QCD Phase Structure
and Relativistic HeavyIon Collisions
Bedanga Mohanty
National Institute of Science Education and Research
India
Tomonaga Center for the History of the Universe (TCHoU)

11th September 2021
1/24

QEDQCDWiki

US NP long range plan, 2015

QCD phase
diagram• Conserved quantities and temperature (T)•Baryon number - µB•
Electric charge - µQ - small•
Strangeness~ µS - small
2/24

Relativistic Heavy Ion Collisions
J. D. Bjorken Physical Review D 27 (1983) 140

ppAAUniverse:
QCD Phase Transition: T ~ 200MeV
EW Phase Transition: T ~ 150 GeV
GUT Phase Transition: T ~1016 GeV

3/24

Mapping QCD phase
diagram andRelativistic Heavy IonCollisions
AGSRHICRHIC FXTFAIRNICA=3Quark-Gluon Plasma

B /TB

156

Collision energy

SISµµ /T=2SPS

Chemicalfre

78toue-ez

Temperature T (MeV)

LHC• Nature of transition• Critical point• Properties of the phases

Gas-Liquid

Hadron Gas
00500

1000

1500

Baryonic Chemical Potential µB (MeV)

STAR: arXiv: 2001.02852

Phys.Rev.C 96 (2017) 4, 044904

Accessing phase diagram of QCD in heavy-ion collisions: varying collision energy changes the T and µB
4/24

Program: Beam Energy
Scan

Requirements• Uniform & wide acceptance• Excellent particle identification• Good momentum reconstruction• Centrality with high resolution• Large statistics

SN0493 : Experimental Study of the QCD
Phase Diagram & Search for the Critical
Point: Selected Arguments for the Run-10
Beam Energy Scan
SN0598 : Studying the Phase Diagram ofQCD Matter at RHIC

5/24

• 𝐶! ~𝜉 !

Tool - Highermoments

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%%,!

PRL105, 22303(10); ibid, 112, 032302(14) PLB633, 275(06); PRL102,032301(09); PLB695,136(11);PLB696, 459(11)Normalized Number of Events

PHYSICAL REVIEW LETTERS 126, 092301 (2021)

0.1
0.08
0.06
0.04
0.02

Au+Au CollisionssNN (GeV)
7.7
11.5
14.5
19.6
2739
54.4
62.4
200

0-5% Central
0.4 < p < 2.0 (GeV/c), |y| < 0.5
TSensitive to:(1) Nature of transition(2) Critical point(3) Freeze-out(4) Thermalization(5) Initial EM fields

0−10Connect to Theory.
Correlation length &Susceptibility

01020Net-Proton (∆Np = Np - Np)

3040

Key topics in the field
6/24

Measurements andLattice QCDAssumptions• Thermalization• Grand Canonical

1.2
1.01

STAR (Sσ)
TSσ = M/ σ2|y| < 0.5
HRG (Sσ)UrQMD (Sσ)
LQCD inspired fit• Net-proton ≡ Net-Baryon• Acceptance

Sσ

0.8

Ensemble, V/T3 > 1

Net-proton
0-5% - Au+Au collisions
0.4 < p < 2.0 GeV/c0.6• Lattice artefacts: mass,0.4

00volume, action,

σSσ(STAR) = σ2stat+σ2sysσSσ(UrQMD) = σstat

0.2
0.2

0.4

0.6

0.8

11.0

continuum limit, finite

1.2

M/σ2

chemical potential
Science 332 (2011) 1525-1528

7/24

MeasurementsandQCD
thermodynamics

Cumulant Ratios

STAR@CPOD-2021(1) 7.7 GeV0(2) 200 GeV

0STAR
Preliminary

0-40% Au+Au Collisions
Net-proton, |y| < 0.50.4 < p < 2.0 GeV/c−10T−10STAR
Data

× 0.1
C
13C1C42
C2

UrQMD
LQCD
FRG

C35C1C46C2C13C1C24C2C35
C1C64C2

Susceptibility ratio orderingPHYS. REV. D 101, 074502 (2020)
8/24

C3/C 1
C4/C 2
C5/C 1

Idea

Freeze-out
20050

LHC 2.76TeV

200GeV

62.4GeV

3927
19.6
11.5

100

7.7GeV

5% Au + Au data (high moments)
5% Au + Au data (yields)
Lattice QCD fit

50

Phase boundary
Chemical freeze-out
Liquid-Gas transition

0010

Distribution has several
order moments

FXT
NICA
FAIR
JPARC-HI

150

ch00

RHIC Collider

ãCbR0604, Models/20180810FREEZE-OUT/01 figures/plot21_cfo_all_June2020.C50

Temperature T (MeV)00

Mean of yields
described by thermalstatistical models

Are all orders thermal ?

