbGl sector comprises
192 supermodules(SM) in an array of 16 Lead Glass SM wide by 12 SM highas shown in the Figure 2.9. Each PbGl SM comprises 24 PbGl modules in aarray of 6 PbGl modules wide by 4 modules high. Modules within the SM are
individually wrapped with aluminized mylar foil and shrink tube and isolated
optically. Steel sheets of 0.5mm thickness are used to house the entire towers
and phototubes.
The PbGl has a nomical energy resolution as,[5.9 ± 0.1]%
σE /E = [0.8 ± 0.1]% ⊕ q.
E(GeV )The measured position resolution is,
σx (E) = [0.2 ± 0.1](mm) ⊕[8.4 ± 0.3](mm)qE(GeV ).

Intrinsic timing resolution is better than 300 ps for electromagnetic showers
above the minimum ionizing peak energy.

CHAPTER 2. EXPERIMENTAL SETUP

30

Cluster Algorithm
Since electromagnetic and hadronic particles produce quite different patternsof energy sharing between calorimeter towers, second moments of the measured showers are often used to differentiate between them. The first stepin the calibration for the EMCal data is the conversion of the raw module
information into energy and timing information, referred to as ”calibrated
towers”. Because an electromagnetic shower usually spreads over more than
one module, this calibrated towers are passed the Cluster Algorithm, whichsummarizes associated areas of towers into the so-called ”clusters”. The
Cluster Algotithm can be divided into the following steps[39]:• Find a cluster, which is a group of adjacent towers each with an energy
above the noise threshold (see the Table 2.1).
• Find the local maxima of the cluster. A local maximum is a module
above the preak threshold, given in the Table 2.1, with the maximum
amplitude in the 3×3 region surrounding it.
• If more than one local maximum is found, split the cluster according
to amplitude and positions of the maxima.
• Calculate the first and second moments of the clusters as the seed forthe determination of the impact position.
• Compare the shape of the cluster with the expectation for an electromagnetic shower for particle identification (χ2 method described next).
• Compute and correct the total energy for the cluster.
For each cluster the newly computed values such as corrected energy andposition are stored in a list of clusters that can be used in the analysis.

Minimum tower energy
Minimum cluster energy
Minimum peak energy

PbSc
10MeV
15MeV
80MeV

PbGl
14MeV
60MeV
80MeV

Table 2.1: The parameters of energy used by the Cluster Algorithm[39]CHAPTER 2. EXPERIMENTAL SETUP

31

The one of the corrected energy, ”Ecore ” are used for the photon analysis.
Assume that there is a cluster from photon; it hit one tower, E5 and spreadout 3×3 towers from E1 to E9 but mainly deposited energy at E2, E4, E5,
E6 and E8 shown as the Figure 2.2.4.

Figure 2.10: Image of a Cluster
The Ecore energy is defined as[38],Ecore =

core
X

Eimeas ,iPwhere Eimeans is the measured energy in i-th tower. coreis defined as sumi
ming of the towers belonging to the ”core” towers. The ”core” towers aredefined in the following condition:
Eipred> 0.02,
meas
Eall

meas
Eall
=

all
X

Eimeas ,imeaswhere Eallis the sum of measured energy in all towers belonging to the”peak area” cluster Eipred is the predicted energy (using the parametrizationand the acual measured impact point) for an electromagnetic particle of
meas
.
Eall
meas
and if mainly deIn above case, E1+E2+· · ·+E9 corresponds to Eall
posited energy passed the ”core” condition, Ecore would be E2 + E4 + E5 +E6+E8. So then Ecore can chose the energy from highly identified as photon.

CHAPTER 2. EXPERIMENTAL SETUP

32

Not only for photons but also electrons to be identified, χ2 method wasintroduced. that is,
X (Eipred − Eimeas )2
χ2 =
σi2
i
where Eimeas and Eipred are same value defined previously. The variance σi isgiven as,Ã

σi2 = q(E)+C ·Eipred ·µ

E predEi
1 + a1 · i+ a2 ·EE¶2

Ã

E pred+ f (E, θ) · 1 − i
E

!!

,

which provides the dependence of the fluctuations on the energy and angle ofincidence, f (E, θ), and on losses to the total energy due to the thresholds usedin the clustering, q(E). This χ2 value characterizes how ”electromagnetic” aparticular shower is and can be used to discriminate against hadrons. The
important new feature of this model is that the fluctuations are also parameterized. Therefore, the resulting χ2 distribution is close to the theoreticalone and it is nearly independent of the energy or the impact angle of theelectron. The χ2 distributions for 2 GeV/c electrons and pions (with energy
deposit above minimum ionization) are shown in the Figure 2.2.4. The arrowmarks the χ2 cut corresponding to 90 % electron efficiency[37].

Figure 2.11: χ2 distribution for showers induced by 2 GeV/c electrons andpions in the PbSc calorimeter [37]

CHAPTER 2. EXPERIMENTAL SETUP

2.3

33

Computing

One cannot collect all data at every crossing since there’s too many empty
crossing at the RHIC; collisions occur at about 10kHz for Au-Au, while thebeam crossing rate occurs at 9.6MHz. These data need to be selected andarchived in order to optimize the physics interest of PHENIX. In this section, we’re going to overview the system of the PHENIX On-Line System[40]which was designed to seamlessly accommodate improvements in the design
luminosity. Furthermore, the PHENIX’s general Off-Line analysis system
will be roughly described subsequently.
The On-Line system has two levels of triggering, denoted as Level-1(LVL1) and Level-2 (LVL2). The LVL1 trigger operates in a synchronous
piplined mode, generates a decision every 106 ns and has an adjustable latency of some 40 beam crossings. It consists of two separate subsystems, theLocal Level-1 (LL1) system which communicates directly with participating
detector system such as BBC, MuID, ZDC, EMCal and RICH and the Global
Level-1 (GL1) which receives and combines these data to provide a trigger
decision. The LVL1 trigger and lower levels of the readout are clock-driven
by bunch-crossing signals from the RHIC clock. The higher levels of readout
and the LVL2 trigger are data-driven where the results of triggering and dataprocessing propagate to the next higher level only after processing of a given
event is completed.
The data collection and storage can be described in the Figure 2.3. Signals from the various PHENIX subsystems (e.g.the DC in the Figure 2.3) areprocessed by Front End Electronics which are fed into Front End Modules(FEM) for each subsystems, that convert detector signals into digital event
fragments. This involves analog signal processing with amplification andshaping to extract the optimum time and/or amplitude information, development of trigger input data and buffering to allow time for data processing
by the LVL1 trigger and digitization. This is carried out for all detector
elements at every beam crossing synchronously with the RHIC beam clock.
The timing signal is a harmonic of the RHIC beam clock and is distributed
to the FEM’s by the PHENIX Master Timing System which are fed into the
Master Timing Modules (MTM). The LVL1 trigger provides a fast filter for
discarding empty beam crossings and uninteresting events before the data isfully digitized. If the LVL1 trigger accepts an event, a signal is transmitted
to the Granule Timing Module (GTM) which generates an accept signal thatis transmitted to the detector FEM’s in the Interaction Region (IR).

CHAPTER 2. EXPERIMENTAL SETUP

GL1
Busy

GTM

MTM

RHIC clocks

So
ut
C
ZD

Data packets
over fiber~350000 ch

DCM

Data Packets
over Parallel
FIFO InterfaceD
ov atapa er Pa
ss NE ck
in V etg
Bu IS ss To
kenPartitioner
DCB

FEM

Clock

RHIC
Computing
Facility
End
User

Busy

Clock, Trigger,
Mode bits
over fiberhA(e S u.g b s.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

Shield Wall

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

34

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

SEB
SEB
SEB
SEB
ATM Switch
ATP

Linux Farm
~600 CPU's

tapestorage
1.2PB

20MB/s
250TB/yr

Figure 2.12: Schematic diagram of the PHENIX On-Line system
Once an event is accepted, the data fragments from the FEM’s and primitives from the LVL1 trigger move in parallel to the Data Collection Modules(DCM). The PHENIX architecture was designed so that all detector-specificelectronics end with the FEM’s, so that there is a single set of DCM’s that
communicate with the rest of the DAQ system. The only connection between
the Interaction Region (IR) where the FEM’s are located and the Counting
House (CH) where the DCM’s are located is by fiber-optic cable. The DCM’s
perform zero suppression, error checking and data reformatting. Many parallel data streams from the DCM’s are sent to the Event Builder (EvB). The
EvB assembles a full event from the individual fragments of data from the
DCM’s. When the event is fully assembled and passed the LVL2 trigger,
it is temporarily stored on a local disk. A fraction of the events are madeavailable to processes on a farm of computer’s running Linux for On-Linemonitoring purposes. Long-term storage is provided by a High Performance
Storage System (HPSS) type robot system operated by the RHIC Computing
Facility (RCF). The average rate of transfer of data to HPSS is 20 Mbytes/s
but for short time intervals rates as high as 60 Mbytes/s have been obtained.

