Quark Physics Laboratory Graduate School of Advanced
Science and Engineering Physics Program

Master thesis
Charged-Particle Multiplicity Dependence of
J/ψ Yield and ρ+ω Mass Width via Dimuon√
Measurement in p-p collisions at s = 13.6
TeV as Potential Signatures of Quark-Gluon
Plasma Production in Small Collision
Systems

Auther: Tomo Ito
Supervisor: Prof. Kenta Shigaki
Chief examiner: Prof. Kenta Shigaki
Examiner: Prof. Tomohiro Inagaki
Examiner: Program-Speciﬁc Prof. Toru Takahashi

Abstract
In the early microseconds after the Big Bang, the state of the universe is
expected to be high temperature and density called Quark-Gluon Plasma(QGP) formed with quark conﬁnement breaking. Using the Large Hadron
Collider (LHC) at the European Organization for Nuclear Research (CERN),
The QGP is observed successfully with heavy-ion collisions. However, evidence for QGP generation in small collision systems, such as p-p and p-Pb
collisions, has not been obtained. In this study, I anticipate QGP generationin high-multiplicity collision events. Some measurements of phenomena athigh charged-particle multiplicity in p-Pb collisions show similar behavior
to results measured by Pb-Pb collisions. This study discusses the chargedparticle multiplicity dependence of J/ψ production and the ρ + ω mass widthwith ALICE which is one of the experiments in CERN. Additionally, discussions of the results from the ϕ meson measurement are also included. Individual extraction of ρ and ω is not easy due to the close masses. Therefore, thisstudy approximates them as a combined signal ρ + ω. The J/ψ production
serves as a probe for QGP generation. J/ψ production is suppressed in QGP
via color screening and observed in Pb-Pb collisions. I anticipate that theρ + ω mass width reﬂects the phenomenon of spontaneous chiral symmetry
breaking recovery near the QGP phase transition temperature.
This study uses proton-proton collision events at the center-of-mass energy of 13.6 TeV from the year 2022. To improve the resolution of trackreconstruction, The new tracking chamber is introduced. J/ψ, ρ, ω, and ϕ
are detected in forward(−3.6 ≤ η ≤ −2.45). The charged-particle multiplicity is measured in central(|η| ≤ 1.22).
In this study, charged-particle multiplicity dependence of the yield, widthand mean mass of J/ψ, ρ + ω, and ϕ are measured with the new data acquired in 2022. As a result, the dependence of self-normalized J/ψ yield on
charged-particle multiplicity shows strange behavior at low charged-particle
multiplicity. I expect the cause is due to accuracy of charged-particle multiplicity measurement. The mass width of ρ + ω and ϕ as a function of
charged-particle multiplicity show weak dependence of charged-particle multiplicity. The mass width of ρ + ω and ϕ is higher than PDG values by afactor of 2 for ρ + ω compared with PDG of ω and 4 for PDG of ϕ due todetector resolution. The ρ mass width in PDG is so high that can be seen

if ρ + ω is separated independently. In case quality of track reconstruction
improves more, the mass width of ω and ϕ can be also observed.

2

Contents
1 Introduction
1.1 QCD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Quark Gluon Plasma (QGP) . . . . . . . . . . . . . . . . . . .
1.3 Small system QGP . . . . . . . . . . . . . . . . . . . . . . . .
1.4 Multi-parton interaction (MPI) . . . . . . . . . . . . . . . . .
1.5 Color reconnection (CR) . . . . . . . . . . . . . . . . . . . . .
1.6 J/ψ production suppression in small systems . . . . . . . . . .
1.7 Spontaneous breaking of chiral symmetry . . . . . . . . . . . .
1.8 Purpose of this study . . . . . . . . . . . . . . . . . . . . . . .

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2 Experimental setup
2.1 LHC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 ALICE setup . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Inner Tracking System (ITS2) . . . . . . . . . . . . . . . . . .
2.4 Forward muon detector system . . . . . . . . . . . . . . . . .
2.5 Muon Forward Tracker(MFT) . . . . . . . . . . . . . . . . . .
2.6 Online-Oﬄine syetem (O2) . . . . . . . . . . . . . . . . . . . .

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3 Analysis
3.1 Data set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Event selection . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Charged-particle multiplicity . . . . . . . . . . . . . . . . . . .
3.4 Invariant mass reconstruction with dimuon . . . . . . . . . . .
3.5 Combinatorial Background(BG) subtraction . . . . . . . . . .
3.5.1 Like-sign (LS) method . . . . . . . . . . . . . . . . . .
3.5.2 Event mixing (EM) method . . . . . . . . . . . . . . .
3.6 Signal extraction . . . . . . . . . . . . . . . . . . . . . . . . .

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4 Result49
4.1 J/ψ analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.2 Low mass vector meson analysis . . . . . . . . . . . . . . . . . 55
5 Summary61

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List of Figures
1.1

Coupling constant with dependence of momentum shift scale(Q2 ).[1] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2 Potential between a quark and a anti-quark with lattice QCD
calculation[2] . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3 Quark conﬁnement . . . . . . . . . . . . . . . . . . . . . . . . 9
1.4 QGP phase transition[3] . . . . . . . . . . . . . . . . . . . . . 10
1.5 Image of ﬂow . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.6 Elliptic ﬂow measurement at Star Collaboration [4] . . . . . . 11
1.7 jet-quenching image . . . . . . . . . . . . . . . . . . . . . . . . 12
1.8 Jet quenching measurement at Star Collaboration[5] . . . . . . 12
1.9 Charm meson ﬂow measurement in p-Pb collision[6] . . . . . . 13
1.10 Enhanced production of multi-strange hadrons in p-Pb [7] . . 13
1.11 Image of MPI at p-p collision . . . . . . . . . . . . . . . . . . 14
1.12 Charged-particle multiplicity measurement vs PYTHIA[8] . . 14
1.13 Color reconnection process [9] . . . . . . . . . . . . . . . . . . 15
1.14 Mean transverse momentum measurement vs PYTHIA w/o CR 16
1.15 J/ψ yield as a function of charged-particle multiplicity with
ALICE in central and forward rapidity with model comparison[10] 17
1.16 Jψ suppression measured by PHENIX in AuAu collisions[11] . 18
1.17 Eﬀective potentials[12] . . . . . . . . . . . . . . . . . . . . . . 20
1.18 Expected value of quark condensation with dependence oftemperature and density[13] . . . . . . . . . . . . . . . . . . . 21
2.1
2.2
2.3
2.4
2.5
2.6

CERN LHC[14] . . . . . . . . . . . . . . . . . . . . . . . . . .
ALICE detectors[15] . . . . . . . . . . . . . . . . . . . . . . .
ITS2[16] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Forwad muon detector system in Run 3 . . . . . . . . . . . . .
MFT[17] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Design of O2 system[18] . . . . . . . . . . . . . . . . . . . . .
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3.1

ϕ angle and mass comparison between two dataset in top. The
ratio of the two distribution (zs / o) is in bottom. . . . . . . .
3.2 Number of ITS tracks contributes to primary vertex ﬁnﬁng . .
3.3 Invariant mass vs Ntrk . . . . . . . . . . . . . . . . . . . . . .
3.4 Combinatorial BG with like-sign method and Rfactor . . . . .
3.5 Combinatorial BG with event-mixing method and the ratio
LS/EM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6 J/ψ signal extraction without combinatorial BG subtraction .
3.7 J/ψ signal extraction with LS method . . . . . . . . . . . . .
3.8 J/ψ signal extraction with EM method . . . . . . . . . . . . .
3.9 ρ+ω and ϕ extraction (combinatorial BG is estimated by LS
method, remaining BG is done by exponential function) . . . .
3.10 ρ+ω and ϕ extraction (Combinatorial BG is estimated by EM
method, remaining BG is done by exponential function) . . . .
3.11 ρ+ω and ϕ extraction (combinatorial BG is estimated by LS
method, remaining BG is done by VWG function) . . . . . . .
3.12 ρ+ω and ϕ extraction (combinatorial BG is estimated by EM
method, remaining BG is done by VWG function) . . . . . . .
Fitting χ2 with function BG + Signal for J/ψ extraction withdependence of charged-particle multiplicity . . . . . . . . . . .
4.2 J/ψ row yield as a function of charged-particle multiplicity . .
4.3 Self-normalized J/ψ yield as a function of charged-particle
multiplicity[19] . . . . . . . . . . . . . . . . . . . . . . . . . .
M B,i
i
MB
/NJ/ψ with dependence of/Nevent
and Ratio NJ/ψ
4.4 Ratio Nevent
charged-particle multiplicity . . . . . . . . . . . . . . . . . . .
4.5 J/ψ mean mass as a function of charged-particle multiplicity .
4.6 J/ψ mass width as a function of charged-particle multiplicity .
4.7 Fitting χ2 with function BG + Signal for ρ+ωandϕ extraction
with dependence of charged-particle multiplicity . . . . . . . .
4.8 Signal ﬁtting χ2 for ρ + ωandϕ extraction with dependence of
charged-particle multiplicity . . . . . . . . . . . . . . . . . . .
4.9 Row yield as a function of charged-particle multiplicity (BG :VWG) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.10 Self-normalized yield as a function of charged-particle multiplicity (BG : VWG) . . . . . . . . . . . . . . . . . . . . . . . .
4.11 Mean mass as a function of charged-particle multiplicity (BG: VWG) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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4.1

4

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55
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58
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4.12 Mass width as a function of charged-particle multiplicity (BG: VWG) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.1
5.2
5.3
5.4
5.5

invariant mass reconstructed by muon pair in mixed events . .
Row yield as a function of charged-particle multiplicity (BG :exp) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Self-normalized yield as a function of charged-particle multiplicity (BG : exp) . . . . . . . . . . . . . . . . . . . . . . . . .
Mean mass as a function of charged-particle multiplicity (BG: exp) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Mass width as a function of charged-particle multiplicity (BG: exp) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

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Chapter 1
Introduction
1.1

QCD

All interactions including strong interaction are described by quantum ﬁeld
theory. Electromagnetic interaction is described by quantum electrodynamics (QED), and quantum chromodynamics (QCD) which explain strong interaction based on QED. Interaction is carried by gauge boson corresponding tothe ﬁeld. Interaction between particles and ﬁeld is described via Lagrangian.
In case Lagrangian is invariant after gauge transformation, Lagrangian has
gauge symmetry. All interactions require Lagrangian to have gauge symmetry. Gauge transformation is as follows.
ψf → eiQf θ(x) ψf
1
Aµ → Aµ + ∂µ θ(x)eBased on these principals, QED Lagrangian is given by

(1.1)
(1.2)

1
LQED = ψ̄f (iγ µ ∂µ − mf )ψf + eQf ψ̄f γ µ ψf Aµ − Fµν F µν
(1.3)
4
The ﬁrst term shows free particles, which are not interacted by the ﬁeld.
The second term describes the interaction between the charged particle andthe electromagnetic ﬁeld. The third term means electromagnetic ﬁeld.
Gauge bosons propagating strong interactions are gluons. Strong interactions work on color-charged particles. The color charge has three degrees of
freedom (red, blue, and green). QCD is constructed on the condition that the6color’s internal degrees of freedom are localized by rotation of them. QCD is
an SU(3) gauge theory, as the 3 × 3 unitary matrix represents this rotationaltransformation. QCD lagrangian is as follows
1 A AµνAψq,b GALQCD = ψ̄q,a (iγ µ ∂µ − mq )ψf + gs ψ̄q.a γ µ Tabµ − Gµν G4(1.4)

The ﬁrst term shows free quark. The second term describes the interaction between quarks and gluon ﬁeld. The third term means gluons. Eachterm is similar to those of QED, but the interaction between gluons describedin the third term is a unique feature of QCD. As electromagnetic interaction
works on charged-particle, photons that is gauge boson of electromagnetic
interaction don’t interact with photons. However, gluons have color.
In QCD, the coupling constant depends on the momentum shift scale Q2
due to the renormalization process. In QED and QCD, divergence occurs
in higher-order calculation and this is called ’Ultraviolet divergence’. This
divergence is removed by the renormalization process. The renormalization
process is determined by the renormalization scale µ which is the free parameter of momentum. Momentum shift scale Q2 is used as a renormalization
scale in general. As a result, the coupling constant depends on the momentum shift scale Q2 . The coupling constant as a function of Q2 is measured
and agreed with theoretical calculation. (Fig 1.1)
This result means that the higher Q2 becomes, the weaker strong interaction
becomes. This phenomenon is called ’Asymptotic freedom’. The high Q2
interaction is called the hard process and the soft process is low Q2 . Perturbative QCD can calculate hard processes. Lattice QCD can describe the softprocess.

