Red hydrodynamic model ofquark matter in nuclear collisions
Akihiko Monnai (Osaka Institute of Technology)
AM, arXiv:2301.00588 [nucl-th]

Interdisciplinary Science Conference in Okinawa (ISCO 2023)
1st March 2023, OIST, Japan

Introductionn The subatomic world
ElectronQuarks

NucleusGluonsPRL 100, 217801

Atom (10-10 m)

Proton/neutron (10-15 m)

Matter is composed of elementary particles called quarks,
bound by the strong force mediated by gluons
Akihiko Monnai (OIT), ISCO 2023, 1st March 2023

2 / 20Introductionn Phases of matter

Ice (solid phase)

Water (liquid phase)

Vapor (gas phase)

Matter takes different states (phases) depending on temperature,pressure, etc.
A change from one phase to another is called phase transition
Akihiko Monnai (OIT), ISCO 2023, 1st March 2023

3 / 20Introductionn Phase transition of quarks

Protons and neutrons “melt” into quark-gluon plasma (QGP)
above around 2 trillion degrees Kelvin
Akihiko Monnai (OIT), ISCO 2023, 1st March 2023

4 / 20Introductionn Where is the quark-gluon plasma?

The QGP had filled the Universe around 10-5 seconds after the Big Bang

Akihiko Monnai (OIT), ISCO 2023, 1st March 2023

5 / 20Introductionn How to make the quark-gluon plasma on earth

Smash two big nuclei (such as gold or lead) almost at the speed of light
BNL Relativistic Heavy Ion Collider (2000-)CERN Large Hadron Collider (2010-)
Akihiko Monnai (OIT), ISCO 2023, 1st March 2023

6 / 20Introductionn What can be observed in experiments?

Hadrons
Quarks are frozen back into “quark ice” called
hadrons (include protons and neutrons)
Photons“Particles of light” are also produced
Charged leptons, weak bosons, etc.

Akihiko Monnai (OIT), ISCO 2023, 1st March 2023

7 / 201 GeV ≃ 1.6×10!"# J
1 GeV/𝑐 ≃ 5.3×10!"$kg 1 m/sIntroductionn Interpretation of the momentum distribution
Eskola et al., PRC 72, 044904 (2005)

310-2

1/2 pT dN/dpTd [1/GeV ]+(h +h )/22101

105 % most central

010-1

10-2

10-3

10-4

10RHIC Au+Au
1/2s = 200 AGeVSTAR 0-5 %PHENIX 0-5 %PHOBOS 0-6 %BRAHMS 0-10 %-510-610-710012345678910 11pT [GeV]
Akihiko Monnai (OIT), ISCO 2023, 1st March 2023

8 / 201 GeV ≃ 1.6×10!"# J
1 GeV/𝑐 ≃ 5.3×10!"$kg 1 m/s

Introductionn Interpretation of the momentum distribution
Eskola et al., PRC 72, 044904 (2005)

310-102

1/2 pT dN/dpTd [1/GeV ]Tdec = 150 MeV+(h +h )/221

105 % most centralLow momentum region (< 2-4 GeV)
Hydrodynamic model (strongly-coupled)

010-1

10-2

10-310-4

10RHIC Au+Au
1/2s = 200 AGeVSTAR 0-5 %PHENIX 0-5 %PHOBOS 0-6 %BRAHMS 0-10 %-510-610-710012345678910 11pT [GeV]
Akihiko Monnai (OIT), ISCO 2023, 1st March 2023

8 / 201 GeV ≃ 1.6×10!"# J
1 GeV/𝑐 ≃ 5.3×10!"$kg 1 m/s

Introductionn Interpretation of the momentum distribution
Eskola et al., PRC 72, 044904 (2005)

310-102

1/2 pT dN/dpTd [1/GeV ]Tdec = 150 MeV
pQCD + E-loss+(h +h )/22
1105 % most central

010-110-210-4

RHIC Au+Au
1/2s = 200 AGeVSTAR 0-5 %PHENIX 0-5 %PHOBOS 0-6 %BRAHMS 0-10 %-510-610-710012345+Mid-high momentum region (> 4-5 GeV)
perturbative QCD (weakly-coupled)

-3

1010

Low momentum region (< 2-4 GeV)
Hydrodynamic model (strongly-coupled)

678910 11

pT [GeV]Akihiko Monnai (OIT), ISCO 2023, 1st March 2023

8 / 20Motivationn Relativistic hydrodynamic model

Equationof state

Initialcondition

Akihiko Monnai (OIT), ISCO 2023, 1st March 2023

Hydroevolution*A relation among state variables
such as pressure, temperature, etc.