1000

100

Baryonic Chemical Potential µ (MeV)B

312 (2021) 1
10 AAPPS Bull. 10103
e-Print: 2004.04681 [hep-ph]99/24

Nature 443 (2006) 675-678

Cross overat µB = 0MeV

• T grows with 6/g2
• Largest volume is eight times bigger than the smallest one.
• First-order phase transition - susceptibility peak that is eight times higher• Do not observe any volume dependence – cross overTransition Temperature: ~ 154 MeV - Phys.Rev.D 85 (2012) 054503

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Eur. Phys. J. C 71 1694 (2011)

JHEP 10 (2018) 205

Cross over– theory
expectation
c6/c2 or C6/C2 < 0PHYSICAL REVIEW D 101, 074502 (2020)

11/23

Cross over – experimental measurements
e-Print: 2105.14698 [nucl-ex]

Systematic trends indicate C6/C2 < 0 at 200 GeV, uncertainties large

12/24GraphSTAR@CPOD2021

Net-proton
0.4 < p < 2.0 GeV/c, |y| < 0.5|y| < 0.5−50561020 30 50

100 200−105 6 1020 30 50−50−100056

10Net-proton

30C(b) 3C2C(a) 2C140.5

BES-I
20New measurement
Poisson baseline
UrQMD

Net-kaon 20-5% - Au+Au collisions
0.2 < p < 1.6 GeV/cT|y| < 0.510Poisson baseline
0-40%
070-80%56
LQCD, PRD.101.074502(2020)20 arXiv:2101.06035
30 50 100 200
FRG,
UrQMD(0-5%)(b < 3 fm)
HRG CE−150Au+Au collisions at RHIC

00−21020 30 50

5102Graph
T020 3050100200sNN (GeV)

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High statistics data collected at BES-II and Fixed Target

563224BES-I
New measurement
Poisson baseline
UrQMD

2Graph−500−100200Poisson baseline70-80%−2HRG CE
70-80%
5 6 10HRG
CE 20s 30(GeV) 100 200−2NN−15056100−200200

1020 30 50

0100−250
Collision Energy sNN (GeV) Poisson baseline

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100Net-proton
0.4 < p < 2.0 GeV/c, |y| < 0.50.55600Au+Au collisions at RHIC

50GraphNet-proton

T0.2 < pT < 1.6 GeV/c10Graph

Net-proton

Cross over –|y| < 0.510futuremeasurements

11STAR Preliminary

Net-proton C6/C
C252Net-proton C /C1

Cumulant Ratios

30Net-kaon
C(a)C
0-5% - Au+Au collisions
20 Net-kaon
0.2 < p 0-5%
< - 1.6GeV/c
Au+Au collisions

T

1

Cumulant Ratios

Net-proton C6/C2C(a) 2C11020

Au+Au collisions at RHIC

5030

Cumulant Ratios

100Poisson
20 3050baseline
100−22000-40%s (GeV)
5 6NN 70-80%1020 30 50 100
PRD.101.074502(2020)
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FRG, arXiv:2101.06035(b < 3 fm)
UrQMD(0-5%)
NN
HRG CE

Collision Energy s

200

510(GeV)0-40%
5 6 1020 30 50
100 200
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PRD.101.074502(2020)
5LQCD,
6 1020 30 NN50 100
FRG, arXiv:2101.06035
UrQMD (b < 3 fm)
HRG CE, NPA.1008.122141(2021)

200

Collision Energy sNN (GeV)
1020 30

50sNN (GeV)

10020013/24

probability

probability

0.95
Phys. Rev. C 98 (2018) 5, 054901
Phys. Rev. C 100 (2019) 5, 051902(b)N

probability

0.95(a)(c)Nprobabilityprobability(1) Multiplicity distribution bimodal (contribution fromtwo phases)(2) Proton factorial cumulants(𝜅&( ' ) increases inmagnitude with increasingorder and flips sign
(3) 𝑃 𝑁 = (1 − 𝛼)𝑃( 𝑁 + 𝛼𝑃) (𝑁)

1.05

T/Tc

First order transition– theory expectation

N(e)

(d)

