Initial state
andthermal equilibrium(Theory)

Hidetoshi Taya
(RIKEN iTHEMS)

What I am going to talk
TimeO(1) fm/c

0 fm/c？

QGPThis talk: Review of what is happening in ？ (focus on the past 10-year developments)
Short summary: No longer a black box, thanks to- Significant progress around 2015
⇐ a weak coupling scenario & hydrodynamization- Sophistication after ~2015 ⇐ ・~2015’s idea is becoming more robust
・gradually making connection to exp.
・making rich interactions to other fields
Plenary by Xing, Thu. 10:00~
Caveats: ・Don’t talk about CGC; please see Talk by Fujii, Wed. 15:05~
・This is a review talk, i.e., don’t talk about my own works

I. Progress ~2015
II. Progress after 2015
III. Summary

Progress ~2015: weak coupling scenario & hydrodynamization
TimeO(1) fm/c

0 fm/c？

QGP

Progress ~2015: weak coupling scenario & hydrodynamization
0 fm/c1/Qs ~ O(0.1) fm/c

TimeO(1) fm/c

QGP
collision“Hydrodynamize”

Diluted by expansion

Gluon saturation➡ pQCD (CGC)
Strong color flux tube (Glasma)➡ Classical YM (+ fluctuation)
Parton matter➡ kinetic theory
Quark-gluon plasma➡ Hydrodynamics

Progress ~2015: weak coupling scenario & hydrodynamization[Epelbaum, Gelis, 1307.2214]

QGPcollision“Hydrodynamize”

Diluted by expansion

Gluon saturation➡ pQCD (CGC)・ Go to free streaming = Never thermalize
Need to switch “field” → “particle”
Strong color flux tube・(Glasma)➡ Classical YM (+ fluctuation)
Parton matter➡ kinetic theory
Quark-gluon plasma➡ Hydrodynamics

Progress ~2015: weak coupling scenario & hydrodynamization

Kinetic (BMSS)

collision

・CYM and kinetics are smoothlyconnected with each other- overlap at 1⁄𝑔𝑔2 ≫ 𝑓𝑓 ≫ 1[Mueller, Son, hep-ph/0212198 ][Jeon, hep-ph/0412121]“Hydrodynamize”

Diluted by expansion- consistent with bottom-up scenario[Baier, Mueller, Schiff, Son, hep-ph/0009237]

Gluon saturation

CYM➡ pQCD (CGC)- non-thermal attractor[Berges, Boguslavski,Schlichting, Venugopalan, 1303.5650]

Strong color flux tube (Glasma)➡ Classical YM (+ fluctuation)
Parton matter➡ kinetic theory
Quark-gluon plasma➡ Hydrodynamics

Progress ~2015: weak coupling scenario & hydrodynamization

QGPcollision“Hydrodynamize”

Diluted by expansion

Gluon saturation➡ pQCD (CGC)●Strong color flux tube (Glasma)➡ Classical YM (+ fluctuation)[Kurkela, Zhu, 1506.06647][Arnold, Moore, Yaffe,・Kinetic theory of QCD (AMY) hep-ph/0209353]

does describe isotropization & thermalization

・BUT, the time scale is too slow 𝜏𝜏 ~ 10 fm/𝑐𝑐

Parton matter➡ kinetic theory
Quark-gluon plasma➡ Hydrodynamics

Progress ~2015: weak coupling scenario & hydrodynamization[Kurkela, Zhu, 1506.06647]

collision“Hydrodynamize”

Diluted by expansion

Gluon saturation➡ pQCD (CGC)
Strong color flux tube (Glasma)➡ Classical YM (+ fluctuation)

・ Hydrodynamics works even away from thermal
equilibrium = “hydrodynamization”[Heller, Spalinski, 1503.07514] [Romatschke, 1704.08699]

Partonmatter≪ 𝜏𝜏・ 𝜏𝜏hydrotherm. : 𝜏𝜏hydro ∼ 𝑂𝑂 1

➡ kinetic theory

fm/𝑐𝑐

Quark-gluon plasma➡ Hydrodynamics

Progress ~2015: weak coupling scenario & hydrodynamization

QGPcollision“Hydrodynamize”

Diluted by expansion

Gluon saturation➡ pQCD (CGC)
Strong color flux tube (Glasma)➡ Classical YM (+ fluctuation)
Parton matter➡ kinetic theory
Quark-gluon plasma➡ Hydrodynamics