CHAPTER 2. EXPERIMENTAL SETUP

35

All raws data coming from detectors have been assembled in the PHENIX
Raw Data Format(PRDF). They are kept to less than 2 Gbytes in size, contain nearly 12 hours to reconstruct. Collections of events over a certain periodof time represent the indivirual ”runs”. Runs are subdivided into segments
to keep the size of the output files low, and to make parallel processing during
the offline Data Summary Table (DST) production possible, where the raw
data are converted into quantities with more physical meaning.
PHENIX reconstruction, analysis and simulation code consists of about
500,000 lines of codes written in the C++ language. All reconstructed data is
kept in HPSS, however, copying groups of files from HPSS, running analysis
code over them before deletion and subsequent copy of the next group is
cumbersome process at best. More importantly, it is not simultaneously
realizable by large groups of users on an individual basis. To solve this
delemma, an Analysis Train that registers individual users code and scansthrough a given dataset in an orderly and optimized fashion was introduced
and has been operating from the data taken in 2003-2004. The Analysis
Train uses the surver called Fun4AllServer [41] which can keep multiple node
trees and chose the data that all calibrations are final. ROOT, an objectoriented analysis framework developed at CERN is used for an output file tofill and visualize histograms. We got in the Analysis Train and could collect
all statistical of the data without calibrations.

Chapter 3
Analysis
3.1

Quest for ω mesons

Figure 3.1: Image of the radiative decay mode of ω hitting to the EMCal
36

CHAPTER 3. ANALYSIS

37

The measurement of ω mesons in the heavy ion collisions is really the”Quest”. About 9% of ωs are going to π 0 and γ, then 98.8% of those π 0
is going to 2γ. That is, we have to reconstruct 3γ from huge number of γ
measured in EMCal ; approximately 300 γ are measured per one collisions.
The formula of the reconstructed ω mass is simple. After identifying γ,
the energy, momentum and hit positions of γ can be measured. The invariant
mass of π 0 is therefore,
Mπ20 = 2E1 E2 (1 − cosθγγ ),(3.1)

where E1 and E2 are the measured energy of 2γ (suppose γ1 and γ2 arbitrarily) and θγγ is the opening angle between 2γ calculated from the hit positions.
First we reconstruct π 0 and select γ1 and γ2 as ”π 0 from ω” candidate. Next
we conbine third γ (suppose γ3 ) and reconstruct as,
Mπ20 γ = (E1 + E2 + E3 )2 − p2x − p2y − p2z ,(3.2)

where,x1

x3+ E3 · q,
x21 + y12 + z12
x22 + y22 + z22
x23 + y32 + z32
y1y2
y3
py = E1 · q+ E2 · q+ E3 · q,
x21 + y12 + z12
x22 + y22 + z22
x23 + y32 + z32
z1z2
z3
pz = E1 · q+ E2 · q+ E3 · q,
x21 + y12 + z12
x22 + y22 + z22
x23 + y32 + z32

px = E1 · q+ E2 · qx2(the coordinates of x,y and z are defined in the Appendix).
The question is, ”does it really possible to search out ω mesons in thehigh multiple collisions that produce huge conbinatorial background?” To
find the feasibility, we execute the simulation in advance then calculate anaccpetance and a multiplicity dependence. Furthermore, we search the bestparameters such as momentum and energy for selecting π 0 and γ using both
simulation and real data. In the last section of this chapter, we describe theselection values for the real data analysis.

CHAPTER 3. ANALYSIS

3.2

38

Data Set

The data-set is Au+Au collisions at C.M.S. collision energy per nucleon pairsof 200GeV taken at the PHENIX from the year of 2003 to 2004; this period
is called, ”Run4”. The Figure 3.2 shows the integrated luminosity delivered
by RHIC during Run4, as well as other Runs. Run4 has consistently higher
bunch intensities (up to 109 for Au+Au) delivered by ingectors than otherprevious runs. The integrated luminosity is up to 1368 µb−1 for PHENIX.
The number of events we used from the data is Nevt = 1.06 × 109 (fullstatistics).

Figure 3.2: The Integrated Luminosity vs Weeks into the Run

CHAPTER 3. ANALYSIS

39

3.3

Simulation

3.3.1

Event Generator

The two ion beams accelerated by RHIC will collide and interact. A single
interaction is called an ”event”. An event is fully specified by the position
coordinate of the interaction point called the ”vertex”, or more specificallythe ”primary vertex”. For purposes of the simulation program, an event isviewed as a list of the particles with their type, energies, momenta, the pointof production and the time of production which can be conveniently chosen
to be the zero of the time. Naturally, the characteristics of the real events
will be known only after the actual experiments begin taking data. Until
then we must rely on various event generators which attempt to simulate
the experimental events by making certain model assumptions. These event
generators are detailed Monte Carlo codes. We used the one of such event
generators called as ”EXODUS”, the package of which was created in 1998.
We generated 1.5 M events, one ω meson per event for following status,• 1.0 < pT < 14.0 [GeV/c], enhanced at low pT (the Figure 3.3 shows
the pT histogram)• −0.5 < y < 0.5• 0.0 < φ < 2π (refer the Appendix A Kinematics for each parameter).
primary pTprimary pT
Entries 1453629
Mean
2.448
2.444
RMS

106

105

104

0

2

4

6

8

10

12

14
[GeV/c]Figure 3.3: The histogram of primary pT

CHAPTER 3. ANALYSIS

3.3.2

40

Detector Simulation

The PHENIX detector is very complex in character with a large variety
of detector types and materials inside it. To simulate such PHENIX detector, ”PISA”, PHENIX Integrates Simulation Application[44] was introduced.
The PISA code is based heavily on the CERN software libraries[45]. Specifically, PISA is the PHENIX implementation of the GEANT geometry andevent particle tracking software system. Using PISA, a PHENIX simulator
can pick which (or all) aspects of the whole PHENIX detector geometry to
introduce into an event simulation.

Figure 3.4: Demonstration of simulated 100 ω mesons’ tracks (red lines denote electron and positron, blue dotted lines denote photons and green dottedlines denote muons). EMCal, PC1/PC2/PC3, and DC are drawn (see theChapter 2, Experimental setup).

CHAPTER 3. ANALYSIS

41

Count

If we input the information of particles that generated bey the event
generator, PISA will make them decay according to their branching ratio andlifetimes. The Figure 3.4 shows a demonstration of 100 ω going to various
decay modes and hitting to (or straying from) the EMCal. We reconstruct
ω mesons by calculating the Formula 3.2 after inputting about 7.5 million
ω into PISA. The Figure 3.5 is an example plot of reconstructed invariant
mass of ω. There is a slight tail at lower region than ω mass (782 MeV/c2 )since some photons convert to electrons due to detectors located in front of
EMCal and deposite lower energies.

18000
16000
14000
12000
10000
8000
6000
4000
2000
0
0

0.2

0.4

0.6

0.8

1

1.2

1.4
2
[GeV/c ]Figure 3.5: Invariant mass spectrum of single ω event for all pT .
The geometrical acceptance can be measured from this simulation bylooking at,
dNω /dpT |reconstructed²geo =,(3.3)
dNω /dpT |input
where dNω /dpT |reconstructed and dNω /dpT |input denote the number of reconstructed ω mesons and input ω mesons for each pT within the 2 sigmas ofω mass, respectively. The calculated acceptance is shown in the Figure 3.12
together with efficiencies of Multiple Dependence Correction (explained in
the next section).