7

Figure 1.1: Coupling constant with dependence of momentum shift scale (Q2 ).[1]The potential between a quark and an anti-quark is calculated by lattice QCD(Fig 1.2). Strength is bigger with distance increasing, This meansthat gluon prohibits quarks and anti-quarks to exist independently. Whenattempting to pull quarks apart, the quarks cannot escape from the bindingof gluons due to reaching the energy required for pair production. (Fig 1.3)
This characteristic is referred to as quark conﬁnement.

8

Figure 1.2: Potential between a quark and a anti-quark with lattice QCD
calculation[2]Figure 1.3: Quark conﬁnement

1.2

Quark Gluon Plasma (QGP)

Quark conﬁnement is expected to be broken at high temperatures and densities. In lattice QCD calculations, this occurs due to crossover. This plasmastate is called quark-gluon plasma (QCD). The relationship between the QCD
phase, temperature, and particle density is shown in Fig 1.4. The QGP has
been conﬁrmed to be produced in high-energy nuclear collisions, for example,
elliptic ﬂow (v2) and jet-quenching.

9

Figure 1.4: QGP phase transition[3]The anticipated generation of QGP is expected in heavy-ion collisions,such as lead-lead collisions. In nucleon-nucleon or nucleon-heavy-ion collisions, where the parton density in the reaction space is low, the productionof QGP is not anticipated.
Elliptic ﬂow refers to geometric features in the phase space of particles.
Collective motion resembling an ellipse typically does not occur, but due tothe ﬂuid-like behavior of QGP, inﬂuenced by the density gradients in the reaction space, a collective expansion takes place. The density gradients arise
from geometric features resembling a rugby ball in the reaction region, causing the expansion, or in other words, the phase space to take on an ellipticalshape. Indeed, elliptic ﬂow was not observed in proton-proton collisions, but
it was observed in lead-lead collisions, thus serving as one of the pieces ofevidence for the generation of QGP.

10

Figure 1.5: Image of ﬂow

Figure 1.6: Elliptic ﬂow measurementat Star Collaboration [4]A jet is a narrow, high-transverse-momentum collective motion of particles generated through the fragmentation process of particles associatedwith hard processes occurring during collisions. The fragmentation process
involves particle generation through particle pair production, as illustrated
in the previous section’s diagram. When two particles associated with a hard
process are involved, they are always generated back-to-back. Observations
from lead-lead collisions have shown a phenomenon where one of the jets
undergoes attenuation. This is interpreted as being caused by energy loss
due to gluon radiation in the QGP. This phenomenon serves as one piece ofevidence for the generation of QGP in lead-lead collisions.

11Figure 1.7: jet-quenching im- Figure 1.8: Jet quenching measurement at Star
age
Collaboration[5]1.3

Small system QGP

In the previous section, it was anticipated that Quark-Gluon Plasma (QGP)
would not be generated in nucleon-nucleon or nucleon-heavy-ion collisions.
However, in recent years, phenomena similar to those observed in heavy-ion
collisions have been measured in collisions involving high charged-particle
multiplicity. Speciﬁcally, phenomena such as elliptic ﬂow, and strangenesshadron enhancement have been observed.
Elliptic ﬂow has been conﬁrmed in high-charged-particle multiplicity pPb collisions. The ﬁgure illustrates the elliptic ﬂow of J/psi.(FIg 1.8) Similarly, in p-Pb collisions with high-charged-particle multiplicity, an increasein the yield of hadrons containing strange quarks has been observed (Fig
1.9). The data plot for p-Pb approaches Pb-Pb as the multiplicity increases.
Thus, high-charged-particle multiplicity p-Pb collisions exhibit behavior similar to Pb-Pb collisions. This challenges the conventional understanding of
the mechanisms of particle production and collective motion. To explainthese phenomena, various models have been proposed, with examples including Multi-Parton Interaction (MPI) and Color Reconnection (CR).

12

Figure 1.9: Charm meson ﬂow measurement in p-Pb collision[6]Figure 1.10: Enhanced production of multi-strange hadrons in p-Pb [7]J/ψ suppression and jet quenching are not observed in p-p and p-Pb collisions. J/ψ suppression is also QGP prove observed in heavy-ion collisions.
(See Sec.1.6)

1.4

Multi-parton interaction (MPI)MPI (Multi-Parton Interaction) is a phenomenon that involves multiple parton scatterings during the collision of nucleons (Fig 1.10). PYTHIA is one
13

of the models that introduces MPI. In PYTHIA, the consideration of impact parameters is extended to proton-proton collisions, and the probabilityof MPI occurrence increases with the rising centrality. The charged-particle
multiplicity observed in LHC’s CDF aligns with the predictions of PYTHIA,
which incorporates MPI (Fig 1.11).

Figure 1.11: Image of MPI at p-p collision

Figure 1.12: Charged-particle multiplicity measurement vs PYTHIA[8]1.5Color reconnection (CR)The color reconnection is introduced to describe collective motion of particles
like elliptic ﬂow. When MPI occurs, diﬀerent parton collisions are initially14considered independent, but as generated particles and colliding partons become connected by strings, they undergo attraction, causing changes in thephase space distribution. CR is a model that captures this behavior.
The Fig 1.12 illustrates the sequence from MPI to CR. In (a), the ﬁrst
parton collision occurs, and in (b), when the second parton collision occurs,
the strings associated with the two collision events undergo reconnection,
resulting in the conﬁguration shown in (c).

Figure 1.13: Color reconnection process [9]Without CR, the string conﬁguration is like (a), causing the generated
particles to be pulled toward the beam. However, when CR occurs, strings
connect particles moving in the direction perpendicular to the beam axis,
leading to an increase in transverse momentum compared to the case without
CR.
Fig 1.13 shows the dependence of average transverse momentum on chargedparticle multiplicity. It compares the results from the PYTHIA event simulator, which incorporates both MPI and CR, with the case where CR isabsent. In the absence of CR, the average values are ﬂat since parton collisions in MPI do not interact with each other. With CR, an increasing trend
is observed, aligning with experimental results.

15

Figure 1.14: Mean transverse momentum measurement vs PYTHIA w/o CR

1.6

J/ψ production suppression in small systems

Charmonium yield as a function of charged-particle multiplicity can reﬂect
both MPI and QGP signature. MPI was originally used to describe particle
generation through soft processes, but in high-energy collisions like thoseat the LHC, there is a possibility of an increase in hard processes as well.
A charm quark is produced at ﬁrst parton interaction, so the number ofcharm production as a function of charged-particle multiplicity can reﬂect
the number of parton scattering. J/ψ is a charmonium state composed of acharm and anticharm quark. While the charm pair production is described bypQCD (perturbative Quantum Chromodynamics) since it is a hard process,the transition to the bound state involves soft processes that are not wellunderstood. Charm pair production can occur through processes like DrellYan, quark-antiquark annihilation via higher-twist mechanisms, and gluon

16

fusion. The most predominant process is gluon fusion.
Fig 1.15 illustrates the charged-particle multiplicity dependence of J/psi
in ALICE pp collisions at center-of-mass energy 13 TeV. With the increased
energy of up to 13 TeV, the self-normalized charged-particle multiplicity
reaches up to 8. Faster than linear trend is observed in p-p collisions at
both forward and central rapidity. Signiﬁcant rapid increasing than linear is
not seen in p-Pb collisions at forward rapidity. PYTHIA tends to underestimate the J/psi yield beyond 4 in multiplicity at both rapidity range. The
diﬀerence between forward and central can be due to CR. Previous studies
have compared various models focusing on J/psi production in addition to
PYTHIA. Those models that approve the data take into account for highgluon density or high order J/ψ production process (3-gluon fusion). The
details of these models are described in appendix.

Figure 1.15: J/ψ yield as a function of charged-particle multiplicity with ALICEin central and forward rapidity with model comparison[10]J/ψ is also one of QGP probe. A bound state formation is prevented
by color ﬁeld of other quarks (color screening) in the QGP. Fig 1.14 shows
nuclear modiﬁcation factor (RAA ) with dependence of charged-particle multiplicity in AuAu at center-of-mass energy 200 GeV in PHENIX collaboration.
(RAA ) means normalized yield by p-p collisions. (RAA ) show unit if there isno diﬀerence between p-p and AuAu except the number of nucleus-nucleus
collisions. The charged-particle multiplicity show how two ions are close17

at the moment of collision (centrality). The ﬁgure show under unit at all
centrality. This proves J/ψ suppression in QGP.

Figure 1.16: Jψ suppression measured by PHENIX in AuAu collisions[11]As a result, J/ψ is a good prove to understand small systems and QGP.

1.7

Spontaneous breaking of chiral symmetry

The mass of hadrons is signiﬁcantly larger than the sum of the masses of theirconstituent quarks. For instance, the sum of the masses of quarks within aproton constitutes only about 1% of the proton’s mass. The remaining massis believed to originate from the spontaneous breaking of chiral symmetry.
Spin exists in both right- and left-handed components. Particles withzero mass, moving at the speed of light, maintain a consistent spin orientation regardless of the reference frame. This reﬂects chiral symmetry, which18

is symmetric under transformations between right- and left-handed components. In fact, the Lagrangian is preserved even if the wave function in equation (QCD) is written in right-handed and left-handed form(ψ → ψL + ψR )and a rotational transformation is applied to swap the right-handed andleft-handed forms.
LQCD =ψ̄L,a (iγ µ ∂µ −)ψL,a + ψ̄R,a (iγ µ ∂µ )ψR,aAµ A
A+ gs ψ̄L,a γ µ Tab
ψL,b GAµ + gs ψ̄R,a γ Tab ψR,b Gµ
1
− GA
GAµν
4 µν

(1.5)

The chiral rotational transformation isψLorR → U (θ)ψLorR
where
U (θ) = e

(1.6)

a T a iγ 5 θ a T a
iθV
V

e

a
The θVa and θA
terms represent vector and axial transformations respectively.
However, mass limits the velocity and changes the orientation of the spin fromthe point of view of the faster system; the QCD Lagrangian also breaks thechiral symmetry due to the presence of the mass term. The mass term is−mq ψ¯L ψR − mq ψ¯R ψL and, This term is not invariant under chiral transformation.
Quarks have mass due to the Higgs mechanism, so the chiral symmetry of
hadrons is approximately broken.
At low temperatures, quark condensation occurs, where quark pairs pair up.
When quark condensation occurs, the potential takes on the shape of thebottom of a wine bottle, as shown in Fig 1.16 (a) to (b).

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Figure 1.17: Eﬀective potentials[12]The bottom edge has the same potential at every location, so there isan inﬁnite number of ground states. If a particle takes any one of them atrandom, it is ’spontaneously’ broken.
According to the Nambu-Goldstone theorem, if rotation or chiral symmetry is spontaneously broken, the Nambu-Goldboson is generated. This isa particle of mass zero, of which the π meson is one. In fact, the pi meson
has mass, because the u,d quarks acquire mass by the Higgs mechanism.
The mass of the π is derived by the Gelman-Oakes-Lenner relation.
¯
fπ2 m2π = −(⟨ūu⟩ + ⟨dd⟩)(m
u + md )(1.7)

The fπ is a constant that represents the strength of the decay process π → µν,
and ⟨q̄q⟩ is the quark condensation vacuum expectation value for each quark
pair. When mu = md = 0, the π mass is zero, indicating that it is a typeof Southern Goldstone. The hadron mass is larger than the sum of thecomponent masses because it gains mass by the quark condensation vacuum
expectation value.