Hadronic
decay

Observables

9 / 20Motivationn Relativistic hydrodynamic model

Equationof state

Initialcondition

Akihiko Monnai (OIT), ISCO 2023, 1st March 2023

Hydro
evolution*A relation among state variables
such as pressure, temperature, etc.

Hadronic
decay

Observables

9 / 20Motivationn Relativistic hydrodynamic model

Equationof state

Initialcondition

Hydro
evolution*A relation among state variables
such as pressure, temperature, etc.

Hadronicdecay

A caveat of the conventional model:
Equation of state & particle production include the contributionof high-momentum particles
Akihiko Monnai (OIT), ISCO 2023, 1st March 2023

Observables?

9 / 20This workn “Red” hydrodynamic modelparticles*low momentum = long wavelength = “red”

particlesppcp

We introduce an upper limit (pc) for the momenta ofstrongly-coupled components

Akihiko Monnai (OIT), ISCO 2023, 1st March 2023

10 / 20

Equation of state

0.1 GeV ≃ 1.16×10"% Kn Results
654
P/T4#!

𝑔! 𝑑 $ 𝑝
𝐸!
Pressure: 𝑃 = ±𝑇 % &$ ln 1 ± exp − 𝑇2𝜋"pc=∞pc=5 GeV
pc=4 GeV
pc=3 GeV
pc=2 GeV!

3i: index for particle species

2Hadronic phase

1QGP phase

000.1

0.2

0.3 0.4T (GeV)

0.5

0.6…
…

Smoothly connect thepressures of the 2 phases

0.7

Effects of momentum cutoff is larger at higher temperatures;
mostly negligible in the hadronic phase
Akihiko Monnai (OIT), ISCO 2023, 1st March 2023

11 / 20

Hydrodynamic evolutionn (2+1)-dimensional inviscid model

AM, PRC 90, 021901(R) (2014)

Initial condition: Monte-Carlo Glauber model (event-averaged)
2.76 TeV Pb+Pb collisions at b = 4.6 fm (~ 0-20%)
Initial time: τini = 0.4 fm/c
Freezeout temperature: Tf = 140 MeV
Thermal photon estimated down to: Tph = 110 MeV
Hadronic decay: Sollfrank, Koch, and Heinz, Phys. Lett. B 252, 256 (1990)

Akihiko Monnai (OIT), ISCO 2023, 1st March 2023

12 / 20

Hydrodynamic evolutionn (2+1)-dimensional inviscid model

AM, PRC 90, 021901(R) (2014)

Initial condition: Monte-Carlo Glauber model (event-averaged)
2.76 TeV Pb+Pb collisions at b = 4.6 fm (~ 0-20%)
Initial time: τini = 0.4 fm/c
Freezeout temperature: Tf = 140 MeV
Thermal photon estimated down to: Tph = 110 MeV
Hadronic decay: Sollfrank, Koch, and Heinz, Phys. Lett. B 252, 256 (1990)
Simulations of nuclear collisions at the Large HadronCollider
Akihiko Monnai (OIT), ISCO 2023, 1st March 2023

12 / 20

Hydrodynamic evolution

1 fm/𝑐 ≃ 3.3×10!%& sn Numerical results
0.6

1.3
1.25
1.2
<uτ>

0.5T (GeV)

1.35

pc=∞
pc=4 GeV
pc=3 GeV
pc=2.5 GeV
pc=2 GeV0.4

1.15
1.1

0.3

1.05

0.2
0.1

pc=∞
pc=4 GeV
pc=3 GeV
pc=2.5 GeV
pc=2 GeV

11τ (fm)

100.951τ (fm)10

Initial temperature is higher with lower cutoff momentum; the flow
development is mostly unaffected
Akihiko Monnai (OIT), ISCO 2023, 1st March 2023

13 / 20

Photons

Review: AM, Int. J. Mod. Phys. A 37(11n12), 2230006 (2022)

n Sources of direct photons (conventional)

Akihiko Monnai (OIT), ISCO 2023, 1st March 2023

14 / 20

Photons

Review: AM, Int. J. Mod. Phys. A 37(11n12), 2230006 (2022)

n Sources of direct photons (conventional)

Akihiko Monnai (OIT), ISCO 2023, 1st March 2023

14 / 20

Photons

Review: AM, Int. J. Mod. Phys. A 37(11n12), 2230006 (2022)

n Sources of direct photons (conventional)

Prompt photons
produced at the collision
Turbide, Rapp and Gale, PRC 69, 014903
Heffernan, Hohler, and Rapp, PRC 91, 027902
Holt, Hohler, and Rapp, NPA 945, 1Berges et. al., PRC 95, 054904 (2017)
Tanji and Venugopalan PRD 95, 094009 (2017)
Akihiko Monnai (OIT), ISCO 2023, 1st March 2023Thermal photons

produced from the medium

particles

p14 / 20

Photons

Review: AM, Int. J. Mod. Phys. A 37(11n12), 2230006 (2022)

n Sources of direct photons (this work)