CHAPTER 3. ANALYSIS

3.3.3

42

Multiplicity Dependence

In the previous section, we calculate the acceptance using single event simulation, that is the so-called ”single function (SPC)” which represents correction
due to geometrical acceptance, decay in flight, reconstruction efficiency andmomentum resolution etc. In addition to this correction function, we haveto take it into acount the multiplicity dependence as long as dealing withmultiple collisions such as Au+Au collisions for this analysis. This is theso called ”multiplicity dependence correction function (MDC)”. Since thematerial for this analysis is γ, we discuss only the EMCal’s MDC. Multiple collisions generate huge backgounds to the EMCal and no wonder thosebackgrounds interfere cluster algorithm. We consider two effects, the one is”cluster merging” and the other is ”cluster splitting”. As shown those images
in the Figure 3.6, backgounds attached to the true clusters coming from ω
cause to merge a cluster or split a cluster.
To evaluate such MDC, we use the technique called ”embedding”[46]; embedding of the simulated particles into a real event. The Figure 3.7 shows
the main flow of the embedding program[39]. A DST(See the Chapter 2
Computing) containing real event is read in together with simulated DST
that generated in previous. For each selected real event, the tower information is extracted from the DST and merged with the tower data from on
simulated event. The merging basically involves the addition of the energies
as illustrated in the Figure 3.7. The list of merged towers is now the basis for a new clustering. Due to the added information from the simulated
event, the resulting list of merged clusters is different from the list of clusters
from the real event. A comparison yields the modified or new clusters in themerged event and the lost clusters from the real event.

True Cluster
Background

Cluster Merging

Cluster Splitting

Figure 3.6: The effect of multiplicity on Cluster Algorithm

CHAPTER 3. ANALYSIS

Figure 3.7: Embedding algorithm [39]43CHAPTER 3. ANALYSIS

44

Count

We input about 1 million single ω to 1.2 million events of real data, andreconstruct the invariant mass using the Formula 3.2 (the Figure 3.8 is an
example). It can been seen that ω mesons merging to the backgrounds.
1800
1600
1400
1200
1000
800
600
400
200
0
0

0.2

0.4

0.6

0.8

1

1.2

1.4
2
[GeV/c ]Figure 3.8: Invariant mass spectrum of simulated ω embedding to the real
data

Count

350

Count

Count

To extract the clear peak position and width of ω mass from the results,
we choose only true clusters that are from the simulated DST and subtract
the background (note that it is possible because we know the input data ofsimulation). After fitting the gaussian, we get the parameters of ω mass (seethe Figure 3.9). The results are shown in the Figure 3.10 and the Figure
3.11. Here, ”0-20% cent”, ”60-92% cent” and ”MinBias” mean the highmultiplicity, low multiplicity and no selection of multiplicity respectively (thedetails are explained in the Section of Data and Signal Selection).
1000

300

0-30% cent

MinBias60-92% cent

300

200

600

250
200

150
400

150

100

100

200

50
0
0

400
350

800

250

450

50
0.2

0.4

0.6

0.8

1

1.2

1.4
2
[GeV/c ]

0
0

0.2

0.4

0.6

0.8

1

1.2

1.4
2
[GeV/c ]

0
0

0.2

0.4

0.6

0.8

1

1.2

1.4
2
[GeV/c ]Figure 3.9: Invariant mass spectrum reconstructed by the true clusters A
peak around 0.1-0.2(GeV/c2 ) is due to the cluster splitting causing the measured energy lower than true energy (the more we go to the high multiplicity,
the more peaks arise).

2ω mass [GeV/c ]CHAPTER 3. ANALYSIS

45

0.8
0.79
0.78
0.77
0.76
0.75
0.74
0.73

SPC

0.72

SPC + MDC(MinBias)

SPC + MDC(60-92% cent)
SPC + MDC(0-20% cent)

0.71
0.7
0

2

4

6

8

10
ω pT [GeV/c]2

ω width [GeV/c ]Figure 3.10: Peak position of ω mass. Black points are from the single ωsimulation (considering only SPC) and the others are from the embedding.

0.1
SPC

0.09

SPC + MDC(60-92% cent)

0.08

SPC + MDC(MinBias)
SPC + MDC(0-20% cent)

0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
0

2

4

6

8

10
ω pT [GeV/c]

Figure 3.11: Width of ω mass. Black points are from the single ω simulation(considering only SPC) and the others are from the embedding.

CHAPTER 3. ANALYSIS46

MDC E fficiency

Efficiency

It can been seen that the peak position gets higher and the width getswider if we go to the higher multiplicity. Needless to say that those corrections are indispensable to the study of the mass modification.
We also calculate the efficiency of MDC together with SPC using the
Formula 3.3. The Figure 3.12 shows the result. Here, note that we don’t
input the kinamitcs cuts for reconstructing ω mesons since we just see the
MDC effect. The total efficiency will be calculated later after inputting theappropriate cuts for ω reconstruction.

1.2
1
0.8

-2

10

0.6
0.4

MDC(60-92% cent) / SPC
MDC(MinBias) / SPC

0.2

-3

10

0
0

SPC

MDC(0-20% cent) / SPC

2

4

6

SPC + MDC(60-92% cent)
SPC + MDC(MinBias)
SPC + MDC(0-20% cent)

10-4

0

2

4

6

8

10
ω p T [GeV/c]

Figure 3.12: Efficiency of SPC and SPC+MDC(left) with the ratio of theefficiency of MDC/SPC for each multiplicity(right).

810
ω p T [GeV/c]

CHAPTER 3. ANALYSIS

3.3.4

47

Cut Optimization

The main issue of this analysis is the huge combinatorial backgound inevitable for reconstructing particles from the three-body decay mode, i.e.
ω → π 0 γ where π 0 → 2γ. If there’s no specific cuts for reconstructing ω,
Signal to Background (include signal) ratio, S/(B +S) ' S/B is less than 103
for all statistics of data(see the Figure 3.23) and that makes extremely hard
to identify√ ω mesons. So then an improvement of S/B or the peak significance, S/ B has a vital importance. Here, we consider following parametersthat should have a great influence on the peak significance.
• Transverse Momentum Cut (pT ) of π 0• Photon Energy Cut (except photons from π 0 candidate)• Width of π 0 Invariant Mass

12000
10000
8000
6000

×10

Count

Count

√
We investigate those cuts by calculating S/ B according to transverse momentum of ω. The Figure 3.13 shows a roughly method. The simulation data
is used for calculating the number of signals and some real data are used for
calculating backgounds (it might be include very few signals but ignorable).

3

1600

SingleSimulation

Real Data

1400

20M evt

1200

7.5M evt

1000(1omega per 1evt)

800
600

4000

400
2000
0
0

200
0.2

0.4

0.6

0.8

1

1.2

1.4
2
[GeV/c ]

S
*

0
0

0.2

0.4

0.6

0.8

B

*
*
*
Cuts of each parameters

Figure 3.13: Method of Cut Optimization

1

1.2

1.4
2
[GeV/c ]CHAPTER 3. ANALYSIS
Photon Energy cuts dependence
no cuts for others

S/ sqrt B

5.5<pT(omega)<6.5 [GeV/c]

48

First Try

7.5
7
6.5
6
5.5
5
4.5

no cut
1.5
1.0
1.25
0.75

1.75

2.0

[GeV]

Pi0 width cuts dependence

Pi0pT cuts dependence

no cuts for others

S/ sqrt B

no cuts for others

S/ sqrt B

11.5
11
10.5
10
9.5
9
8.5
8

8

7.8

7.6

7.4

7.2

7.5
7

3.0
2.5
no cut 1.5
2.0
2.75
1.75
2.25
1.25

[sigma][GeV/c]
2

1.75

1.5

1.25

1.0

0.75

Pi0pT: >1.5(GeV/c)
Pi0 width: within 1.25(sigma)

Second Try
14
12
10
8
6
4

[GeV]

Energy: no cut
Pi0 width: within 1.25(sigma)

Pi0pT: >1.5(GeV/c)
Energy: no cut
12

12

11

11

10

10

9

9

8

8

[GeV/c]7More Try ...
Energy: >0.75(GeV)
Pi0 width: within 1.25(sigma)

7

Pi0pT: >1.5(GeV/c)
Pi0 width: within 1.25(sigma)[sigma]Pi0pT: >1.5(GeV/c)
Energy: > 0.75(GeV)

Figure 3.14: Flow chart of Cut Optimization√
If calculated S/ B has a peak, so then the cut value which makes thepeak is the best cut. However, the best cut cannot be determined by one trial
since those cuts, mostly pT cut and energy cut, are correlative. The Figure
3.14 shows √a flow chart of this study (e.x. 5.5< pT (ω) < 6.5). First, we
calculate S/ B with no cuts for each value and find the point that makes
the√peak (yellow stars in the Figure 3.14). Next, we again calculate S/ B after
applying cuts that make the peak before. The trial is continued until best
cuts do not change anymore. The results are shown in the Figure 3.15, 3.16
and 3.17. Cuts are determined
four times showing in the succeeding Tables.
√
Note that calculated S/ B is relative value since we put single omega muchmore
√ than estimated number of ω from the collisions. Therefore, absolute
S/ B will be calculated in the next section after estimating the number ofω and considering efficiency for all cuts.