NN

μ/μc

1.05

14/24

First order – experimental measurements and future
Au+Au collisions at RHIC

GraphGraph

STAR@CPOD2021

20 30 50056

100 200−101T0
5 6 10Poisson baseline0-40%
070-80%
LQCD, PRD.101.074502(2020)
101020 30 50 1005 6200
FRG, arXiv:2101.06035
UrQMD(b < 3 fm)
HRG CE, NPA.1008.122141(2021)

Collision Energy sNN (GeV)

56

1020 3050sNN (GeV)

10020020 30 50

−252−5100 200−10Graph

C4C2TNet-proton
0.4 < p < 2.0 GeV/c, |y| < 0.5

1501Proton STAR Preliminary
0.4 < p < 2.0 GeV/c, |y| < 0.5 Graph0(c)Au+Au collisions0at RHIC

1020 Net-kaon30
BES-I
2 (a) CC
New measurement0-5% - Au+Au collisions
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10 |y| < 0.5|y|<0.50100.5−54Au+Au at T sNN = 7.7 GeV

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−50

0100

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0.2 < p < 1.6 GeV/c
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LQCD, PRD.101.074502(2020)20 arXiv:2101.06035
30 50 100 200
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01000070-80%

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4C2Graph−500−100−2(2) κ 6020

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CEs (GeV)

100200NN−15056

10100−2002000baseline20 Poisson
30 50
100200s 70-80%(GeV)
5 6 NN
10 20 30 50

100 2000-40%

PRD.101.074502(2020)
20 30 50 100 200LQCD,FRG, arXiv:2101.06035

1000Collision Energy s (GeV)−Collision
150−Energy
0 Poisson baseline−250s (GeV)
56

Poisson baseline
STAR0-5%, Twocomponent Model
0-5%, UrQMD

C(b) 3 30000
C2Au+Au collisions at RHIC
Net-proton

50C
(a) 2
C1

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10BES-I
New measurement
Poisson baseline
UrQMD−500−10030C(b) 3C2Cumulant Ratios

0C3C2C(a) 2C1Net-proton C /C1(b)5Cumulant Ratios

5STAR PreliminaryCumulant Ratios+Au collisions
1.6 GeV/cC2C1Net-proton C /C1(a)130C6C250

T

Net-proton
0.4 < p < 2.0 GeV/c, |y| < 0.5

Net-proton

Net-proton
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Au+Au collisions at RHIC

C
Net-proton 6C22
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100

Proton Factorial Cumulant

Au+Au collisions at RHIC

Net-proton C6/C210(b < 3 fm)
UrQMD(0-5%)
HRG CE

NN−251020 30 50 100 200

0−20-40%5 6 1020 30 50 100 200
70-80%s (GeV)
PRD.101.074502(2020)
5LQCD,
62001020 30 NN 50 100−10000
200
510100100
FRG, arXiv:2101.06035
200300100200UrQMD (b < 3 fm)
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NPA.1008.122141(2021)
Averageno. of participant nucleons(〈 N 〉)

100200Collision Energy sNN (GeV)

1020 3050100

20 30 50 1300

part

200sNN (GeV)High statistics data collected at BES-IIand Fixed target

15/24

First ordertransition –alternatemeasurements
Nonmonotonic variation ofdv1/dy with collision energy

PHYSICAL REVIEW LETTERS 120, 062301 (2018) 16/24

QCD criticalpoint –theoryexpectation(1)QCD critical point - Characteristic “Oscillating pattern”(2) Exact shape depends on the location of freeze-out withrespect to the location of CP - Critical Region (CR)PRL 102, 032301 (2009)

PRL 107, 052301 (2011)

17/24

QCD critical point – experimental measurement
PHYSICAL REVIEW LETTERS 126, 092301 (2021)

Collision energy (GeV)

Collision energy (GeV)

18/24

QCD critical point – experiment vs. non-CP models

1.24Sσκσ21.0
30.8
20.6
10.400.2

PHYSICAL REVIEW LETTERS 126, 092301(2021)
5Net-proton

Net-protonSTAR
0-5% - Au+Au collisions
UrQMD
0.4 < p < 2.0 GeV/c
HRG
TCanonical Ensemble|y| < 0.5
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STAR
HRG Interacting (R = 0.5 fm)
Van der Waals HRG
UrQMD
HRG
Canonical Ensemble
HRG Interacting (R = 0.1 fm)
HRG Interacting (R = 0.5 fm)
Van der Waals HRG432
κσ2
κσ5321Net-proton
0-5% - Au+Au collisions
0.4 < p < 2.0 GeV/c