20

As a result, when quark condensation occurs and spontaneous chiral symmetry breaking occurs, a Nambu Goldboson is produced and gains mass. The
Fig 1.17 illustrates the temperature and density dependence of the vacuum
expectation value of quark condensation. Similar to the Quark-Gluon Plasma(QGP), this dependence on temperature and density results in a decrease in
the expectation value at high temperatures and densities, ultimately reaching zero. This signiﬁes the recovery of chiral symmetry breaking.

Figure 1.18: Expected value of quark condensation with dependence of temperature and density[13]1.8

Purpose of this study

This purpose of this study is to observe the generation of QGP in small
systems with data taken in 2022 (Run 3)
In Run 3 taken from 2022, the center-of-mass energy of p-p collision improves
to 13.6 TeV, whereas 13 TeV in Run 2. The trigger is not imposed (Minimumbias) and statistics are expected to increase by a factor of 10. For forward
muon analysis, the spatial resolution is expected to increase by installing the
Muon Forward Tracker (MFT) in front of the hadron absorber to remove
multiple scattering eﬀects. (See Section 2.4,2.5)21In order to observe QGP in small systems, I measured two physics. theone is J/ψ suppression. The charged-particle multiplicity dependence of
J/psi production should show slower increasing than linear with increasingof charged-particle multiplicity.
The other is restoration of spontaneously chiral symmetry breaking. The
ρ+ω mass width should broad in high charged-particle multiplicity.
J/ψ yield as a function of charged-particle multiplicity can reﬂect small system phenomena like MPI. If QGP is formed in small systems at high chargedparticle multiplicity, J/ψ yield suppression should be observed. In proceeding
charmonium analysis, There are problems in comparing previous measurement results with models. Speciﬁcally, most models (except PYTHIA) calculate only prompt J/psi, while experimental results include contributions
from bottomonium (feed-down), which could constitute around 10% of theresults. The introduction of new detector is expected to improve position
resolution and help eliminate feed-down contributions. In this study, separation between prompt/non-prompt J/ψ is not done.
The measurement of the mass width of the ρ + ω resonance peak aims toreﬂect the partial restoration of chiral symmetry, a phenomenon associatedwith spontaneous symmetry breaking. Low mass vector meson; ρ, ω, andϕ are well proves of it because of their short lifetime which can makes it
possible to decay in the QGP. Furthermore, they decay into dimuon which is
not interacted with strong ﬁeld. Ideally, measuring the mass width of the ρ
meson would be preferred. However, due to the close masses of the ρ and ω
mesons, making their separation challenging, this study approximates themas a combined ρ+ω peak. The expectation is that, in a high-temperaturestate like QGP, where chiral symmetry is expected to be restored, the mass
should decrease, thus examining the charged-particle multiplicity dependenceof the mass width.
Additionally, this study includes a discussion of the measurement results
for the φ meson.

22Chapter 2
Experimental setup
2.1

LHC

The Large Hadron Collider (LHC) is a particle accelerator ring establishedby CERN. CERN is located on the border between Swiss and France. LHC
consists of two 27km rings and is buried underground. Particles, such as
protons and lead ions, are accelerated within a ring, moving in opposite
directions in two separate rings. Collision is processed at two beam crossing
points.
Run 2 started in 2015 and ended in 2018. Until Run3 which started in 2018,
LHC was shut down (LS2). Some upgrade
LHC and√ was done during LS2 in √TeV in pp and s = 5.5
ALICE. Energy increased√and reached s = 13.6 √TeV in Pb-Pb, whereas s = 13 TeV in pp and s = 5.02 TeV in Pb-Pb
in Run2. Luminosity was also improved and reach to 13nb −1 in PbPb as
integrated luminosity, where as 0.4nb−1 in Run 2. The beam pipe radius of
the crossing point at ALICE is reduced from 29.8 to 19.2 mm.

23

The CERN accelerator complex
Complexe des accélérateurs du CERNCMSNorth Area

LHC

GIF++

2008 (27 km)

CENF

ALICE

2015

LHCb

2016

TT20

TT40

TT41

SPS
1976 (7 km)

TI2

TT10

TI8

AWAKE

ATLAS

HiRadMat
2011

2016

TT66

TT2

AD

ELENA

1999 (182 m)

2016 (31 m)

ISOLDEBOOSTER

1992

1972 (157 m)
RIBs
p

p

REX/HIE

2001

1959 (628 m)

p

CLEAR

LINAC 2e-

LEIR

LINAC 3
Ions

ions

IRRAD/CHARMPSnp (protons)

East Area

2001/2015

n-ToF

2017

2005 (78 m)

RIBs (Radioactive Ion Beams)n (neutrons)– (antiprotons)pe- (electrons)

LHC - Large Hadron Collider // SPS - Super Proton Synchrotron // PS - Proton Synchrotron // AD - Antiproton Decelerator // CLEAR - CERN Linear
Electron Accelerator for Research // AWAKE - Advanced WAKefield Experiment // ISOLDE - Isotope Separator OnLine // REX/HIE - Radioactive
EXperiment/High Intensity and Energy ISOLDE // LEIR - Low Energy Ion Ring // LINAC - LINear ACcelerator // n-ToF - Neutrons Time Of Flight //HiRadMat - High-Radiation to Materials // CHARM - Cern High energy AcceleRator Mixed field facility // IRRAD - proton IRRADiation facility //GIF++ - Gamma Irradiation Facility // CENF - CErn Neutrino platForm

Figure 2.1: CERN LHC[14]2.2

ALICE setup

A Large Ion Collider Experiment (ALICE) is one of the experiment groups
with LHC in CERN. ALICE aims to reveal the QGP signature. ALICE
consists of a central rapidity barrel (|η| ≤ 0.9) and forward rapidity muonchamber (−3.6 ≤ η ≤ −2.5). The coordinate system in ALICE takes thebeam axis as the Z-axis, with positive values extending from the muon chamber towards the central barrel (from right to left in Figure 2.2). The origin
point is at the center of the Inner Tracking System (ITS), and collisions are
set to occur at it.
Large ALICE upgrades are as follows
・ITS2 install replacing ITS
・Muon Foward Tracker (MFT) install24

Figure 2.2: ALICE detectors[15]・Online Oﬂine (O2) system install
ITS2 has seven planes obtained by silicon pixel sensors. MFT is a new
tracking detector located in front of the hadron absorber to improve spatial
resolution for the muon detector system. Show detail in section 2.5. O2
system is developed to make it possible to read out events continuously andreconstruct physics parameters online. In Run 2, event triggers, for example,
dimuon trigger, and transverse momentum threshold, are required due topoor readout speed. The O2 system is described with details in Sec.2.6.

2.3

Inner Tracking System (ITS2)

ITS2 is the innermost detector covering the beam pipe. The acceptance is|η| ≤ 1.22. ITS plays roles in collision vertex reconstruction, event planeﬁnding, tracking, and measurement of charged-particle multiplicity.
For Run 3, Updated ITS is installed and called ITS2. ITS2 has seven layers
whereas ITS has 6 layers. All layers of ITS2 consist of silicon pixel sensors
that are excellent in terms of spatial resolution. Silicon pixel sensor is usedin ITS inner two layers, but ITS2 has new sensors based on monolithic active
silicon sensor (MAPS).

25

Figure 2.3: ITS2[16]2.4

Forward muon detector system

The muon spectrometer identiﬁes muons by hadron absorber to absorb andremove particles except muon. Their acceptance is −4 ≤ η ≤ −2.5. Beyond
the hadron absorber, it consists of the Muon Chamber (MCH), composedof ﬁve tracking detectors and a dipole magnet for momentum measurement,
the Muon Identiﬁer (MID) consisting of two resistive plate chambers, andthe MID-Shield designed to eliminate particles except muon that have passed
through the hadron absorber. It’s a massive detection system spanning 16.2m
from the hadron absorber to the second layer of MID. The characteristics ofeach component are described below.[20]・Hadron Absorber: A 4m thick absorber made of carbon, iron, andconcrete. It allows muon with a momentum of p 4 to pass through (-5.03m
z -0.9m).
・MCH: Consists of ﬁve tracking detectors with a position resolution of 100
μ m. Two are placed in front of the dipole magnet, one in the middle, andtwo at the back.
・Dipole Magnet: Generates a 0.7T magnetic ﬁeld parallel to the beam axis

26

Figure 2.4: Forwad muon detector system in Run 3(-9.85m z -5m).
・MID-Shield: A 1.2m thick iron absorber designed to absorb hadrons thathave passed through the hadron absorber.
・MID: Consists of two resistive plate chambers with a time resolution of 2ns
for triggering and identifying muon more precisely than MCH standalone (17.1m z -16.1m).
Previously, the muon detector system had inaccuracies in vertex reconstruction due to multiple scattering in the hadron absorber, but it is expected
to be improved with the introduction of MFT.

2.5

Muon Forward Tracker(MFT)This is a new tracking detector to be added to the muon detector system,as mentioned earlier. It is introduced to improve the resolution of the vertex position measurement by performing track reconstruction in front of thehadron absorber. It covers the pseudorapidity range −3.6 ≤ η ≤ −2.5. It
consists of ﬁve plates composed of silicon pixel sensors and is installed in
the range of -0.768 z -0.460 along the Z-axis. The position resolution is approximately 5 μ m. With the introduction of MFT, the ability to distinguishmuon originating from mesons containing charm quarks (e.g., D mesons) andmesons containing beauty quarks (e.g., B mesons) is anticipated.

27

Figure 2.5: MFT[17]2.6

Online-Oﬄine syetem (O2)This system is introduced to enable continuous data readout, designed tooversee online data readout, data compression, and oﬄine data analysis.
The background of introducing O2 lies in the challenges posed by statisticalquantities and data volume in the upgrade. The challenge of statistical quantities arises from the low signal-to-background ratio, while the challenge ofdata volume comes from the increase in data readout in the Pb-Pb collisionexperiment in Run 3. The data volume exceeds 1TB/s, roughly 100 times
that of Run 1. Therefore, it is necessary to reduce the vast amount of data
during readout.
The concept of O2 is to transfer all data sent from detectors to the computing system. It involves dividing time into ﬁnely segmented time frames
and even ﬁner sub-time frames based on the clock of the LHC. Data fromeach detector is synchronized within sub-time frames and then within timeframes. Calibration and data reconstruction for each detector are performed
within sub-time frames and time frames to compress the data, reducing it
to 60-70GB/s when sent to the archive. Further asynchronous data reconstruction and parameter calibration for managing data quality are conducted
before the ﬁnal data is stored.

28

Figure 2.6: Design of O2 system[18]29Chapter 3
Analysis
3.1

Data set

The data set used
√ in this study is Minimum-bias (MB) events with centerof-mass energy s = 13.6 TeV at pp collision taken in period Run 3. Theinteraction rate is 500 kHz. The number of reconstructed events is 3.11×1011
It should be noted that the data set LHC22o pass4 that is used in the following discussion has a problem in ϕ angle reconstruction at MCH. Fig
3.1 shows the comparison between LHC22o pass4 and LHC23 pass1 MCH.
LHC23zs pass1 mch is one of the labels of the dataset taken in 2023 and ﬁxedversion for ϕ angle reconstruction. Asymmetrical distribution is ﬁxed as seenin Fig 3.1 (a). Fig 3.1 (b) illustrates the invariant mass distribution with two
datasets. The ϕ angle ﬁxed data show a sharper peak around 3.096GeV/c2
than the other. However, the number of selected events in ϕ angle ﬁxed data
is lower than it of the other by the factor of 40. The LHC23zs pass1 mch
has 7.46 × 109 , where as LHC22o pass4 has 3.11 × 1011 . The statistics affect signal extraction (especially, low mass vector meson) by charged-particle
multiplicity separation. Therefore, I selected the LHC22o pass4 dataset inthis study.