CHAPTER 3. ANALYSIS

no cut

1.25

1.5

49

1.75 2.0 2.25 2.5 2.75 3.0
0.16

0.03

0.14
0.025

0.12

0.02

0.1
0.08

0.015

0.06

0.01

0.04
0.005

0.02

0

0

0.5 < pT(omega) < 1.5(GeV/c)[GeV/c]1.5 < pT(omega) < 2.5
3.5

0.8
0.7

3

0.6

2.5

0.5

2

0.4
1.5

0.3

1

0.2

0.5

S / sqrt B

0.1
0

0

2.5 < pT(omega) < 3.5

3.5 < pT(omega) < 4.5
60

14
12

50

10

40

8

30

6
20

4

10

2
0

0

4.5 < pT(omega) < 5.5
200

5.5 < pT(omega) < 6.5
500

180
160

400

140
120

300

100
80

200

60
40

100

20
0

0

7.5 < pT(omega) < 8.5

6.5 < pT(omega) < 7.5
1000

1600
1400

800

1200
600

1000
800

400

600
400

200

200
0

0

8.5 < pT(omega) < 9.5

9.5 < pT(omega) < 10.5√
Figure 3.15: S/ B calculation for π 0 pT . Black: First Trial(with no cut),
Red: Second Trial(with Cut#1 except π 0 pT cut), Green: Third Trial(withCut#2 except π 0 pT cut), Blue: Forth Trial (with Cut#3 except π 0 pT cut),
Magenta: Fifth Trial(with Cut#4 except π 0 pT cut).

CHAPTER 3. ANALYSIS

no cut

0.75

1.0

1.25

50

1.5

1.75

2.0
0.16

0.03

0.14
0.025

0.12

0.02

0.1
0.08

0.015

0.06

0.01

0.04
0.005

0.02

0

0

0.5 < pT(omega) < 1.5(GeV/c)[GeV]

1.5 < pT(omega) < 2.5
3.5

0.8
0.7

3

0.6

2.5

0.5

2

0.4
1.5

0.3

1

0.2

0.5

S / sqrt B

0.1
0

0

2.5 < pT(omega) < 3.5

3.5 < pT(omega) < 4.5
60

14
12

50

10

40

8

30

6
20

4

10

2
0

0

4.5 < pT(omega) < 5.5
200

5.5 < pT(omega) < 6.5
500

180
160

400

140
120

300

100
80

200

60
40

100

20
0

0

7.5 < pT(omega) < 8.5

6.5 < pT(omega) < 7.5
1800

1000

1600
800

1400
1200

600

1000
800

400

600
400

200

200
0

0

8.5 < pT(omega) < 9.5

9.5 < pT(omega) < 10.5√
Figure 3.16: S/ B calculation for photon energy cut. Black: First Trial(withno cut), Red: Second Trial(with Cut#1 except γ energy cut), Green: Third
Trial(with Cut#2 except γ energy cut), Blue: Forth Trial (with Cut#3 except γ energy cut), Magenta: Fifth Trial(with Cut#4 except γ energy cut).

CHAPTER 3. ANALYSIS

2

1.75

1.5

1.25

51

1.0

0.75
0.16

0.03
0.15

0.028
0.14

0.026
0.13

0.024
0.12

0.022
0.11

0.02

0.5 < pT(omega) < 1.5(GeV/c)[sigma]1.5 < pT(omega) < 2.5
3.6

0.8

3.4

0.75

3.2
0.7

3
2.8

0.65

2.6

0.6

2.4

S / sqrt B

0.55

2.2

2.5 < pT(omega) < 3.5

3.5 < pT(omega) < 4.5
60

15

55

14

50

13

45

12

40

11

35

10

30

9

25

8

20

7

15

6

4.5 < pT(omega) < 5.5

5.5 < pT(omega) < 6.5
500

180
160

400

140
120

300

100
80

200

60
40

100

20
0

0

7.5 < pT(omega) < 8.5

6.5 < pT(omega) < 7.5
2000
900

1800

800

1600

700

1400

600

1200

500

1000

400

800

300

600

200

400

100

200

0

0

8.5 < pT(omega) < 9.5

9.5 < pT(omega) < 10.5√
Figure 3.17: S/ B calculation for π 0 mass width. Black: First Trial(withno cut), Red: Second Trial(with Cut#1 except π 0 mass width cut), Green:
Third Trial(with Cut#2 except π 0 mass width cut), Blue: Forth Trial (with
Cut#3 except π 0 mass width cut), Magenta: Fifth Trial(with Cut#4 except
π 0 mass width cut).

CHAPTER 3. ANALYSIS

52

0.5 < pT (ω) < 1.5
1.5 < pT (ω) < 2.5
2.5 < pT (ω) < 3.5
3.5 < pT (ω) < 4.5
4.5 < pT (ω) < 5.5
5.5 < pT (ω) < 6.5
6.5 < pT (ω) < 7.5
7.5 < pT (ω) < 8.5
8.5 < pT (ω) < 9.5
9.5 < pT (ω) < 10.5

Cut #1π 0 pT Cut γ energy Cut
no cutno cutno cutno cut1.25<
no cut1.5<
no cut1.5<
no cut1.75<
no cut1.75<
no cut2.0<
no cut2.0<
no cut2.0<0.75<

π 0 mass width
1.25σ
1.25σ
1.25σ
1.25σ
1.25σ
1.5σ
1.5σ
1.5σ
1.25σ
1.25σ

0.5 < pT (ω) < 1.5
1.5 < pT (ω) < 2.5
2.5 < pT (ω) < 3.5
3.5 < pT (ω) < 4.5
4.5 < pT (ω) < 5.5
5.5 < pT (ω) < 6.5
6.5 < pT (ω) < 7.5
7.5 < pT (ω) < 8.5
8.5 < pT (ω) < 9.5
9.5 < pT (ω) < 10.5

Cut #2π 0 pT Cut γ energy Cut
no cutno cutno cutno cut
1.25<
0.75<
1.5<
0.75<
1.5<
0.75<
1.75<
1.0<
1.75<
1.25<
2.0<
1.25<
2.0<
1.5<
2.75<
1.5<

π 0 mass width
1.25σ
1.25σ
1.25σ
1.25σ
1.25σ
1.5σ
1.5σ
1.5σ
1.25σ
1.5σ

0.5 < pT (ω) < 1.5
1.5 < pT (ω) < 2.5
2.5 < pT (ω) < 3.5
3.5 < pT (ω) < 4.5
4.5 < pT (ω) < 5.5
5.5 < pT (ω) < 6.5
6.5 < pT (ω) < 7.5
7.5 < pT (ω) < 8.5
8.5 < pT (ω) < 9.5
9.5 < pT (ω) < 10.5

Cut #3π 0 pT Cut γ energy Cut
no cutno cutno cutno cut
1.25<
0.75<
1.5<
0.75<
2.0<
0.75<
2.25<
1.0<
2.75<
1.25<
3.0<
1.25<
3.0<
1.5<
3.0<
1.5<

π 0 mass width
1.25σ
1.25σ
1.25σ
1.25σ
1.25σ
1.5σ
1.5σ
1.5σ
1.25σ
1.5σ

0.5 < pT (ω) < 1.5
1.5 < pT (ω) < 2.5
2.5 < pT (ω) < 3.5
3.5 < pT (ω) < 4.5
4.5 < pT (ω) < 5.5
5.5 < pT (ω) < 6.5
6.5 < pT (ω) < 7.5
7.5 < pT (ω) < 8.5
8.5 < pT (ω) < 9.5
9.5 < pT (ω) < 10.5

Cut #4π 0 pT Cut γ energy Cut
no cutno cutno cutno cut
1.25<
0.75<
1.5<
0.75<
2.0<
1.0<
2.25<
1.25<
2.75<
1.5<
3.0<
1.5<
3.0<
1.5<
3.0<
1.5<

π 0 mass width
1.25σ
1.25σ
1.25σ
1.25σ
1.25σ
1.5σ
1.5σ
1.5σ
1.25σ
1.5σ

CHAPTER 3. ANALYSIS

3.3.5

53

Feasibility

10

1

a)

-1

-2

10

-3

PHENIX Data

-4

KKP FF-5

Kretzer FF

10
10

-6

10

-7

10

∆σ/ σ (%)

PHENIX ω/ π0 d+Au sNN=200GeV

1.6
1.4
1.2
1.0

-8

0.8

10

(Data-QCD)/QCD

pi 0 cross-section andomega/pi 0 ratio
Ratioω / π03E*d σ/dp-2(mb⋅GeV ⋅c3)

10

3

We evaluate√ the SPC and the MDC. Furthermore, we find the cuts that
improve S/ B ratio. So then everyone would think that, ”In the Real Dataof Au+Au, can ω mesons (via radiative decay mode)√ be truely seen?”. Here,
we study it’s actual feasibility, that is, absolute S/ B value for full statistics.
First, let us estimate the number of measured ω coming from Au+Au
collisions. We take advantage of the cross section of π 0 [47] and the ratioof ω/π 0 [48] that are already shown up for the PHENIX’s results in p+p
collisions (see the the Figure 3.18). The cross section of π 0 are fit to the

40
20
0
-20
-40

b)

4

c)

0.6

1.8
1.6

2

ω/ π0 p+p sNN=200GeV

ω → π0π+πω → π0γ
PYTHIA

1.4
1.2
1.0

0

0.8

4

0.6

d)

2

0.4
0.2

0
0

5

10

15

pT (GeV/c)

0

2

4

6

8

10

p T (GeV/c)

Figure 3.18: The invariant differential cross section for inclusive π 0 production and the results from NLO pQCD calculations with equal renormalizationand factorization scales of pT [47] (left). ω/π 0 in d+Au and p+p collisions√
at sN N = 200GeV [48] (right).