20-5%- Au+Au collisionsNet-proton
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collisions
T< p < 2.0 GeV/c|y|0.4< 0.5
T|y| < 0.5

STARSTAR
UrQMD
HRGUrQMD
HRG Ensemble
Canonical
Ensemble
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Interacting= 0.1
HRGHRGInteracting(R =(R0.5fm) fm)
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Van der
HRG (R = 0.5 fm)
Van der Waals HRG

100

T|y| < 0.5

5 6 1020 30 50
100 200
5 6 1020 30 50
100 200
Collision Energy
Collision
EnergysNNs(GeV)
NN (GeV)5 6 1020 30 50
100 200
5 6 1020 30 50
100 200
Collision Energy
Collision
EnergysNNs(GeV)
NN (GeV)

Phys.Lett.B 726 (2013) 691-696, e-Print: 1905.09311
1
Phys.Rev.C 90 (2014) 3, 034909, e-Print: 2007.02463 [nucl-th]

19/24

QCD critical point – future measurements
STAR@RHIC collider mode

STAR@RHIC fixed target mode

Energy(GeV)

Events(106)

BES II /BES I year

µB
(MeV)

Tch
(MeV)

Energy(GeV)

Events(106)

BES IIµB
(MeV)

Tch
(MeV)

200238

2010

25

166

7.7

112/50

420

140

62.4

462010

73165

2020/
2019

54.4

1200201783165

6.2

118

2020

487

130

39

86

2010

112

164

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103

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541

121

27

560/302018/2011

156

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4.5

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589

112

19.6

538/15

2019/2011

206

160

3.9

117

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633

102

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325/13

2019/2014

264

156

3.5

116

2020

666

93

17.3*

250

2021

227

158

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200

2019

699

86

11.5

230/7

2020/2010

315

152

3.0

259

2018

720

80

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100/3

2021/2010

420

140

3.0*

2000

2021

720

80

*Proposed
Tch and µB:Phys. Rev. C 73 (2006) , 034905

High statistics data has been collected over a wide µB range
20/24

Experimental program for high baryon
density matter

ch15050

LHC 2.76TeV

200GeV

62.4GeV392719.6
11.5

1007.7GeV

5% Au + Au data (high moments)
5% Au + Au data (yields)
Lattice QCD fit

50Phase boundary
Chemical freeze-out
Liquid-Gas transition

00101000

100

Baryonic Chemical Potential µ (MeV)
B

10102

108107106105104103102

JPARC-HI

Heavy Ion CollisionInteraction Rates (Hz)FAIR SIS100 2025
HIAF 2025
HADES

NICA 2023

sPHENIXSTAR FXTSTAR BES-II 2019 - 2021

10110100Collision Energy √sNN (GeV)AAPPS Bull. 31 (2021) 1103ALICECollider

Temperature T (MeV)

100FXTNICAFAIRJPARC-HI
ãCbR0604, Models/20180810FREEZE-OUT/01 figures/plot21_cfo_all_June2020.C

150

RHIC Collider

Fixed-Target

20020021/24

• Programs to carry out systematic study of thephase structure of QCD phase diagram throughrelativistic heavy ion collisions underway

Summary

Higher moments measurements seem to follow•

Au+Au collisions at RHIC

QCD thermodynamics

Experimental evidences of signatures related•Graphto critical point observed at a 3 s level
100−5056

1020 30 50

100 200−105 6 1020 30 50

056

1010Net-kaon 20-5% - Au+Au collisions
0.2 < p < 1.6 GeV/cT|y| < 0.5

Poisson baseline
0-40%
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LQCD, PRD.101.074502(2020)20 arXiv:2101.06035
30 50 100 200
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100−200200

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New measurement
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5 6 10HRGCE 20s 30(GeV) 100 200−2NN−15056

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1000-40%−2200s (GeV)
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PRD.101.074502(2020)
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UrQMD(0-5%)
HRG CE

510NN (GeV)

0-40%
5 6 1020 30 50
100 200
70-80%sNN (GeV)
PRD.101.074502(2020)
5LQCD,
6 10
20 30 50 100
FRG, arXiv:2101.06035
UrQMD (b < 3 fm)
HRG CE, NPA.1008.122141(2021)

C4C22Graph−100(c)22Collision Energy s0 Poisson baseline−250NN (GeV)sNN (GeV)−250(a)C6C2BES-I
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New measurement
Poisson baseline
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1040.5C220
MeVobservedat<2s level
2GraphTNet-proton

−100

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BES-I
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0.5
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Au+Au collisions at RHIC
Net-proton

Net-proton
0.4 < p < 2.0 GeV/c, |y| < 0.550Graph

100Net-proton

T0.2 < pT < 1.6 GeV/c|y| < 100.5|y| < 0.5

1Graph0Au+Au collisions at RHIC

Net-proton C6/C
C251STAR Preliminary

Lattice QCD clearly shows cross over at µB = 0.