30

ϕ distribution
0.005

LHC22o_pass4
LHC23zs_pass1_mch

10−2
0.004

0.003
−3

10
0.002

Phi angle in LHC22o_pass4
Fixed phi angle in LHC23zs_pass1_mch

0.001

zs / o

−3

−2

−1

0

1

2

zs / o

10−4

1.2
−3
1.15
1.1
1.05
1
0.95
0.9
0.85
0.8

3
ϕ (rad.)

1.3
0
1.2

0.5

1

1.5

2

2.5

3

3.5

4

4.5
5
mass (GeV/c2)

0.5

1

1.5

2

2.5

3

3.5

4

4.5
5
Mass [GeV/c2]

1.1
1
0.9
0.8

−2

−1

0

1

2

3

0.7

0

φ

(a) ϕ angle(b) Mass

Figure 3.1: ϕ angle and mass comparison between two dataset in top. The ratioof the two distribution (zs / o) is in bottom.

3.2

Event selection

Taken events are MB triggered, but events are selected via some criteria tosecure quality. There are two criteria, INEL> 0 and |zcol | ≤ 10cm. INEL ¿ 0means that there is at least one particle hit in ITS or FIT detector covering
beam pipe. zcol cut is to ensure the uniformity of the ITS acceptance.

3.3

Charged-particle multiplicity

Charged-particle multiplicity is measured by ITS detector covering pseudorapidity range |η| ≤ 1.22. Charged-particle multiplicity(dNch /dη) should
be calculated with the correction number of the reconstructed number oftracks (Ntrk ) to the number of charged-particle (Nch ) via detection eﬃciency with Monte Carlo simulation. In this study, the number of thereconstructed track is not corrected because there is no anchored (corresponding setup to real data taking) MC simulation in the current status.
The deﬁnition of Ntrk in this study is the number of ITS tracks that contributeto vertex ﬁnding. The criterion is |DCAy| < 3σtotal , where σtotal =
√

2
2
2
2
σDCAy
+ σvertexX+ σvertexY+ σextra. The σextra is an extra error to meanvertex sigma used when selecting tracks. The σvertex are given by collisionvertex distribution. The σDCAy is given by the DCAy distribution. Chargedparticle multiplicity is normalized by self-expectation value. Fig 3.2 illustrates Ntrk distribution. The number of events in each multiplicity interval

31

is referred by it.
(dNch /dη)iNi
NM B= trk × i⟨dNch /dη⟩Ntrk NM B(3.1)

NM B is the number of minimum bias triggered events. The correspondence
between dNtrk /dη and (dNch /dη)i /⟨dNch /dη⟩ is shown in Table. The Ntrk
interval is adjusted for J/ψ and ρ, ω, ϕ.
Table 3.1: The Ntrk interval and corresponding charged-particle multiplicity densities

J/ψ
Ntrk
1-10
11-20
21-30
31-40
41-50
51-70
71-100ρ, ω, ϕ
Ntrk
1-10
11-20
21-30
31-50
51-100i(dNch /dη) /⟨dNch /dη⟩
0.294
0.776
1.30
1.81
2.32
3.02
4.24

(dNch /dη)i /⟨dNch /dη⟩
0.294
0.776
1.30
2.00
3.33

Figure 3.2: Number of ITS tracks contributes to primary vertex ﬁnﬁng

3.4

Invariant mass reconstruction with dimuon

Stored forward tracks contain MCH tracks. All tracks used in this study
are matched to both MFT and MID and called Global-Muon-Track (GMT).
32

MFT-MID matching secure muon identiﬁcation due to the iron wall locatedbetween MCH and MID. MFT-MCH matching improves spatial resolution.
Muon track cuts required to GMT are shown in Table.
Table 3.2: Muon track selection

Indicator
Rabs
pDCA
η

criteria
17.5 ≤ Rabs ≤ 89.5
pDCA ≤ 594(17.5 ≤ Rabs ≤ 26.5)
pDCA ≤ 324(26.5 ≤ Rabs ≤ 89.5)−4 ≤ η ≤ −2.5

Rabs is the distance from the z-axis at the end of the absorber. That isused to remove tracks that go through the high-density part of the absorber.
The tracks are aﬀected by multiple scattering signiﬁcantly. The pDCA means
moment times distance from the closest approach (DCA). DCA is the distance from the z-axis to the point propagated to zcol . DCA is multiplied bymomentum to cancel its momentum dependence. The larger the lifetime ofa particle is, the larger its pDCA tends to be. The pDCA selection removes
muon from long lifetime particles, π, K. The η selection reﬂects MCH acceptance.
Invariant mass reconstruction is for signal particle extraction. Resonancepeak in mass distribution indicates signal.
√
Mµµ = 2m2µ + 2(Eµ1 Eµ2 − pµ1 · pµ2 )
(3.2)
where
Eµ =

√
m2µ + p2µ(3.3)

Fig 3.3 is the 2D-histogram via the invariant mass reconstructed in forward
and Ntrk measured in central. The following analysis is based on it.

33Vtx contrib.

MassMult
300

250

Entries9.249221e+07

Mean x

1.106

Mean y22.68

Std Dev x

0.8546

Std Dev y

20.33

×10

3

120
100

200
80
150
60
100
40
50

0
0

20

2

4

6

8

10

12

14
mass (GeV/c2)

0

Figure 3.3: Invariant mass vs Ntrk

3.5

Combinatorial Background(BG) subtraction

Invariant mass distribution is calculated by all opposite sign track pairs in thesame event. Pairing can contain no correlation and is called combinatorial
BG. There are two well-known methods to subtract combinatorial BG, likesign method and event mixing method.

3.5.1

Like-sign (LS) method

The like-sign (LS) method uses the invariant mass spectrum via the like-signpairs (plus-plus or minus-minus pairs). Correlated muon pair production is
via dimuon pair production, so the like-sign pairs are considered noncorrelation pairs.
√++ dN ++
dNBG
dNsame
same
= 2R
(3.4)
dm
dm
dm
where
+−
dNmix
dm

R = √ ++ ++dNmix dNmix
2
dm
dm

(3.5)

R factor is to correct the diﬀerence between plus charge and minus charge
same
mix
acceptance. Ndm
is obtained by event mixing pairing where as Ndm
iscontained by same event pairing. Event mixing pairing means that the counterpart of a pairing originates from diﬀerent events. The Fig3.3 shows mass
34

distribution with combinatorial BG estimated by the LS method at the top
and Rfactor at the bottom. Interval of Ntrk dependence of Rfactor is weak.
Rfactor shows unit in mµµ leq0.5, where as smaller than unit in mµµ geq0.5.
Rfactor aﬀects low mass region, but not resonance peak of signals.

35

dN/dm1.000000 < Mult < 10.000000
610Same event opositte-sign
Same event like-sign (++)
Same event like-sign (--)
Geometory mean with Rfactor
5

10

104

Rfactor

3
1.5
10
1.40
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5

0

0.5

1

1.5

0.5

1

1.5

2

2.5

3

3.5

4

4.5
5
Mass [GeV/c2]

2

2.5

3

3.5

4

4.5
5
Mass [GeV/c2]

0.000000 < Mult < 10.000000(a) 1 ≤ Ntrk ≤ 10
Same event opositte-sign
Same event like-sign (++)
Same event like-sign (--)
Geometory mean with Rfactor

510

21.000000 < Mult < 30.000000

dN/dm

dN/dm

11.000000 < Mult < 20.000000

Same event opositte-sign
Same event like-sign (++)
Same event like-sign (--)
Geometory mean with Rfactor

5

10

104
104

3

10
3

1.5
1.40
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5

0

0.5

1

1.5

0.5

1

1.5

2

2.5

3

3.5

4

4.5
5
Mass [GeV/c2]

2

2.5

3

3.5

4

4.5
5
Mass [GeV/c2]

10.000000 < Mult < 20.000000

RfactorRfactor

10

1.5
1.40
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5

0

0.5

1

1.5

0.5

1

1.5

(b) 11 ≤ Ntrk ≤ 20

3

3.5

4

4.5
5
Mass [GeV/c2]

2

2.5

3

3.5

4

4.5
5
Mass [GeV/c2]

41.000000 < Mult < 50.000000

dN/dm

dN/dm

Same event opositte-sign
Same event like-sign (++)
Same event like-sign (--)
Geometory mean with Rfactor

52.5(c) 21 ≤ Ntrk ≤ 30

31.000000 < Mult < 40.000000

102

20.000000 < Mult < 30.000000

510Same event opositte-sign
Same event like-sign (++)
Same event like-sign (--)
Geometory mean with Rfactor

104
104

3

10
3

dN/dm

0

0.5

1

1.5

0.5

1

1.5

2

2.5

3

3.5

4

4.5
5
Mass [GeV/c2]

2

2.5

3

3.5

4

4.5
5
Mass [GeV/c2]

30.000000 < Mult < 40.000000

Rfactor

1.5
1.40
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5

1.5
1.40
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5

0

0.5

1

1.5

0.5

1

1.5

2

2.5

3

3.5

4

4.5
5
Mass [GeV/c2]

2

2.5

3

3.5

4

4.5
5
Mass [GeV/c2]

40.000000 < Mult < 50.000000(d) 31 ≤ Ntrk ≤ 40(e) 41 ≤ Ntrk ≤ 50

51.000000 < Mult < 70.000000

71.000000 < Mult < 100.000000

dN/dm

Rfactor10510Same event opositte-sign
Same event like-sign (++)
Same event like-sign (--)
Geometory mean with Rfactor

Same event opositte-sign
Same event like-sign (++)
Same event like-sign (--)
Geometory mean with Rfactor
104

104

3

10
3

1.5
1.40
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5

0

0.5

1

1.5

0.5

1

1.5

2

2.5

3

3.5

4

4.5
5
Mass [GeV/c2]

2

2.5

3

3.5

4

4.5
5
Mass [GeV/c2]

51.000000 < Mult < 70.000000

102
1.5
1.40
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5

RfactorRfactor100(f ) 51 ≤ Ntrk ≤ 70

0.5

1

1.5

0.5

1

1.5

2

2.5

3

3.5

4

4.5
5
Mass [GeV/c2]

2

2.5

3

3.5

4

4.5
5
Mass [GeV/c2]

71.000000 < Mult < 100.000000(g) 71 ≤ Ntrk ≤ 100

Figure 3.4: Combinatorial BG with like-sign method and Rfactor

36

3.5.2

Event mixing (EM) method

The event mixing method forms combinatorial BG via opposite sign track
pair, but their origination is not the same. Two events are independent ofeach other, so pairing in mixed events does not correlate.
+−
dNBG
dNmix
=S
dm
dm

∫

where
S=

Like−sign++−−dNsameNsame+ Nsame
∫
=
+−
+−
dNmix
Nmix

(3.6)

(3.7)

S is the scaling factor.
Fig 3.5 illustrates the invariant mass distribution and combinatorial BG estimated by the LS and EM method at the top and the ratio of each at thebottom. The interval of Ntrk dependence of the LS/EM ratio is weak. Combinatorial BG via the EM method is lower than the LS method in mµµ ≥ 1,
whereas higher than it in mµµ ≤ 1. the LS method can reﬂect event-by-event
massive motion like ﬂow and jets, whereas the EM method can’t. However,the diﬀerence in the shape of combinatorial BG via two methods is unclear.
All results in this study are done with both combinatorial BG.