CHAPTER 3. ANALYSIS

54

following Hargedorn-type function [47] as,
E · d3 σ/dp3 = A · (p0t )n /(pT + p0T )n .

(3.4)

The fit parameters are A=386mb·GeV−2 · c3 , p0 =1.219 GeV/c and n=9.99
for both PbSc and PbGl. So then the estimated ω cross section in Au+Au
collisions is,(E · d3 σ/dp3 )ω = (E · d3 σ/dp3 )π0 · Rω/π0 /σpp ,(3.5)

where Rω/π0 is the ω/π 0 ratios in p+p collisions, (supposed 0.85 as seen in√
the Figure 3.18), σpp is the total cross section of p+p at sN N = 200GeV as
42.2 mb[5]. The Figure 3.19 shows the slope of the estimated cross sectionof ω. While the estimated number of measured ω is written as,Nωraw = 2πpT · (E · d3 σ/dp3 )ω · BR · Nevt · Ncoll · ef f,

(3.6)

3

Ed3σ/dp ω

where BR is the branching ratio of ω → π 0 γ as 8.9%[5], Nevt is the number of
events which can be evaluated from the real data analysis, Ncoll is the numberof binary collisions calculated from the Au+Au Glauber Monte Carlo[49],which is based on a simple geometrical picture of a nucleus-nucleus collisionand ef f is the total efficiency including all cuts.

1

10-1

10-2
10-3
10-4
10-5
10-6
10-7
10-8
10-9

0

1

2

3

4

5

6

7

8

9
10
pT [GeV/c]

Figure 3.19: Estimated cross section of ω by the Formula 3.5 ignoring all
errors.

CHAPTER 3. ANALYSIS

55

Total Efficiency

So then we calculate the total efficiency for each cuts determined in previous. The Figure 3.20, 3.21 and 3.22 show the results for three multiplicity.
Applying all values, we estimate the number of ω that could be measured inthis analysis ignoring an effect of the matter that created in the heavy ion
collisions. The number is tabulated in the√ Table 3.3.5. Using this number
and saling down the relative S/B and S/ B that we calculated
for the cut√
optimization, finally we evaluate the absolute S/B and S/ B for the real
data analysis√ (see the Figure 3.23 and 3.24). It shows that tighter cuts improve S/ B significantly at high pT in MinBias and central events, at mid
pT in peripheral events. The value is up to 4, implying that it is possible tomeasure ω if we use the appropriate cuts and read full statistics.

-2

10

-3

10

10-4

Cut#1 (MinBias)
Cut#2 (MinBias)
Cut#3 (MinBias)
Cut#4 (MinBias)
0

2

4

6

8

10
ω pT [GeV/c]

Figure 3.20: Total Efficiency for each Cuts (see the previous section) in the
MinBias Event

Total Efficiency

CHAPTER 3. ANALYSIS

56

-2

10

-3

10

10-4

Cut#1 (0-20% cent)Cut#2 (0-20% cent)Cut#3 (0-20% cent)Cut#4 (0-20% cent)
0

2

4

6

8

10
ω pT [GeV/c]

Total Efficiency

Figure 3.21: Total Efficiency for each Cuts in the 0-20% centrality event

-2

10

-3

10

10-4

Cut#1 (60-92% cent)Cut#2 (60-92% cent)Cut#3 (60-92% cent)Cut#4 (60-92% cent)
0

2

4

6

8

10
ω pT [GeV/c]

Figure 3.22: Total Efficiency for each Cuts in the 60-92% centrality event

CHAPTER 3. ANALYSIS

0.5 < pT (ω) < 1.5

1.5 < pT (ω) < 2.5

2.5 < pT (ω) < 3.5

3.5 < pT (ω) < 4.5

4.5 < pT (ω) < 5.5

5.5 < pT (ω) < 6.5

6.5 < pT (ω) < 7.5

7.5 < pT (ω) < 8.5

8.5 < pT (ω) < 9.5

9.5 < pT (ω) < 10.5

Cuts
#1
#2
#3
#4
#1
#2
#3
#4
#1
#2
#3
#4
#1
#2
#3
#4
#1
#2
#3
#4
#1
#2
#3
#4
#1
#2
#3
#4
#1
#2
#3
#4
#1
#2
#3
#4
#1
#2
#3
#4

Nωest (MinBias)
7.70×105 ±1.02×105
7.70×105 ±1.02×105
7.70×105 ±1.02×105
7.70×105 ±1.02×105
2.46×105 ±1.68×104
2.46×105 ±1.68×104
2.46×105 ±1.68×104
2.46×105 ±1.68×104
8.71×104 ±5.89×103
6.93×104 ±5.08×103
6.93×104 ±5.08×103
6.93×104 ±5.08×103
2.29×104 ±1.67×103
1.92×104 ±1.53×103
1.92×104 ±1.53×103
1.92×104 ±1.53×103
7.72×103 ±5.54×102
6.82×103 ±5.2×102
5.72×103 ±4.76×102
5.06×103 ±4.47×102
2.71×103 ±1.91×102
2.27×103 ±1.74×102
2.02×103 ±1.64×102
1.81×103 ±1.55×102
1.03×103 ±7.04×10
8.54×102 ±6.40×10
6.56×102 ±5.60×10
5.80×102 ±5.26×10
3.73×102 ±2.63×10
3.08×102 ±2.38×10
2.66×102 ±2.21×10
2.50×102 ±2.14×10
1.72×102 ±1.18×10
1.43×102 ±1.07×10
1.20×102 ±9.77
1.20×102 ±9.77
7.76×10±5.447.24×10±5.25
6.98×10±5.15
6.98×10±5.15

57Nωest (0-20%)
3.92×105 ±8.35×104
3.92×105 ±8.35×104
3.92×105 ±8.35×104
3.92×105 ±8.35×104
1.06×105 ±1.27×104
1.06×105 ±1.27×104
1.06×105 ±1.27×104
1.06×105 ±1.27×104
3.66×104 ±4.23×103
2.88×104 ±3.75×103
2.88×104 ±3.75×103
2.88×104 ±3.75×103
1.21×104 ±1.39×103
1.03×104 ±1.28×103
1.03×104 ±1.28×103
1.03×104 ±1.28×103
4.03×103 ±4.59×102
3.51×103 ±4.28×102
2.89×103 ±3.88×102
2.58×103 ±3.66×102
1.46×103 ±1.61×102
1.16×103 ±1.43×102
1.06×103 ±1.37×102
9.73×102 ±1.31×102
5.22×102 ±5.74×10
4.67×10±5.38×10
3.79×102 ±4.88×10
3.54×102 ±4.72×10
1.67×102 ±2.01×10
1.46×102 ±1.88×10
1.22×102 ±1.71×10
1.15×102 ±1.66×10
6.19×10±8.04
5.46×10±7.55
4.43×10±6.79
4.43×10±6.79
3.23×10±4.01
2.88×10±3.78
2.79×10±3.72
2.79×10±3.72

Nωest (60-92%)
1.34×104 ±2.09×103
1.34×104 ±2.09×103
1.34×104 ±2.09×103
1.34×104 ±2.09×103
6.39×103 ±4.22×102
6.39×103 ±4.22×102
6.39×103 ±4.22×102
6.39×103 ±4.22×102
2.08×103 ±1.37×102
1.51×103 ±1.16×102
1.51×103 ±1.16×102
1.51×103 ±1.16×102
6.19×102 ±4.27×10
5.03×102 ±3.84×10
5.03×102 ±3.84×10
5.03×102 ±3.84×10
1.49×102 ±1.20×10
1.34×102 ±1.13×10
1.19×102 ±1.07×10
9.83×10±9.69
5.99×10±4.41
5.16×10±4.08
4.14×10±3.66
3.88×10±3.542.39×10±1.64
1.96×10±1.51
1.58×10±1.35
1.52×10±1.33
1.07×10±0.69
9.52±0.65
8.00±0.60
7.69±0.59
3.70±0.27
3.10±0.24
2.66±0.23
2.66±0.23
1.66±0.12
1.46±0.12
1.41±0.11
1.41±0.11

Table 3.1: Estimated number of measured ω at Nevt = 1.06 × 109 . Only theerror of efficiency is considered.