Prompt photons
produced at the collision
Turbide, Rapp and Gale, PRC 69, 014903
Heffernan, Hohler, and Rapp, PRC 91, 027902
Holt, Hohler, and Rapp, NPA 945, 1Berges et. al., PRC 95, 054904 (2017)
Tanji and Venugopalan PRD 95, 094009 (2017)
Akihiko Monnai (OIT), ISCO 2023, 1st March 2023

Thermal photons

produced from the medium(low momentum only)
particles

High pT photons

produced from the nonthermal components

particlespcppc

p15 / 20

Elliptic flow

Ollitrault, PRD 46, 229 (1992)
Poskanzer and Voloshin, PRC 58, 1671 (1998)

n From spatial anisotropy to momentum anisotropy

yPressure gradients drive particles faster in thedirection of the minor axisxThe momentum distribution of hadrons has
anisotropy (elliptic flow v2)

Direct photons are also anisotropic

Prompt photons: isotropic
Thermal photons: anisotropic
High pT photons: isotropic*High pT photons are conjectured as thermal photons with no anisotropy in this study
Akihiko Monnai (OIT), ISCO 2023, 1st March 2023

16 / 20

Elliptic flown Numerical results
thermal + prompt + *high pT

pc=∞
pc=4 GeV
pc=3 GeV
pc=2.5 GeV
pc=2 GeV

0.05
0.04

0.04

0.03
0.02
0.01

22.5pT (GeV)

33.5

40
0.5

pc=∞
pc=4 GeV
pc=3 GeV
pc=2.5 GeV
pc=2 GeV

0.05

v2γ,th+pr

pc=∞
0.18
pc=4 GeV
0.16
pc=3 GeV
0.14 pc=2.5 GeV
pc=2 GeV
0.12
0.1
0.08
0.06
0.04
0.02
00.5
1
1.5

thermal + prompt

v2γ,th+prv2γ,ththermal

0.03
0.02
0.01

11.5

22.5
pT (GeV)

33.5

4

00.5

11.5

2
2.5
pT (GeV)

3

3.5

4

Photon v2 is sensitive to the choice of pc; whether it isenhanced or not depends on the high pT contributions
Akihiko Monnai (OIT), ISCO 2023, 1st March 2023

17 / 20

Summaryn We developed a “red” hydrodynamic model of the QGP
654

P/T4

Equation of state is constructed only with low
momentum components
High pT photon emission is assumed to be
non-thermal

3210Initial temperature can be higher

00.2

0.3 0.4T (GeV)

0.5

0.6

0.7

3.5

4

pc=∞
pc=4 GeV
pc=3 GeV
pc=2.5 GeV
pc=2 GeV

0.04
0.03
0.02
0.01
00.5

Akihiko Monnai (OIT), ISCO 2023, 1st March 2023

0.1

0.05

v2γ,th+pr

Direct photon elliptic flow can be sensitive tothe cutoff momentum pc

pc=∞
pc=5 GeV
pc=4 GeV
pc=3 GeV
pc=2 GeV

11.5

22.5pT (GeV)

318 / 20

Outlookn Future directions
E d N3 (GeV -2)
dp

Introduction of viscous corrections (includingestimation of transport(b) v
100.2coefficients)
0.15
1
Event-by-event estimation for quantitative 10analyses of elliptic0.1 flow(a) Invariant yield

2

3

PRL114, 072301
and priv. comm.

QGP w/o viscous
QGP w/ viscoussemi-QGP
w/o viscous(All three include HG)-1Comparison with the experimental data for understanding
10
the photon puzzle*
1010-2E d N3 (GeV -2)
dp-3

10-4
1-5
1010-1(a) Invariant yield

PRL114, 072301
and priv. comm.

Au+Au 20-40%
QGP w/o viscous
sNN=200GeV QGP w/ viscous

Data
Solid line

3

*The discrepancy between the theoretical estimations andexperimental data of direct photon v2
410.150.1

0.05

234p (GeV/c)
T

00.2

-4

10
Akihiko Monnai (OIT), ISCO 2023, 1st March 2023

-5

10

CalorimeterConversion(All three include HG)

310-300064901 (2016)(b) v 2(c)PHENIX
30.2

semi-QGP

w/o064904
viscous
Yield is from PRC 91,

102-2
100.05PHENIX, Phys. Rev. C 94,

Au+Au 20-40%
sNN=200GeV

0.15

01(c) v3

234

PHENIXp (GeV/c)
TCalorimeter
Conversion

19 / 20

The endThank you for listening!

Akihiko Monnai (OIT), ISCO 2023, 1st March 2023

20 / 20