37

dN/dm1.000000 < Mult < 10.000000
6

10

Data
Like-sign with Rfactor
Mixing
5

10

104

LS/EM

3
1.5
10
1.40
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5

0

0.5

1

1.5

0.5

1

1.5

2

2.5

3

3.5

4

4.5
5
Mass [GeV/c2]

2

2.5

3

3.5

4

4.5
5
Mass [GeV/c2]

1.000000 < Mult < 10.000000(a) 1 ≤ Ntrk ≤ 10
Data
Like-sign with Rfactor
Mixing5

10

21.000000 < Mult < 30.000000

dN/dm

dN/dm

11.000000 < Mult < 20.000000

Data
Like-sign with Rfactor
Mixing

5

10

104
104

3

10
3

0

0.5

1

1.5

0.5

1

1.5

2

2.5

3

3.5

4

4.5
5
Mass [GeV/c2]

2

2.5

3

3.5

4

4.5
5
Mass [GeV/c2]

11.000000 < Mult < 20.000000

LS/EM

LS/EM

10

1.5 0
1.4
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5

1.5
1.40
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5

0

0.5

1

1.5

0.5

1

1.5

(b) 11 ≤ Ntrk ≤ 20

3

3.5

4

4.5
5
Mass [GeV/c2]

2

2.5

3

3.5

4

4.5
5
Mass [GeV/c2]

41.000000 < Mult < 50.000000

dN/dm

dN/dm

Data
Like-sign with Rfactor
Mixing5

2.5(c) 21 ≤ Ntrk ≤ 30

31.000000 < Mult < 40.000000

10221.000000 < Mult < 30.000000

5

10

Data
Like-sign with Rfactor
Mixing

104
104

3

10
3

dN/dm

0

0.5

1

1.5

0.5

1

1.5

2

2.5

3

3.5

4

4.5
5
Mass [GeV/c2]

2

2.5

3

3.5

4

4.5
5
Mass [GeV/c2]

31.000000 < Mult < 40.000000

LS/EM

1.5
1.40
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5

1.5
1.40
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5

0

0.5

1

1.5

0.5

1

1.5

2

2.5

3

3.5

4

4.5
5
Mass [GeV/c2]

2

2.5

3

3.5

4

4.5
5
Mass [GeV/c2]

41.000000 < Mult < 50.000000(d) 31 ≤ Ntrk ≤ 40(e) 41 ≤ Ntrk ≤ 50

51.000000 < Mult < 70.000000

71.000000 < Mult < 100.000000

dN/dm

LS/EM

10

5

10

Data
Like-sign with Rfactor
MixingData
Like-sign with Rfactor
Mixing

104

104

3

10
3

1.5
1.40
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5

0

0.5

1

1.5

0.5

1

1.5

2

2.5

3

3.5

4

4.5
5
Mass [GeV/c2]

2

2.5

3

3.5

4

4.5
5
Mass [GeV/c2]

51.000000 < Mult < 70.000000

102
1.5
1.40
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5

LS/EM

LS/EM

10

0

(f ) 51 ≤ Ntrk ≤ 70

0.5

1

1.5

0.5

1

1.5

2

2.5

3

3.5

4

4.5
5
Mass [GeV/c2]

2

2.5

3

3.5

4

4.5
5
Mass [GeV/c2]

71.000000 < Mult < 100.000000(g) 71 ≤ Ntrk ≤ 100

Figure 3.5: Combinatorial BG with event-mixing method and the ratio LS/EM

38

3.6

Signal extraction

Resonance peak should follow Breit-Wigner formula.
f (x) =wherek=k(x2 − M 2 )2 + M 2 Γ2√
2sqrt2M Γγ√, γ = M 2 (M 2 + Γ2 )π M2 + γ

(3.8)

(3.9)

However, the decay width Γ can be broad due to momentum and opening angle resolution and energy loss in detectors and other objects. As aresult, a Gaussian-based function is used to extract signals. The doublesided crystal ball function and Gaussian are used for J/ψ and ρ, ω, andϕ
extraction as signal functions. Remaining BG are estimated with double
exponential function for high mass (2 ≤ M ≤ 4(GeV /c2 )) region, and Variable Width Gaussian (VWG) function and single exponential function forlow mass (0.5 ≤ M ≤ 1.35(GeV /c2 )) region. The double-sided crystal ballfunction has two tails on both the high-mass side and low-mass side. Tails
can reﬂect detector resolution and energy loss eﬀects. CB2 function is
α2

β1 β1 − 21 β1
()( |α1 | − |α1 | − x−m)−β1 ( x−m≤ α1 )eσσ
 |α1 |
fCB2 =(x−m)2e− 2σ2(α2 < x−m
< α1 )σ2α2 ( β2 )β2 e− 2 ( β2 − |α | + x−m )−β2 ( x−m ≥ α )
2
2
|α2 |
|α2 |
σ
σ

and VWG function is
fV W G = e−(x−m)22σ(x)2(3.10)(3.11)

where

x−m
)
(3.12)m
The yield at each Ntrk interval is normalized by its expectation value ofmultiplicity integrated yield.
σ(x) = A + B(i
NSig(dNSig /dy)i
NM B
=
× i
⟨dNSig /dy⟩
NSig NM B(3.13)

Fig 3.6 3.8 illustrate J/ψ extraction with CB2 function in each multiplicity interval in case w/o LS and EM method to estimate combinatorial BG.
39

The remaining BG is ﬁt by the double exponential function. The remaining
BG is ﬁt well. Fitting χ2 is shown in the next chapter. The asymmetry
behavior of J/ψ resonance peak is illustrated by the tails of CB2 function(red line).

40

1.000000 < Mult < 10.000000
dN/dm

Mass_MuMu_SEPM_MultSep_0

10

6

10

5

10

4

10

3

EntriesMean
Std Dev

Data
Fit Total
Fit Sig
Fit BG

2

2.5

3

3.5

741
2.565
0.50884
Mass [GeV/c2](a) 1 ≤ Ntrk ≤ 10
10

6

10

5

10

4

10

3

21.000000 < Mult < 30.000000
Mass_MuMu_SEPM_MultSep_1

EntriesMean
Std Dev

Data
Fit Total
Fit Sig
Fit BG

2

2.5

3

3.5

Mass_MuMu_SEPM_MultSep_2

dN/dm

dN/dm

11.000000 < Mult < 20.000000
741
2.574
0.5211

10

5

10

4

10

3

4
Mass [GeV/c2]

EntriesMean
Std Dev

Data
Fit Total
Fit Sig
Fit BG22.5(b) 11 ≤ Ntrk ≤ 20

3

3.5

4
Mass [GeV/c2](c) 21 ≤ Ntrk ≤ 30

31.000000 < Mult < 40.000000

41.000000 < Mult < 50.000000

5

10

4

10

3

EntriesMean
Std Dev

Data
Fit Total
Fit Sig
Fit BG2

2.5

Mass_MuMu_SEPM_MultSep_4

dN/dm

dN/dm

Mass_MuMu_SEPM_MultSep_3

10

741
2.579
0.5034

3.5

10

3

10

2

4
Mass [GeV/c2]

EntriesMean
Std Dev

Data
Fit Total
Fit Sig
Fit BG

104

3

2

2.5

(d) 31 ≤ Ntrk ≤ 40

3

3.5

4
Mass [GeV/c2]

71.000000 < Mult < 100.000000

5

10

4

10

3

EntriesMean
Std Dev

Mass_MuMu_SEPM_MultSep_6

dN/dm

dN/dm

Mass_MuMu_SEPM_MultSep_5

10

741
2.555
0.5027(e) 41 ≤ Ntrk ≤ 50

51.000000 < Mult < 70.000000
Data
Fit Total
Fit Sig
Fit BG741
2.561
0.5074741
2.515
0.5086