Absolute S/
B

CHAPTER 3. ANALYSIS

58

-1

10

MinBias

10-2
-3

10

-4

10

-5

10

-6

10

10-7

2

4

6

8

10
ω p T [GeV/c]

6

8

10
ω p T [GeV/c]

6

8

10
10
ω
ωp
pTT [G[GeeV/
V/cc]]

Absolute S/
B

10-1
-2

10

cent 0-20%

-3

10

10-4
-5

10

-6

10

bsoluteS/S/
BB
AA
bsolute

10-7

2

4

-1
10
2.5

-2

10

2

cent 60-92%

-3

10
1.5
10-4

1

-5

10

0.5
-6
10
10-70

2

44

Figure 3.23: Absolute S/B for MinBias(Nevt =1,057,22,600.) ,0-20% and60-92% central. Black: no cut, Red: with Cut#1, Green: with Cut#2, Blue:with Cut#3, Magenta: with Cut#4)

Absolute S/ B

CHAPTER 3. ANALYSIS

59

4.5
4

MinBias

3.5
3
2.5
2
1.5
1
0.5

Absolute S/ B

0

2

4

6

8

10
ω p T [GeV/c]

6

8

10
ω p T [GeV/c]3
2.5

cent 0-20%

2
1.5
1
0.5

Absolute S/ B

0

2

4

2.5

cent 60-92%

2

1.5

1

0.5

0

2

4

6

8

10
ω p T [GeV/c]√
Figure 3.24: Absolute S/ B for MinBias(Nevt =1,057,22,600.) ,0-20% and60-92% central. Black: no cut, Red: with Cut#1, Green: with Cut#2, Blue:with Cut#3, Magenta: with Cut#4)

CHAPTER 3. ANALYSIS

3.4

60

Signal Selection

We now discuss in detail of the real data analysis step by step. First, we chose
the Trigger and put cuts for the Photon Identification in EMCal. Next, wereconstruct π 0 from 2γ. Distribution of π 0 Invariant Mass shows that π 0 ’s
mean and width depend on transverse momentum of π 0 . And because ofthat, we have to carefully chose π 0 s for reconstructing ω. In the end, we put
Best Cuts for Reconstructing ω done by the feasibility study in the previous
section.

3.4.1

Trigger

Minimum Bias Trigger
The condition for accepting an inelastic Au+Au reaction is given by the BBC
and the ZDC. The collision has to trigger at least two photomultipliers at atime in both BBCs and cause a signal in both ZDCs. The Minimum Bias
Trigger is as the logical AND(&&) of a coincidence between the north andsouth BBC, as well as the north and south ZDC. This trigger accepts 92%
of the geometrical cross section for Au+Au collisions.
BBC Vertex Cuts
We require that the z vertex (determined by BBC) of a given event lies within
the range as,√|z| < 30 cm,

in order to exclude regions that are shadowed by the pole tips of the central
magnet and to minimize the background of scattered particles.

CHAPTER 3. ANALYSIS

61

Event Centrality
The ”centrality”, the value to characterize the heavy ion collisions is determined via the correlation between the energy deposit in the ZDC and thecharge deposit in the BBC (see the Figure 3.26). A brief explanation is shownin the Figure 3.25. For this analysis, we consider 3 parts of centrality, 0-20%
cent 60-92% and MinBias.
ZDC

ZDC

BBC

BBC

ZDC
BBC

BBC

ZDC

cent 60 - 92 %

BBC

BBC

ZDC

cent 20 - 60 %ZDC

cent 0 - 20 %Figure 3.25: The more the collisions is central, the more BBC collects theparticipants of the collisions and the less ZDC collects the spectators.

Figure 3.26: Correlation of BBC and ZDC

CHAPTER 3. ANALYSIS

3.4.2

62

Photon Identification

Excluded Modules
We use both PbSc and PbGl for measuring photons. Since there’re somebad modules in the EMCal that distort the energy measurement of a hit, wehave to apply quality criteria to the clusters. Modules without any energy
signal mostly due to faulty photomultipliers are denoted as ”dead”. It isalso critical to exclude modules that only sporadically contribute in a wrong
way to the signal. Those are denoted as ”warn” determined by suspicious
energy spectra. Additionally, the edge modules of the detector are considered
to have a dead neighbor to exclude clusters that suffer from leakage at thecalorimeter edge. So then we cut those modules, too.
√deadmap and warnmap cut

A map of the excluded area in each detector is shown in the Figure 3.27.
White area considered as dead and warn is all excluded during this analysis.

CHAPTER 3. ANALYSIS

63

35

1800

30

1600

25

1400
1200

20

1000

15

800

10

600

1800

30

1600

25

1400
1200

20

1000
15

800
600

10

400

5
0

35

200
0

0

35

1800

35

30

1600

30

0

10

20

30

40

50

60

70

1400

25

1200
20
15

200
0

10

20

30

40

50

60

70

0
2200
2000
1800
1600

25

1000

20

800

15

600

10

400

5

1400
1200
1000
800

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5
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200
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10

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35
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45

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35

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30

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5

0

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5
0

0

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70

20

30

40

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60

1600

30

1400
25

1200

20

1000

15

800
600

10

400
5

0

10

20

30

40

50

60

70

0

70

700
600
500
400
300
200
100
0

10

20

30

40

50

60

70

80

90

1800

35

0

10

0

800

45
40

700

35

600

30

500

25

400

20

300

15

200

10

200

5

0

0

100
0

10

20

30

40

50

60

70

80

90

0

Figure 3.27: Excluded Modules in the EMCal. Maps on the left side are in
the west arm and maps on the right side are in the east arm. Lower twomaps on the right side are PbGl and the others are PbSc.

CHAPTER 3. ANALYSIS

64

Corrected Energy
To facilitate the measurement of photons in the EMCal, certain valuables fortheir identification are introduced. First of all, we put raw energy cut as,√

Raw Energy Cut, E > 0.2 (GeV),

since there’s a lot of background from hadrons in low energy region. Furthermore, a cut on the shower shape is more effective to subtract hadrons
because an hadronic shower usually spreads over more modules than an electromagnetic shower. We select the corrected energy and apply χ2 as,√Ecore (prob > 0.02)), χ2 < 3

Definitions of Ecore and χ2 are described in the Section 2.2.4.
TOF Cut
In addition to the energy cut, a Time-Of-Flight cut can also reject hadrons
since harons have heavier mass. We put following cut from the width of the
TOF distribution (see the Figure 3.28),√|T OF − bbct0| < 2.0(ns), where bbct0 denotes a time of collisions measured by BBC.
6

Raw Energy

160

Count

Count

3

×10

180

3000

×10

TOF

2500

140
2000

120
100

1500

80
60

1000

40

500

20
0
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1
[GeV]

0
-20

-15

-10

-5

0

5

10

15

20
[nsec]

Figure 3.28: The distributions of Energy (left) and TOF(right). A plateau
seen in the energy distribution is generated by Minimum Ionizing Particles.

CHAPTER 3. ANALYSIS

3.4.3

65

Distribution of π 0 Invariant Mass

Before going to reconstruct ω mesons, π 0 going to 2γ is needed to reconstructed, first. We put following selections for chosing π 0 .
π 0 Legs Selection√√

Both photons in the same EMCal Sector
Energy Assymmetry Cut |E1 − E2 |/|E1 + E2 | < 0.8

Count

We require above conditions to cut some asymmetric pairs.
400
350
300
250
200
150
100
50
0
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7
0.8
2
[GeV/c ]Figure 3.29: Example of Invariant Mass reconstructed from 2 photons
As seen in the Figure 3.29, an example spectrum, π 0 around 0.135 GeV/c2
clearly can be identified(also, η can be seen around 0.56 GeV/c2 ).
Dependence on π 0 pT
The position of π 0 mass and the width have a dependence on π 0 pT as seen in
the Figure 3.30 and 3.31. Observed position shift upward due to the effectof photon conversion before arriving to EMCal and due to the pT smearing
caused from the steep pT distribution of pi0 . Also, the multiplicity affects
those value. We consider this shift parameter according to the pi0 pT and thecentrality when reconstructing ω.