•T

1Cumulant Ratios

Net-proton C6/C2

2

Net-proton C /C1

30Net-kaon
C(a)C0-5% - Au+Au collisions
20 Net-kaon
0.2 < p 0-5%
< - 1.6GeV/c
Au+Au collisions

Cumulant Ratios

Cumulant Ratios

C(a) 2C11010Net-proton
0.4 < p < 2.0 GeV/c, |y| < 0.5503020Au+Au collisions at RHIC

•20 30 50

Need to continue the dedicated programs in the
100 200−2high baryon density regime to unfold the QCD
20051020 30 50 100 200

phase diagram.

Collision Energy sNN (GeV)
1020 3050sNN (GeV)

100200•Experiments: STAR@RHIC BES-II, CBM@FAIR,NICA@JNIR, SHINE@CERN-SPS, J-PARC-HI
and CEE-HIAF complementary to each other22/24

4.0(1) Ss

0.8

2.00.4

HRG 0-5%
UrQMD 0-5%

Net-proton|y| < 0.5, 0.4 < pT< 2.0 (GeV/c)

510200 - 5%
70 - 80%
Stat. uncertainty
Syst. uncertainty
Projected BES-II
Stat. uncertainty

High baryondensity
experiments

1.00.2 Au+Au Collisions at RHIC
0.0STAR Data

3.0

CP

0.6(2) ks2

HADES

Net-proton High Moments

1.0STAR FXT

0.0

50 100 200

521020

CEE@HIAF

50 100 200

Criticality20050
Baryon density
at freeze-out

0.20.1

Data Thermal fit

K+/ π+

0.80.0-K / π-

Test ofThermal
10models

GCE, thermalmodel102
rsc (fm)
2.2
3.24.26.20.4}

StrangenessCE0.225102050100200

Collision Energy √sNN (GeV)
10102

3927
19.6
11.5

100

7.7GeV

Femto-Nova
5% Au + Au data (high moments)
5% Au + Au data (yields)
Lattice QCD fit

50

Phase boundary
Chemical freeze-out

10−1

ThermalSTAR Au+Au 20%-50%
Nature548.62 (2017)
LL

𝑳+𝑺L

10102

1010-1Λ

L

STAR prelim. 54.4 GeV
LL

STAR prelim. 27 GeV (y2018)
L+L

UrQMD+vHLLE, L
primary
primary+feed-down
AMPT, L
primaryCollectivity

1103102

10sNN [GeV]

103He3
ΛH4He

10-5

HyperNuclei

5ΛΛ H

10-710-96ΛΛ HeEOS

7ΛΛΞ He

10-11

STAR FXT

2351020Collision Energy √sNN (GeV)

Xu, Fukushima, Mohanty AAPPS Bull. 31 (2021) 1
1030

Nucleiprimary+feed-down

0310-3L

HADES prelim. Au+Au 10-40%

PRC98.014910 (2018)
LL

51000

100

ALICE Pb+Pb 15-50%

PRC76.024915 (2007)
LL

B

10-13

0.0

62.4GeVPolarization

Baryonic Chemical Potential µ (MeV)

7(2) N(φ)/N(K ) ratiosData
10200GeV

Liquid-Gas transition

0-0.6

LHC 2.76TeV

010dN/dy (Central HI Collisions)

Strange Particle Ratios(1) N(K)/N(π) ratios

Freeze-out ρB (fm-3)

0.3

FXT
NICA
FAIR
JPARC-HI

150

ch100

RHIC Collider

ãCbR0604, Models/20180810FREEZE-OUT/01 figures/plot21_cfo_all_June2020.C

150

200

Temperature T (MeV)QGP

PH [%]

Collision Energy sNN (GeV)23

Acknowledgements
All members of the STAR Collaboration, F. Karsch & S. Gupta.
Thanks to the organizers for the invitation.

24/24