EntriesMean
Std Dev

Data
Fit Total
Fit Sig
Fit BG
10

4

10

3

741
2.513
0.5097

102
2

2.5

3

3.5

4
Mass [GeV/c2]

2(f ) 51 ≤ Ntrk ≤ 70

2.5

3

3.5

4
Mass [GeV/c2](g) 71 ≤ Ntrk ≤ 100

Figure 3.6: J/ψ signal extraction without combinatorial BG subtraction

41

1.000000 < Mult < 10.000000
dN/dm

Mass_MuMu_SEPM_afterCutLikesign_MultSep_0

10

EntriesMean
Std Dev

Data
Fit Total
Fit Sig
Fit BG

5

1772692.72
0.5498

104

10

3

2

2.5

3

3.5

4
Mass [GeV/c2](a) 1 ≤ Ntrk ≤ 10
11.000000 < Mult < 20.000000

21.000000 < Mult < 30.000000
EntriesMean
Std Dev

10

4

10

3

2

2.5

3

3.5

Mass_MuMu_SEPM_afterCutLikesign_MultSep_2

dN/dm

dN/dm

Mass_MuMu_SEPM_afterCutLikesign_MultSep_1

Data
Fit Total
Fit Sig
Fit BG

1008812.769
0.5137

EntriesMean
Std Dev

Data
Fit Total
Fit Sig
Fit BG
10

4

10

3

4
Mass [GeV/c2]

2

2.5(b) 11 ≤ Ntrk ≤ 20

3

3.5

4
Mass [GeV/c2](c) 21 ≤ Ntrk ≤ 30

31.000000 < Mult < 40.000000

41.000000 < Mult < 50.000000

104

10

EntriesMean
Std Dev

Mass_MuMu_SEPM_afterCutLikesign_MultSep_4

dN/dm

dN/dm

Mass_MuMu_SEPM_afterCutLikesign_MultSep_3

Data
Fit Total
Fit Sig
Fit BG58658
2.726
0.533635899
2.764
0.5144

10

4

10

3

EntriesMean
Std Dev

Data
Fit Total
Fit Sig
Fit BG

22377
2.695
0.5537

3

102
2

2.5

3

3.5

4
Mass [GeV/c2]

2(d) 31 ≤ Ntrk ≤ 40

4

10

3

10

2

10

4
Mass [GeV/c2]

71.000000 < Mult < 100.000000
EntriesMean
Std Dev

Data
Fit Total
Fit Sig
Fit BG

2

2.5

3

3.5

Mass_MuMu_SEPM_afterCutLikesign_MultSep_6

dN/dm

dN/dm

3.5

Mass_MuMu_SEPM_afterCutLikesign_MultSep_5

5

10

3

(e) 41 ≤ Ntrk ≤ 50

51.000000 < Mult < 70.000000
10

2.5

19804
2.718
0.5375

4
Mass [GeV/c2]

10

4

10

3

10

2

2

(f ) 51 ≤ Ntrk ≤ 70

EntriesMean
Std Dev

Data
Fit Total
Fit Sig
Fit BG

2.5

3

3.5

4
Mass [GeV/c2](g) 71 ≤ Ntrk ≤ 100

Figure 3.7: J/ψ signal extraction with LS method

42

6400
2.736
0.5215

1.000000 < Mult < 10.000000
dN/dm

Mass_MuMu_SEPM_afterCutMixing_MultSep_0

10

EntriesMean
Std Dev

Data
Fit Total
Fit Sig
Fit BG

53203692.78
0.5255

104

2

2.5

3

3.5

4
Mass [GeV/c2](a) 1 ≤ Ntrk ≤ 10
11.000000 < Mult < 20.000000

21.000000 < Mult < 30.000000
EntriesMean
Std Dev

10

4

10

3

Mass_MuMu_SEPM_afterCutMixing_MultSep_2

dN/dm

dN/dm

Mass_MuMu_SEPM_afterCutMixing_MultSep_1

Data
Fit Total
Fit Sig
Fit BG

1848722.75
0.5572

EntriesMean
Std Dev

Data
Fit Total
Fit Sig
Fit BG
104

10

2

2.5

3

3.5

3

4
Mass [GeV/c2]

2

2.5(b) 11 ≤ Ntrk ≤ 20

3

3.5

4
Mass [GeV/c2](c) 21 ≤ Ntrk ≤ 30

31.000000 < Mult < 40.000000

41.000000 < Mult < 50.000000

4

10

3

EntriesMean
Std Dev

Data
Fit Total
Fit Sig
Fit BG

2

2.5

3

3.5

Mass_MuMu_SEPM_afterCutMixing_MultSep_4

dN/dm

dN/dm

Mass_MuMu_SEPM_afterCutMixing_MultSep_3

10

66243
2.761
0.5298

10

4

10

3

EntriesMean
Std Dev

Data
Fit Total
Fit Sig
Fit BG

4
Mass [GeV/c2]

2(d) 31 ≤ Ntrk ≤ 40

2.5

3

3.5

4
Mass [GeV/c2]

71.000000 < Mult < 100.000000

10EntriesMean
Std Dev

4

Mass_MuMu_SEPM_afterCutMixing_MultSep_6

dN/dm

dN/dm

Mass_MuMu_SEPM_afterCutMixing_MultSep_5

Data
Fit Total
Fit Sig
Fit BG

40465
2.714
0.5458(e) 41 ≤ Ntrk ≤ 50

51.000000 < Mult < 70.000000

101082902.773
0.521836336
2.747
0.5341

10

4

10

3

EntriesMean
Std Dev

Data
Fit Total
Fit Sig
Fit BG

3

11718
2.75
0.5356

102
2

2.5

3

3.5

4
Mass [GeV/c2]

2(f ) 51 ≤ Ntrk ≤ 70

2.5

3

3.5

4
Mass [GeV/c2](g) 71 ≤ Ntrk ≤ 100

Figure 3.8: J/ψ signal extraction with EM method43Fig 3.9 3.12 show ρ+ω and ϕ extraction in each multiplicity range in caseof using the LS and EM method to estimate combinatorial BG. Diﬀerent fromJ/ψ extraction, low mass meson resonance peak is so signiﬁcantly aﬀected by
combinatorial BG (see Fig 3.3) that extraction is done after combinatorial BG
subtraction. The size of the signals strongly depends on the estimation of theremaining BG after combinatorial subtraction. Two remaining BG functions
are used, the VWG function and the single exponential function. Fig 3.9
and 3.10 are results with exponential function and Fig 3.11 and 3.12 are with
VWG function. See Fig 3.10 (d), the remaining BG function (exponential)
overestimates between ρ + ω and ϕ peaks. In the highest multiplicity interval(51 ≤ Ntrk ≤ 100), signal resonance peaks are not clear to ﬁt, especially ϕwith the LS method.

44

1.000000 < Mult < 10.000000
dN/dm

Mass_MuMu_SEPM_afterCutLikesign_MultSep_0

EntriesMean
Std Dev

Data
Fit all
Fit rhoomega
Fit phiFit BG

10

5

10

4

0.5

0.6

0.7

0.8

0.9

1

1.1

1772690.86280.24281.2
1.3
Mass [GeV/c2](a) 1 ≤ Ntrk ≤ 10
11.000000 < Mult < 20.000000

21.000000 < Mult < 30.000000
EntriesMean
Std Dev

Mass_MuMu_SEPM_afterCutLikesign_MultSep_2

dN/dm

dN/dm

Mass_MuMu_SEPM_afterCutLikesign_MultSep_1

Data
Fit all
Fit rhoomega
Fit phiFit BG

1008810.86170.24251010EntriesMean
Std Dev

Data
Fit all
Fit rhoomega
Fit phiFit BG

4

4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2
1.3
Mass [GeV/c2]

0.5

0.6

(b) 11 ≤ Ntrk ≤ 20

0.7

0.8

0.9

1

1.1

1.2
1.3
Mass [GeV/c2](c) 21 ≤ Ntrk ≤ 30

31.000000 < Mult < 50.000000

51.000000 < Mult < 100.000000
EntriesMean
Std Dev

Data
Fit all
Fit rhoomega
Fit phiFit BG

Mass_MuMu_SEPM_afterCutLikesign_MultSep_4

dN/dm

dN/dm

Mass_MuMu_SEPM_afterCutLikesign_MultSep_3

58296
0.86680.2478

EntriesMean
Std Dev

Data
Fit all
Fit rhoomega
Fit phiFit BG

10

10

58658
0.86350.241826125
0.86390.2424

4

4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2
1.3
Mass [GeV/c2]

0.5(d) 31 ≤ Ntrk ≤ 40

0.6

0.7

0.8

0.9

1

1.1

1.2
1.3
Mass [GeV/c2](e) 41 ≤ Ntrk ≤ 50

Figure 3.9: ρ+ω and ϕ extraction (combinatorial BG is estimated by LS method,
remaining BG is done by exponential function)45

1.000000 < Mult < 10.000000
dN/dm

Mass_MuMu_SEPM_afterCutMixing_MultSep_0

10

EntriesMean
Std Dev

Data
Fit all
Fit rhoomega
Fit phiFit BG

53203690.87490.2457

104
0.5

0.6

0.7

0.8

0.9

1

1.1

1.2
1.3
Mass [GeV/c2](a) 1 ≤ Ntrk ≤ 10
11.000000 < Mult < 20.000000

21.000000 < Mult < 30.000000

5

10

4

EntriesMean
Std Dev

Data
Fit all
Fit rhoomega
Fit phiFit BG

Mass_MuMu_SEPM_afterCutMixing_MultSep_2

dN/dm

dN/dm

Mass_MuMu_SEPM_afterCutMixing_MultSep_1

101848720.87770.2465

EntriesMean
Std Dev

Data
Fit all
Fit rhoomega
Fit phiFit BG

1082900.88560.2517

104

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2
1.3
Mass [GeV/c2]

0.5

0.6

(b) 11 ≤ Ntrk ≤ 20

0.7

0.8

0.9

1

1.1

1.2
1.3
Mass [GeV/c2](c) 21 ≤ Ntrk ≤ 30

31.000000 < Mult < 50.000000

51.000000 < Mult < 100.000000
EntriesMean
Std Dev

Data
Fit all
Fit rhoomega
Fit phiFit BG

10

Mass_MuMu_SEPM_afterCutMixing_MultSep_4

dN/dm

dN/dm

Mass_MuMu_SEPM_afterCutMixing_MultSep_3

1066030.87570.2473

EntriesMean
Std Dev

Data
Fit all
Fit rhoomega
Fit phiFit BG

10

4

10

3

47880
0.88190.2507

4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2
1.3
Mass [GeV/c2]

0.5(d) 31 ≤ Ntrk ≤ 50

0.6

0.7

0.8

0.9

1

1.1

1.2
1.3
Mass [GeV/c2](e) 51 ≤ Ntrk ≤ 100

Figure 3.10: ρ+ω and ϕ extraction (Combinatorial BG is estimated by EM
method, remaining BG is done by exponential function)46

1.000000 < Mult < 10.000000
dN/dm

Mass_MuMu_SEPM_afterCutLikesign_MultSep_0

EntriesMean
Std Dev

Data
Fit all
Fit rhoomega
Fit phiFit BG

10

5

10

4

0.5

0.6

0.7

0.8

0.9

1

1.1

1772690.86280.24281.2
1.3
Mass [GeV/c2](a) 1 ≤ Ntrk ≤ 10
11.000000 < Mult < 20.000000

21.000000 < Mult < 30.000000

10

5

10

4

EntriesMean
Std Dev

Mass_MuMu_SEPM_afterCutLikesign_MultSep_2

dN/dm

dN/dm

Mass_MuMu_SEPM_afterCutLikesign_MultSep_1

Data
Fit all
Fit rhoomega
Fit phiFit BG

1008810.86170.2425

EntriesMean
Std Dev

Data
Fit all
Fit rhoomega
Fit phiFit BG

58658
0.86350.2418

104

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2
1.3
Mass [GeV/c2]

0.5

0.6

(b) 11 ≤ Ntrk ≤ 20

0.7

0.8

0.9

1

1.1

1.2
1.3
Mass [GeV/c2](c) 21 ≤ Ntrk ≤ 30

31.000000 < Mult < 50.000000

51.000000 < Mult < 100.000000

10

5

10

4

EntriesMean
Std Dev

Data
Fit all
Fit rhoomega
Fit phiFit BG

Mass_MuMu_SEPM_afterCutLikesign_MultSep_4

dN/dm

dN/dm

Mass_MuMu_SEPM_afterCutLikesign_MultSep_3

58296
0.86050.2429105EntriesMean
Std Dev

Data
Fit all
Fit rhoomega
Fit phiFit BG

26125
0.86880.2462

104

10

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2
1.3
Mass [GeV/c2]

3

0.5(d) 31 ≤ Ntrk ≤ 40

0.6

0.7

0.8

0.9

1

1.1

1.2
1.3
Mass [GeV/c2](e) 41 ≤ Ntrk ≤ 50

Figure 3.11: ρ+ω and ϕ extraction (combinatorial BG is estimated by LS
method, remaining BG is done by VWG function)

47

1.000000 < Mult < 10.000000
dN/dm

Mass_MuMu_SEPM_afterCutMixing_MultSep_0

10

5

10

4

EntriesMean
Std Dev

Data
Fit all
Fit rhoomega
Fit phiFit BG

0.5

0.6

0.7

0.8

0.9

1

1.1

3203690.88210.25111.2
1.3
Mass [GeV/c2](a) 1 ≤ Ntrk ≤ 10
11.000000 < Mult < 20.000000

21.000000 < Mult < 30.000000
EntriesMean
Std Dev

Mass_MuMu_SEPM_afterCutMixing_MultSep_2

dN/dm

dN/dm

Mass_MuMu_SEPM_afterCutMixing_MultSep_1

Data
Fit all
Fit rhoomega
Fit phiFit BG

1848720.88490.251710
10EntriesMean
Std Dev

Data
Fit all
Fit rhoomega
Fit phiFit BG

4

4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2
1.3
Mass [GeV/c2]

0.5

0.6

(b) 11 ≤ Ntrk ≤ 20

0.7

0.8

0.9

1

1.1

1.2
1.3
Mass [GeV/c2](c) 21 ≤ Ntrk ≤ 30

31.000000 < Mult < 50.000000

51.000000 < Mult < 100.000000
EntriesMean
Std Dev

Data
Fit all
Fit rhoomega
Fit phiFit BG

Mass_MuMu_SEPM_afterCutMixing_MultSep_4

dN/dm

dN/dm

Mass_MuMu_SEPM_afterCutMixing_MultSep_3

1066030.87570.2473

EntriesMean
Std Dev

Data
Fit all
Fit rhoomega
Fit phiFit BG

10101082900.8776
0.245947880
0.88190.2507

4

4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2
1.3
Mass [GeV/c2]

0.5(d) 31 ≤ Ntrk ≤ 50

0.6

0.7

0.8

0.9

1

1.1

1.2
1.3
Mass [GeV/c2](e) 51 ≤ Ntrk ≤ 100

Figure 3.12: ρ+ω and ϕ extraction (combinatorial BG is estimated by EM
method, remaining BG is done by VWG function)

48

Chapter 4
Result4.1

J/ψ analysis

χ2

Fig 4.1 shows ﬁtting χ2 of BG + signal total function. The three plots in low
charged-particle multiplicity interval (i = 0,1,2) with the LS method are lower
than the other two, whereas higher multiplicity plots show similar values. As
a result, the case with the LS method shows the most stable ﬁtting.

no subtraction
Like-sign method
Mixing method

350
300
250
200
150
100
50
0
0

0.5

1

1.5

2

2.5

3

3.5

4
4.5
dNchdη/<dN dη>chFigure 4.1: Fitting χ2 with function BG + Signal for J/ψ extraction with dependence of charged-particle multiplicity

49

Fig 4.2 shows the row yield of J/ψ as a function of charged-particle multiplicity. The appearance of the distribution of each plot does not dependon the method or presence of combinatorial BG estimation, but the size
varies and always maintains the relationship EM¿LS¿no-subtraction of combinatorial BG. Table 4.1 summarizes each value and statistics error shownin Fig 4.2. In summary, the yield with the EM method and LS method ishigher than it with no subtraction case by 13% (32σ of statistics error) for
the EM method and by 6.2%(16σ of statistics error) for the LS method. For
resonance peak analysis, peak extraction has a weak dependence on the combinatorial BG estimation method since the remaining BG is removed after
combinatorial subtraction. However, statistics errors aﬀect the method, andﬁtting can be inﬂuenced it. I expect that this rho yield diﬀerence is due tothe ﬁtting process.
[H]
Table 4.1: Fitting χ2 for lowmass analysis

i
0
1
2
3
4
5
6
Summary

no subtraction
110521
64291
39371
26809
17576
8802
2226
269632

error
683
520
414
346
287
148
62
1066

50

LS
117600
66090
41129
29817
19831
9318
2497
286282

error
468
456
282
230
190
96
38
725

EM
123303
71539
45364
30853
20400
9995
2562
304016

error
506
382
304
251
206
105
43
782

dNJ/ψ /dy

10

no subtraction
Like-sign method
Mixing method

5

104

10

3

0

0.5

1

1.5

2

2.5

3

3.5

4
4.5
dNchdη/<dN dη>chFigure 4.2: J/ψ row yield as a function of charged-particle multiplicity

Fig 4.3 shows the self-normalized yield of J/ψ as a function of chargedparticle multiplicity. The self-normalizing process makes the dependenceof the combinatorial BG estimation method weak. The three behaviors ofnormalized yield distribution are similar. Self-normalized yield is increasing
gradually from the third charged-particle interval. Statistics error indicatesthat these enhancement are beyond the margin of error, but the physicalmeaning of these arguments is unclear, as no correction or systematic error
has yet been discussed.