2

π 0 mass [GeV/c ]CHAPTER 3. ANALYSIS

66

0.15
0.148

0-20% cent0.146

min bias event
60-92.2% cent

0.144
0.142
0.14
0.138
0.136
0.134
0.132
0.13
0

1

2

3

4

5
6
π0 pT [GeV/c]2

π 0 width [GeV/c ]Figure 3.30: Position of π 0 peak as a function of π 0 pT
0.02
0.018

0-20% cent

0.016

min bias event
60-92.2% cent

0.014
0.012
0.01
0.008
0.006
0.004
0.002
0
0

1

2

3

4

5
6
π0 pT [GeV/c]

Figure 3.31: Width of π 0 mass as a function of π 0 pT

CHAPTER 3. ANALYSIS

3.4.4

67

Best Cuts for Reconstructing ω

Thanks to the cut optimization √study in advance, we know the other parameters that improve expected S/ B most. We consider following values andapply the Cut # 4 tabulated in the Table 3.4.4√

Transverse Momentum Cut of π 0√

Photon Energy Cut except π 0 candidate√

Width of π 0 Invariant Mass

0.5 < pT (ω) < 1.5
1.5 < pT (ω) < 2.5
2.5 < pT (ω) < 3.5
3.5 < pT (ω) < 4.5
4.5 < pT (ω) < 5.5
5.5 < pT (ω) < 6.5
6.5 < pT (ω) < 7.5
7.5 < pT (ω) < 8.5
8.5 < pT (ω) < 9.5
9.5 < pT (ω) < 10.5

π 0 pT Cut
no cutno cut
1.25<
1.5<
2.0<
2.25<
2.75<
3.0<
3.0<
3.0<

γ energy Cut
no cutno cut
0.75<
0.75<
1.0<
1.25<
1.5<
1.5<
1.5<
1.5<

π 0 mass width
1.25σ
1.25σ
1.25σ
1.25σ
1.25σ
1.5σ
1.5σ
1.5σ
1.25σ
1.5σ

Table 3.2: Cut #4 values

Chapter 4
Results and Discussion
Here, we show the results after analyzing Nevt = 1.06 × 109 Minimum Bias
events(full statistics). Invaiant mass spectra are shown first and we consider
the background from that. Next, an innovative way for the background subtraction is applied and we look ω mass with simulated results. The outlook
for the further analysis is discussed in the end.

4.1

Invariant Mass Spectra

The invariant mass spectra according to ωpT are shown in the Figure 4.1,4.3
and 4.3, according to three centrality, MinBias, 0-20% and 60-92.2%. ω,around 0.78(GeV/c2 ), is getting to appearin high pT region. The backgroundaround 0.6-0.7(GeV/c2 )(will be discussed in the next) is an obstruction on
the signal of ω.

68CHAPTER 4. RESULTS AND DISCUSSION

MinBias

9

69

6

×10

×10

50

8000

0.5<pT<1.5

1.5<pT<2.5

7000

40

6000
5000

30

4000
3000

20

2000

10

1000

0
0

0.2

0.4

0.6

0.8

1

1.2

0
0

1.4

0.2

0.4

0.6

0.8

1

1.2

1.4

[GeV/c^2][GeV/c^2]

6

×10

3

25

2000

2.5<pT<3.5

20

×10

3.5<pT<4.5

1800
1600
1400

15

1200
1000

10

800
600

5

400
200

Count

0
0

0.2

0.4

0.6

0.8

1

1.2

1.4

[GeV/c^2]

3

×10

0
0

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0.4

0.6

0.8

1

1.2

1.4

[GeV/c^2]
16000

100

4.5<pT<5.5

80

5.5<pT<6.5

14000
12000
10000

60

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40

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4000

20

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[GeV/c^2]

0
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[GeV/c^2]

900
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2000

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100
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[GeV/c^2][GeV/c^2]300
1608.5<pT<9.5

250

9.5<pT<10.5

140
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100

60
40

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20
0
0

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0.8

1

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1.4

[GeV/c^2]

0
0

0.2

0.4

0.6

0.8

1

1.2

Figure 4.1: The Invariant Mass Spectra at MinimumBias

1.4[GeV/c^2]

CHAPTER 4. RESULTS AND DISCUSSION

70

cent 0-20%
9

×10

6

×10

8000

0.5<pT<1.550

1.5<pT<2.5

7000
6000

40

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30

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3000

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[GeV/c^2]

0
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[GeV/c^2]

×10

×10

2.5<pT<3.5

22
20
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1600
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Count

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[GeV/c^2]4.5<pT<5.5

80000
70000
60000

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[GeV/c^2]

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[GeV/c^2]

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0

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1.2

Figure 4.2: The Invariant Mass Spectra at 0-20% central

1.4[GeV/c^2]

CHAPTER 4. RESULTS AND DISCUSSION

71

cent 60-92%
6

18

×10

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0
0

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Figure 4.3: The Invariant Mass Spectra at 60-92.2% central[GeV/c^2]

CHAPTER 4. RESULTS AND DISCUSSION

72

4.2

Background Consideration

4.2.1

Combinatorial BackgroundWe reconstruct ω via radiative decay mode, 3γ. It leads to produce hugebackground due to their multiple combinations. Such conceivable combinations are lined in the Figure 4.5. We first reconstruct 2γ and set as ”π 0candidate” by selecting the invariant mass within 1.25σ or 1.5σ(see the tableof Cut#4), but there’s a probability that the uncorrelated 2γ satisfies thecriteria of π 0 candidate. The shape of reconstructed invariant mass shows
the behavior of such combination (see the Figure 4.4). The high peak in
the low mass region, around 0.2∼0.4(GeV/c2 ) is due to the combination ofπ 0 γ(π 0 → 2γ) failed to reconstruct ω (”Fail1” and ”Fail2” in the Figure 4.12
correspond to it). And the another peak around 0.5∼0.7(GeV/c2 ) is due tothe combination of ηγ(η → 2γ)(”Fail1” in the Figure 4.12). Those peaks areslightly above their mesons since the additional energy of photons (besides
their decay photons) are used to reconstruct them.

Count

300
250

Fail_1 Fail_2

Success

200
150

Fail_1100
50
00

Fail_3
0.2

0.4

0.6

0.8

1

1.2

1.4

[GeV/c2]

Figure 4.4: The combination behaviour in the invariant mass (picked the
MinBias at 6.5 < pT < 7.5 for example).

CHAPTER 4. RESULTS AND DISCUSSION

73

RarelySuccess

Success2

13

pi 0 candidation

3

2

1

pi 0 candidation
Fail_2
Fail_1

1

2

2

1

3

3

pi candidation0

pi 0 candidation

Fail_31

2

3

pi 0 candidation

Figure 4.5: Conceivable conbinations during 3γ reconstruction. Suppose γ1and γ2 are the π 0 candidation (selected as π 0 mass) that we reconstruct first.

CHAPTER 4. RESULTS AND DISCUSSION

4.2.2

74

Mixed Events Trail

The event mixing method is a widely used technique to determine the combinatorial background. The Figure 4.6 shows a schematic of the event mixing.
The basic idea is to compare the result obtained by combining particles within
one event to the result for particle combinations from different events, which
are a priori not correlated. It is usually used for two pair reconstruction, such
as π 0 and η. Before going to ω reconstruction, We extract the mean and thewidth of π 0 by using this method. The Figure 4.7 shows the invariat mass
spectra of π 0 for each π 0 pT . The foreground(reconstructed with same event)and the background(reconstructed with mixed event) are drawn together on
the left side for each pT . Right side of the plot is the spectra after subtractionof the background. Obviously, π 0 stands out after subtraction of the event
mixing. Although it is not simple in the case of multiple decay mode, we
consider this method for this analysis since ω can’t be seen so clearly due tocombinatorics.

Mixed Event

Same Event
Correlated
pairs
3

1

2

Some are2
uncorrelated
pairs

1

2

Only uncorrelated pairs

Figure 4.6: A schematic of Event mixing. Red and Blue γ image is comingfrom different events.