51

/dy>
J/ψ

dNJ/ψ /dy/<dN

no subtraction
like-sign method
Mixing method

1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0

0.5

1

1.5

2

2.5

3

3.5

4
4.5
dNchdη/<dN dη>chFigure 4.3: Self-normalized J/ψ yield as a function of charged-particle
multiplicity[19]As seen in Fig 1.16, Linear increase at low charged-particle multiplicity
has been shown. Increasing may mean that J/ψ production has dependenceof multiple parton interaction. Charged-particle multiplicity indicates number of parton-interaction. As a results, Fig 4.3 can imply same behavior
as MPI prove. However, Fig 4.3 at low charged-paricle multiplicity doesn’tshow linear trend.
In order to reveal the cause of yield at low charged-particle multiplicity,
I compare with proceeding study.[19] The left one shows the ratio of thenumber of events at each charged-particle multiplicity intervals. The gaps ofvalues enhance with increasing of charged-particle multiplicity. These imply
that results in this study should show more rapid increasing trend. However,there is no evidence to show the cause of strange behavior at low multiplicity
range. The right one illustrates the ratio of J/ψ yields with dependenceof charged-particle multiplicity. In contrary to the left one, the gaps of thevalues are shown at the lowest charged-particle multiplicity interval. This gap
can cause the enhancement of self-normalized yield at low charged-particle
multiplicity range. The strange enhancement of J/ψ yield is not via signal
extraction process. This means that accuracy of charged-particle multiplicity
52

10

3

NJ/i ψ /NJ/ψ

Nevent /Nievent

measurement should be investigated more. Ratio of the number of eventsshould be also aﬀected by accuracy of charged-particle multiplicity. Fig 4.3(a) imply that it may be account for it because this study at the lowest
interval show higher value than proceeding study.

Preceeding results

0.045

Preceeding results

0.04

my results

my results

0.035
102

0.03
0.025
0.02

10

0.015
0.01
0.005

1
0

20

40

60

80

0
0

100

20

40

60

80

Nch

100
Nch

i
(b) Ratio NJ/ψ
/NJ/ψ

M B,i
MB
/Nevent(a) Ratio Nevent

M B /N M B,i and Ratio N i /N
Figure 4.4: Ratio Nevent
J/ψ with dependence of
event
J/ψ
charged-particle multiplicity

Fig 4.4 illustrates mean mass of J/ψ as a function of charged-particle
multiplicity. Mean mass of J/ψ is m̄J/ψ = 3096.900±0.006[MeV/c2 ] in PDG.
The reconstructed mean mass of J/ψ shows weak dependence of chargedparticle multiplicity and PDG value within uncertainties. However, detailsof the charged-particle multiplicity dependence are not unclear because of its
error.

53

Mean mass [GeV/c 2]

no subtraction
Like-sign method
Mixing method

3.12
3.115
3.11
3.105
3.1
3.095
3.09
3.085
3.08
0

0.5

1

1.5

2

2.5

3

3.5

4
4.5
dNchdη/<dN dη>chFigure 4.5: J/ψ mean mass as a function of charged-particle multiplicity

Fig 4.5 shows the mass width of J/ψ as a function of charged-particle
multiplicity. Decay width of J/ψ is ΓJ/ψ = 94.1 ± 2.7[keV] with dimuon
decay mode in PDG. However, the reconstructed width of J/ψ is higher
than PDG one by a factor of 1000 due to detector resolution and energy loss
eﬀect. This implies that mass width measurement of J/ψ is diﬃcult to see
due to the measurement resolution of the detector.

54

σ [GeV/c2]

0.12

no subtraction
Like-sign method
Mixing method

0.1

0.08

0.06

0.04

0.02

0
0

0.5

1

1.5

2

2.5

3

3.5

4
4.5
dNchdη/<dN dη>chFigure 4.6: J/ψ mass width as a function of charged-particle multiplicity

χ2

Low mass vector meson analysis

χ2

4.2

70

Like-sign method

60

Mixing method100

Like-sign method
Mixing method

80

50
60

40
30

40

20
20
10
0
0

0.5

1

1.5

2

2.5

0
0

3
3.5
dNchdη/<dN dη>
ch

0.5

1

1.5

2

2.5

3
3.5
dNchdη/<dN dη>ch(a) BG : VWG(b) BG : Exponential

Figure 4.7: Fitting χ2 with function BG + Signal for ρ + ωandϕ extraction withdependence of charged-particle multiplicity

55

χ2

χ2
50

40

Like-sign method40

Like-sign method

35

Mixing method

Mixing method

30
25

30

20
20

15
10

10
5
0
0

0.5

1

1.5

2

2.5

0
0

3
3.5
dNchdη/<dN dη>

0.5

1

1.5

2

2.5

ch

ch

χ2

(b) ρ + ω ﬁtting (BG : Exponential)

χ2(a) ρ + ω ﬁtting (BG : VWG)

30

Like-sign method

25

3
3.5
dNchdη/<dN dη>

Like-sign method25

Mixing method

Mixing method

20
20
15

15

10

10

5

5

0
0

0.5

1

1.5

2

2.5

0
0

3
3.5
dNchdη/<dN dη>
ch

0.5

1

1.5

2

2.5

3
3.5
dNchdη/<dN dη>ch(c) ϕ ﬁtting (BG : VWG)(d) ϕ ﬁtting (BG : Exponential)

Figure 4.8: Signal ﬁtting χ2 for ρ + ωandϕ extraction with dependence of
charged-particle multiplicity

Fig 4.6 and 4.7 show ﬁtting χ2 in the case of BG + signal total and signal
only with VWG and exponential function. Two distributions of χ2 ﬁt by
VWG and exponential are similar, but averages of χ2 are a bit diﬀerent.
Table 4.2 summarizes averages of χ2 . Two distributions of χ2 by using theLS method and EM method are also similar. The diﬀerence between the two
is not larger than of remaining BG dependence, but the case with the LS
method is larger than it with the EM method. Following ﬁtting χ2 and Fig
3.10 (d) discussed in Sec (3.6), The results with VWG function are discussed
in this study. The results with exponential are shown in the appendix.
Fig 4.9 shows the row yield of ρ + ω and ϕ as a function of chargedparticle multiplicity. The dependence of the combinatorial BG estimation
method is not small. Table 4.3 summarizes each value and statistics error
shown in Fig 4.9. The row yield with the EM method is higher than it with
the LS method except for ϕ yield at intervals i = 3 and 4. At the highest
charged-particle multiplicity interval, the row yield of ϕ with the LS method
is higher than it with the EM method signiﬁcantly contrary to other plots.
56

Table 4.2: Fitting χ2 for lowmass analysis

VWG
BG + signal total
ρ+ωϕExponential
BG + signal total
ρ+ω
ϕ

LS

EM

34.8
14.5
8.3

42.9
18.9
11.4

45.8
14.5
14.7

46.5
16.4
11.1

This can be attributed to the ϕ peak being buried in the remaining BG, as
can be seen in Fig 3.11 (e). In summary, the yield with the EM method ishigher than it with the LS method by 16% (20σ of statistics error) for ρ + ωand by 7.6%(9.5σ of statistics error) for ϕ. For resonance peak analysis,
peak extraction has a weak dependence on the combinatorial BG estimation
method since the remaining BG is removed after combinatorial subtraction.
However, statistics errors aﬀect the method, and ﬁtting can be inﬂuenced it.
I expect that this rho yield diﬀerence is due to the ﬁtting process.
[H]
Table 4.3: Fitting χ2 for lowmass analysisiρ+ω : 01
2
3
4
Summary
ϕ: 0
1:
2:
3:
4:
Summary

LS
55449
38856
25309
15798
2189
137601
40086
24352
11752
11584
3968
91742

error
715
557
548
275
63
1096
497
429
282
157
71
735

57

EM
67154
42752
28640
18488
2682
159716
43807
27060
15093
11098
1653
98710

error
587
498
410
201
59
735
528
429
282
166
47
756

dNφ/dydNρ+ω/dy

Like-sign method
10

5

10

4

Mixing method

Like-sign method
10

Mixing method

5

104

10

0

0.5

1

1.5

2

2.5

3
3.5
dNchdη/<dN dη>

3

0

0.5

1

1.5

2

2.5

ch

3
3.5
dNchdη/<dN dη>ch(a) ρ + ω(b) ϕFigure 4.9: Row yield as a function of charged-particle multiplicity (BG : VWG)

dNφ/dy/<dN /dy>dNρ+ω/dy/<dN

like-sign method

2

φ

ρ+ω

/dy>

Fig 4.10 shows the self-normalized yield of ρ + ω and ϕ as a function of
charged-particle multiplicity. The self-normalizing process makes dependence
on the combinatorial BG estimation method weak for ρ + ω. However, thetwo behaviors of normalized yield distribution of ρ + ω and ϕ are same of thenormalized yield distribution of J/ψs. I expect the cause is same, accuracyof charged-particle multiplicity measurement.

Mixing method
1.5

3.5

like-sign method3

Mixing method

2.5
2

1
1.5
1
0.5
0.5
0
0

0.5

1

1.5

2

2.5

0
0

3
3.5
dNchdη/<dN dη>

0.5

1

1.5

2

ch

2.5

3
3.5
dNchdη/<dN dη>ch(a) ρ + ω(b) ϕFigure 4.10: Self-normalized yield as a function of charged-particle multiplicity(BG : VWG)

Fig 4.11 illustrate the mean mass of ρ + ω and ϕ as a function of chargedparticle multiplicity. Mean mass of low mass vector mesons are m̄ρ =775.26 ± 0.23[MeV/c2 ], m̄ω = 782.66 ± 0.13[MeV/c2 ] and m̄ω = 1019.461 ±0.016[MeV/c2 ] in PDG. The charged particle multiplicity dependence ofmean mass is unclear because of their error, but the mean mass of ρ + ω58

shows it of both ρ and ω within uncertainties, and plots of ϕ are within PDG
value of ϕ within uncertainties.
Mean mass [GeV/c 2]

Mean mass [GeV/c 2]

Rho&omega mean mass at each Mult (like-sign method)
0.8

Like-sign method
0.795

Mixing method
0.79

1.05

Like-sign method
Mixing method

1.04

1.03

0.785
0.78

1.02
0.775
1.01

0.77
0.765
0

0.5

1

1.5

2

2.5

1
0

3
3.5
dNchdη/<dN dη>

0.5

1

1.5

2

ch

2.5

3
3.5
dNchdη/<dN dη>ch(a) ρ + ω(b) ϕFigure 4.11: Mean mass as a function of charged-particle multiplicity (BG :VWG)

The Fig 4.12 show mass width of ρ + ω and ϕ as a function of chargedparticle multiplicity. Decay width of low mass vector mesons are 142.1 ±8.9[MeV] for ρ, 8.70 ± 0.39[MeV] for ω, and 4.065 ± 0.275[MeV] for ϕin PDG
with dielectron channel. However, reconstructed width of ρ + ω and ϕ ishigher than PDG values by a factor of 2 for ρ + ω compared with PDG of ωand 4 for PDG of ϕ due to detector resolution. The ρ mass width in PDG is
so high that can be seen if ρ + ω is separated independently. In case qualityof track reconstruction improves more, the mass width of ω and ϕ can bealso observed. In this study, MFT-MCH matching chi2. which reﬂect how
matching is well done is not used for track selection.

59

σ [GeV/c2]

σ [GeV/c2]

0.07

Like-sign method

0.06

Mixing method

0.08

Like-sign method

0.07

Mixing method

0.05

0.06

0.04

0.05
0.04

0.03
0.03
0.02
0.02
0.01
0
0

0.01

0.5

1

1.5

2

2.5

0
0

3
3.5
dNchdη/<dN dη>

0.5

1

1.5

2

ch

2.5

3
3.5
dNchdη/<dN dη>ch(a) ρ + ω(b) ϕFigure 4.12: Mass width as a function of charged-particle multiplicity (BG :
VWG)

60

Chapter 5
Summary
In this study, in order to observe QGP in small systems,
I measured two√
physics with p-p collisions at center-of-mass energy s =13.6 TeV with updated detector systems in 2022. the one is J/ψ suppression. The chargedparticle multiplicity dependence of J/psi production should show slower increasing than linear with increasing of charged-particle multiplicity. The
other is restoration of spontaneously chiral symmetry breaking. The ρ+ωmass width should broad in high charged-particle multiplicity.
As a result, the dependence of self-normalized J/ψ yield on charged-particle
multiplicity shows strange behavior at low charged-particle multiplicity. Itshould behave in such a way that it passes through the origin. The J/ψ
yield and the number of events are compared with results of proceeding
study. The number of events in this study has weak diﬀerence from proceeding study at the low charged-particle multiplicity, whereas large at the highcharged-particle multiplicity by a factor of 10−1 . J/ψ yield in this study
shows signiﬁcant enhancement at low multiplicity, but its cause is not via
yield estimation process. This implies that accuracy of charged-particle multiplicity measurement may be cause and should be investigated more. hemass width of ρ + ω and ϕ as a function of charged-particle multiplicity show
weak dependence of charged-particle multiplicity. The mass width of ρ + ωand ϕ is higher than PDG values by a factor of 2 for ρ + ω compared with
PDG of ω and 4 for PDG of ϕ due to detector resolution. The ρ mass widthin PDG is so high that can be seen if ρ + ω is separated independently. In
case quality of track reconstruction improves more, the mass width of ω andϕ can be also observed. In this study, the data has a problem of phi angle
reconstruction. Reconstructed invariant mass peak is expected to be more61

sharp with ﬁxing it and additional track selection. To check the chargedparticle multiplicity measurement can make it possible to see yield and mass
width as a function of charged-particle multiplicity. The separation between
prompt and non-prompt J/ψ is remaining task to see J/ψ suppression.

Acknowledgement
At the ﬁrst, I appreciate all member of laboratory, family, friends and others
who encouraged me in most. I would like to express my sincere gratitude to
staﬀs in quark physics laboratory. Dear Kenta shigaki who is my supervisor,
thanks for his guidance and discussion during my laboratory life including
analysis and how to built strategy to face issues, I’m able to summarize mystudy for this thesis. Dear Yorito Yamaguchi, I completed my tasks in CERNMFT DCS on-call shift otherwise there are many problems, and oﬀ course mystudy via mainly help in meeting. Dear Satoshi Yano, not only discussion,
but also analysis method and general issues in ALICE are driven. I was able
to proceed my analysis with his concrete direction. Dear Masanori Ogino, I
am indebted to his help in discussion. He often summarized my message thatis hard for me during meeting. Dear Kensuke Honma, all of his comments issurprising for me and unencountered. Dear Takahiro Miyoshi, programmingand knowledge of basis of nuclear physics are from him. I am deeply gratefulto it.
I wish to extend my appreciation to students in laboratory. Special thanks
for Motomi Oya are due to analysis discussion and knowledge to deal withtechnical problem. I also deeply appreciate comrades in my master life. I
was encouraged from them signiﬁcantly. They inspired me to do my jobs.
At the end of this section, I am deeply grateful to all again. Thank you.

62

Reference[1] Particle Data Group, Quantum Chromodynamics, revised in August2023.
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Y. Kuramashi, Y. Namekawa, M. Okawa, Y. Taniguchi, A. Ukawa,
N. Ukita, and T. Yoshié. 2 + 1 ﬂavor lattice qcd toward the physicalpoint. Phys. Rev. D, 79:034503, Feb 2009.
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[9] A. Ortiz Velasquez, P. Christiansen, E. Cuautle Flores, I. A. Maldonado Cervantes, and G. Paić. Color reconnection and ﬂowlike patterns in
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[10] S. The ALICE collaboration., Acharya, D Adamová, andet al.
Forward rapidity j/ψ production as a √functionof charged-particle multiplicity in pp collisions ats=
5.02and13tev. J.HighEnerg.P hys.2022, 15, (2022).
[11] j/ψ production versus centrality, transverse momentum, andrapidity in Au+√
Au collisions at sN N = 200 GeV. Phys. Rev. Lett., 98:232301, Jun 2007.
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OPEN-PHO-ACCEL-2018-005.
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[19] S. Adamová D. et al The ALICE collaboration., Acharya. Measurement ofψ (2s) production as a function of charged-particle pseudorapidity density
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LHC ; ALICE, Aug 2013.

64

Appendix
J/ψ production models- Color Glass Condensate (CGC)
Color Glass Condensate (CGC) is a phenomenon where the gluon density
inside hadrons increases in relativistic systems, reaching a saturation state.
In addition to the components within hadrons, repeated quark-antiquark
pair generation and annihilation occur. When hadrons are accelerated, thelifetime of gluons increases, leading to a longer duration of pair generation
and a higher parton density. However, as the parton density increases, gluon
fusion also occurs, saturating the parton density. This is a common feature in
relativistic systems involving hadrons. Consequently, charm pair production
through gluon fusion increases. The formation of charmonium from charm
pairs is described by the Improved Color Evaporation method (ICEM). ICEM
is a model that describes J/psi production within the framework of pQCD. It
involves gluon radiation after charm pair production, leading to the formationof charmonium. Color evaporation signiﬁes the transition to a white color
during charmonium formation. ICEM is an improved version of the Color
Evaporation Model (CEM), incorporating interactions with other partonsin addition to gluon radiation. Although the production quantity remains
unchanged, it alters the phase-space distribution of the ﬁnal state. This
allows ICEM to explain the momentum distribution ratio between J/psi and
Psi(2S), which the traditional CEM model could not.
- 3-Pomeron CGC
3-Pomeron CGC is a model that considers not only double gluon fusion but
also higher-order triple gluon fusion.
- Percolation
Percolation is a model based on the assumption that strings have a ﬁnite size.
Gluon fusion occurs due to geometric overlap, becoming more likely withan increase in gluon density. As a result, the charged-particle multiplicity
decreases. On the other hand, J/psi, being a lighter particle, is not aﬀectedby gluon fusion, so its yield remains unchanged and is proportional to thenumber of strings. Therefore, the ratio of J/psi production and chargedparticle multiplicity shows an increasing trend.
- Color Precession Percolation (CPP) CPP (Color Precession Percolation)65

is a phenomenological model based on p-Pb collisions. It describes pp collisions by normalizing with the number of nucleon collisions. Additionally, it
incorporates the eﬀects of mutual boosting at the saturation scale on a more
microscopic scale.

Invariant mass reconstructed by event mixing
Invariant mass reconstructed by like-sign and unlike-sign muon pair in mixed
events. These distribution are used for combinatorial BG estimation.

66

dN/dm1.000000 < Mult < 10.000000
10

5

10

4

10

3

MEPM
MEPP
MEMM

102

10

0

2

4

6

8

10

12

14
Mass [GeV/c2](a) 1 ≤ Ntrk ≤ 10
10

5

10

4

21.000000 < Mult < 30.000000
dN/dm

dN/dm

11.000000 < Mult < 20.000000
10

5

10

4

10

3

MEPM

MEPM

MEPP

MEPP

MEMM
10

3

10

2

MEMM

102

10
10
1
4

6

8

10

12

14
Mass [GeV/c2]

0

2

4

10

4

MEPP

10

3

10

2

10

2

10

10

10

MEMM

1

1
2

4

6

8

10

12

14
Mass [GeV/c2]

0(d) 31 ≤ Ntrk ≤ 40

2

4

8

10

12

14
Mass [GeV/c2]

dN/dm

71.000000 < Mult < 100.000000

MEPM
4

6

(e) 41 ≤ Ntrk ≤ 50

51.000000 < Mult < 70.000000
dN/dm

14
Mass [GeV/c2]

MEPM

MEPP
3

10

4

MEPM

MEPP

MEPP
MEMM

MEMM
3

10
10

12

41.000000 < Mult < 50.000000

MEMM

10

10

(c) 21 ≤ Ntrk ≤ 30

MEPM

0

8

31.000000 < Mult < 40.000000

104

10

6

(b) 11 ≤ Ntrk ≤ 20
dN/dm

2

dN/dm

1
0

3

2

102

10

1
0

2

4

6

8

10

12

14
Mass [GeV/c2]

0(f ) 51 ≤ Ntrk ≤ 70

1

2

3

4

5
Mass [GeV/c2](g) 71 ≤ Ntrk ≤ 100

Figure 5.1: invariant mass reconstructed by muon pair in mixed events67Results : BG functin is single exponential

10

dNφ/dydNρ+ω/dy

Low mass vector meson analysis results with single exponential function toestimate remaining BG after combinatorial BG subtraction.

Like-sign method

6

Mixing method10Like-sign method
10

5

10

4

10

3

Mixing method

5

10

4

10

3

0

0.5

1

1.5

2

2.5

3
3.5
dNchdη/<dN dη>

0

0.5

1

1.5

2

2.5

ch

3
3.5
dNchdη/<dN dη>ch(a) ρ + ω

(b) ϕ

2

like-sign methodφlike-sign method

ρ+ωdNρ+ω/dy/<dN

dNφ/dy/<dN /dy>/dy>

Figure 5.2: Row yield as a function of charged-particle multiplicity (BG : exp)

Mixing method

1.5

3

Mixing method

2.5

2
1.5

1

1
0.5
0.5

0
0

0.5

1

1.5

2

2.5

0
0

3
3.5
dNchdη/<dN dη>

0.5

1

1.5

2

ch

2.5

3
3.5
dNchdη/<dN dη>ch(a) ρ + ω(b) ϕFigure 5.3: Self-normalized yield as a function of charged-particle multiplicity(BG : exp)

68

Mean mass [GeV/c 2]

Mean mass [GeV/c 2]

0.81

Like-sign method
0.8

Mixing method

0.79

1.05

Like-sign method
Mixing method

1.04

1.03
0.78
1.02
0.77
1.01
0.76

0

0.5

1

1.5

2

2.5

1
0

3
3.5
dNchdη/<dN dη>

0.5

1

1.5

2

2.5

ch

3
3.5
dNchdη/<dN dη>ch(a) ρ + ω(b) ϕ

σ [GeV/c2]

σ [GeV/c2]

Figure 5.4: Mean mass as a function of charged-particle multiplicity (BG : exp)

0.08

Like-sign method

0.07

Mixing method

0.06

0.1

Like-sign method
Mixing method

0.08

0.05
0.06
0.04
0.04

0.03
0.02

0.02
0.01
0
0

0.5

1

1.5

2

2.5

0
0

3
3.5
dNchdη/<dN dη>

0.5

1

1.5

2

ch

2.5

3
3.5
dNchdη/<dN dη>ch(a) ρ + ω(b) ϕFigure 5.5: Mass width as a function of charged-particle multiplicity (BG : exp)

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