CHAPTER 4. RESULTS AND DISCUSSION

mass_0

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0

0.1

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[GeV/c^2]

CHAPTER 4. RESULTS AND DISCUSSION

76

There are 3 ways to mix events in the 3 decay mode as shown in the
Figure 4.8; I.π 0 candidate is slected from the same event(having a correlation) and chose a different event for third photon, II.π 0 candidate is slectedfrom different events(having no correlation) and chose third photon as thesame event with one of the candidate. III. All 3 photons are different events.
First we try MethodI., however, the event mixing spectra seems too differ-

II.

I.
1

2
pi 0 candidation

3

III.

1

2
pi 0 candidation31

2
pi 0 candidation

Figure 4.8: A schematic of Event mixing for 3 decay modeCount

ent from the foreground shape especially in the lough mass region (see the
Figure 4.9) and can’t be considered as ”background”.The main backgroundwe want to exclude is comingfrom the correlation between theone of π 0 candidate and third
1000
photon, i.e. ”Fail1” in the Figure4.5. It turn out that Method II.
800
is including this correlation and600
create the ”π 0 γ” and ”ηγ” spectrum. We introduce this method
400
and compare the results with200
foreground spectrum. Following figures shows the compari0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
[GeV/c ]son between foreground and mixing event scaling down by the fit
Figure 4.9: Example plot of the event mix- region of 1.2-1.4(GeV/c2 ). The
ing of Method.I(red line) with the fore- results after subtraction of mixground plot(black line).
ing event are shown on the rightside. We also draw the simulated
ω mass as green line in the subtracted mass spectra; the peak position andthe width are coming from the embedding simulation and integrated number
is coming from the Nω estimation (see the Table 3.3.5).
2

3

CHAPTER 4. RESULTS AND DISCUSSION

77

cent 0-20%
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[GeV/c^2]

Figure 4.10: Comparison between the foreground(black lines) and background using Method II.()(red lines) on the left, and the subtracted spectraon the right at 0-20 % centrality collisions. Green lines denote the expectedω mass calculated by simulation.

CHAPTER 4. RESULTS AND DISCUSSION

78

MinBias
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[GeV/c^2]

Figure 4.11: Comparison between the foreground(black lines) and background using Method II.()(red lines) on the left, and the subtracted spectraon the right at Minimum Bias collisions. Green lines denote the expected ωmass calculated by simulation.

CHAPTER 4. RESULTS AND DISCUSSION

79

cent 60-92%
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Figure 4.12: Comparison between the foreground(black lines) and background using Method II.()(red lines) on the left, and the subtracted spectraon the right at 60-92 % centrality collisions.

CHAPTER 4. RESULTS AND DISCUSSION

4.3

80

Outlook

From the results, we can see the conceivable ω mesons plateau and it shows
not unconsistent with the simulated ω meson, however, it is hard to evaluate the values such as yield, peak and width. The more fully subtraction of
background additional to the event mixing is needed. We’re going to pushforward simulation study and see the other particle’s contribution, such as
KS → π 0 π 0 and also evaluate the ω to π 0 ratio in the Au+Au collisions.
This particle contribution works will allow to extract the background in detail and help to approach the low momentum region where the in-medium
modification mainly dominate.
Other thing we’re going to touch is the systematic study. Cu+Cu collisions are also taken at PHENIX during 2004-2005, and the calibration is
on-going. We will also analysis ω → π 0 γ in this different multiplicity (lower
than Au+Au, and so ω mesons can be identified relatively clear) and see thedifferences. More statistics of Au+Au collisions are expected to taken in thenear future and there is no reason not to analyze them, too.

Chapter 5
Conclusion
We measure ω mesons via radiative decay mode in Au+Au collisions at
C.M.S. collisions energy per nucleon pair of 200GeV. The simulation is carried out in advance to calculate an acceptance and to check a multiplicity.
0
Furthermore, we search the best cuts; transverse√ momentum of π , energy
0of γ and width of π mass; that improve S/ B the most by using both
simulation
and real data. After applying determined best cuts, it turns out√
S/ B goes up to 4 for all statistics and it is sufficiently possible to measureω mesons in the heavy ion collisions.
Seeing the results of reconstructed invariant mass after applying the best
cuts, ω appears in the high pT region, however, the combinatorial backgroundespecially the contribution of ”ηγ” makes them hide. To try to extract
them, we introduce event mixing method and subtract the background that
correlating to ”ηγ”. Finally, ω mesons come to appear more than before thesubtraction. The further analysis to evaluate parameters such as yield, mean
and width of ω mesons is on-going.

81

Acknowledgment
First, I would like to express my gratitude to Prof. Kenta Shigaki who
mainly supervise this work. The study of ω mesons via radiative decay
mode at RHIC is coming from his idea. Prof. Toru Sugitate, the boss of
our laboratory gave me many chances to go to the BNL and international
conferences. Needless to say, those experiences had been good educations andstrongly helped to maintain my motivation. I appreciate Sasha Milov who
instructed me the vector mesons’ analysis in the BNL and Chris Pinkenburg
who had been taking care of the computing system. Dr. Kensuke Homma
and Dr. Hisayuki Torii gave me crucial suggestions a lot and helped an
improvement of this analysis. I would like to thank Dr. Takuma Horaguchi,
Tomoaki Nakamura, Yuji Tsuchimoto and Yoshihide Nakamiya for giving
me precious advices and teaching some computing techniques. I also give mythanks to Kazuhisa Yamaura and Megumi Oki for the mutual encouragement.
I could not keep working without the existence of my family. It is impossible to fully express my thanks to my father and mother; Nobuyuki
and Chizuko, two brothers; Tomoki and Tsukasa, and two sisters; Killa andLaicca. In the end, I would like to dedicate this thesis to my best partner,
John, who had been with me for 13 years and passed away in 2006 February.

Appendix A
Kinematics
Here, we describe the coordinate and kinematic variables that are used in
the relativistic heavy ion experiments.
Coordinate
The coordinate system for the experiment is shown in the Figure A.1. The
axis of collision (beam axis) is defined as the z axis. Components along thebeam axis are called as the longitudinal components, while components lying
in the x-y plane are called as the transverse components. φ is the polar angle
measured from the z axis and θ is the azimuthal angle measured clockwisefrom the x axis.

83

APPENDIX A. KINEMATICS

Figure A.1: Coordinates of the PHENIX experiment84

APPENDIX A. KINEMATICS

85

Energy and Momentum
The relativistic energy allows to use the natural units, c = h̄ = 1. So thenthe energy of the particle is written as,q

p2 + m,E=

and the momentum comosed of 4-vectors is written as,
p = (E, p),
The component along the beam-axis, the longitudinal momentum is definedas,pz = p cos θ,
where p is the magnitude of particle’s momentum. While the transverse
momentum, which is a Lorentz invariant is given as,
pT =q

p2x + p2y = p sin θ.

Rapidity and Pseudorapidity
The longitudinal variable, the rapidity y, is commonly used. It is defined as,
µ

y=

¶

µ

E + pz1 + β cos θ
1
1
ln
= ln
2
E + pz2
1 − β cos θ¶

If we go to higher energy that the momentum relatively much higher thanthe mass, i.e. E ' p, the rapidity is translated as the pseudorapidy defined
as,
µ
¶
1
θ
η = − ln tan .
22

Bibliography[1] Frank Wilczek, Physics Today August 2000, p.22
[2] Mikhail A.Stephanov, Int.J.Mod.Phys.A20:4387-4392(2005)[3] P.Braun-Munzinger, K.Redlich and J.Stachel, nucl-th/0304013[4] Itzhak Tserruya, talk in the PHENIX Focus 2006
[5] W.-M.Yao et al., Journal of Physics G 33,1(2006)[6] R.Rapp and J.Wambach, hep-ph/9909229v1(1999)[7] Y.Nambu and G.Jona-Lasinio, Phys.Rev.122,345-358(1961)[8] C.Djalali for the CLAS Collaboration, talk in the Quark Matter 2006
[9] K.Adcox et al., Nucl.Phys.A757,184-282(2005)[10] R.Rapp, nucl-th/0608022[11] R.Rapp, H.Hees and T.Strong, hep-ph/0611339[12] M.F.M.Lutz, Gy.Wolf and B.Friman, Nucl.Phys.A706,431-496(2002)[13] T.Hatsuda and S.H.Lee, Phy.Rev.C46(1992)R34[14] R.Rapp and J.Wambach, hep-ph/9909229v1(1999)[15] Volker Metag, talk in the Quark Matter 2006[16] M.Naruki et al., Phys.Rev.Lett.96,092301(2006)[17] KEK-PS E325 Collaboration: R.Muto et al., nucl-ex/0511019
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