I. Progress ~2015
II. Progress after 2015
III. Summary

0 fm/ccollision

1/Qs ~ O(0.1) fm/c

TimeO(1) fm/c

“Hydrodynamize”

Diluted by expansion

Gluon saturation➡ pQCD (CGC)

Developments in classical YM

Strong color flux tube (Glasma)➡ Classical YM (+ fluctuation)

1. Beyond boost invariance (2D → 3D glasma)
Parton matter
2. Quark production➡ kinetic theory
Quark-gluon plasma➡ Hydrodynamics

1. Beyond boost invariance (2D → 3D glasma)
Idea: Solve classical Yang-Mills eq.

with finite-thickness source

Boost invariant (2D)

Non-boost invariant (3D)

thickness[Schlichting, Singh, 2010.11172][Lappi, McLerran, hep-ph/0602189]

at mid-rapidity~

at mid-rapidity

thickness~
・ Early times: purely longitudinal・ Late times: free streaming

・ Two ways to introduce thickness:[Schenke, Schlichting, 1605.07158]- JIMWLK [McDonald,Jeon, Gale, 2001.08636 (proceeding)]
Muller, 1703.00017]- Gaussian smearing [Ipp,[Schlichting, Singh, 2010.11172]

Talk by Matsuda, Mon. 13:50~

・ Early times: Not purely longitudinal ・ Late times: free streaming

Lessons: ・ Non-boost invariance does affect the physics at early times
・ Theorists have started to make a better modelling for longitudinal observables
cf. reproduces longitudinal dependencies of multiplicity and flow [McDonald, Jeon, Gale, 2001.08636 (proceeding)]

2. Quark production
Idea: Solve Dirac eq. in the presence of glasma field
Quark production under 2D SU(2) glasma[Tanji, Berges, 1711.03445](color/spin/flavor summed)Kajantie, Lappi, hep-th/049508 & 0508229]
・ Quark production is very fast: [Gelis,[Gelfand, Hebenstreit, Berges, 1601.03576] [HT, 1609.06189] [Tanji, Berges, 1711.03445]⇒quarks (per rapidity) are produced within

・ Q: Why so fast ?
A: Schwinger effect ⇒ occurs when energy supply by the fieldexceeds the mass gap⇒

Lessons: ・ Fast & abundant quark production

Exp: [STAR, 1608.04100]
Thr. [Hirono, Hongo, Hirano, 1211.1114] [V. Voronyuk et al., 1410.1402]

・ Can leave experimental imprints, e.g., charged flow in asymmetric collisions

0 fm/ccollision

1/Qs ~ O(0.1) fm/c

O(1) fm/c

Time“Hydrodynamize”

Diluted by expansion

Gluon saturation➡ pQCD (CGC)

Developmentstheory
Strong incolorkinetic
flux tube (Glasma)➡ Classical YM (+ fluctuation)

1. Inclusion of quarks

2. Numerical code: KфMPфSTParton matter➡ kinetic theory
Quark-gluon plasma➡ Hydrodynamics

1. Inclusion of quarks
Idea: Add quark D.o.G. to relativistic kinetic eq.
・ 2 nice developments(1) Quark chemical equilibration[Kurkela, Mazeliauskas, 1811.03040 & 1811.03068]

・ Hierarchy of time scales
・ Consistent with the two-stage equilibration picture:
Gluons equilibrate first and then quarks [Shuryak, PRL (1992)]
Poster by Abdi, Tue. 18:00~(2) Impacts on isotropization/hydrodynamization[Du, Schlichting, 2012.09068 & 2012.09079]

・ Quark D.o.G lower the longitudinal pressure⇒ Slower isotropization
・ Finite μ significantly affects
the effective constitutive relation

Lessons: ・ Theorists are now able to discuss the initial quark dynamics in the kinetic phase⇒ Will provide an input for, e.g., photon production at early times
・ Quark D.o.G can affect the early-time behaviors(・ No glasma contr. in both. Including both of glasma & kinetic contr. is interesting. )2. Numerical code: KфMPфST (1/2)
Idea: New hydro input accounting for the pre-equilibrium kinetic phase

Initial-state models:Glauber, MC-KLN, IP-Glasma, …

Hydro models:MUSIC, VISUNU, …

STEP 3: Use the energy density
as hydro inputs

STEP 2: KфMPфST evolution= evolve the system using
linear response theory
STEP 1: Get initial energy densitywith some initial-state model[Kurkela, Mazeliauskas, Paquet, Schlichting, Teaney, 1805.00961 & 1805.01604]

・Model of pre-equilibrium kinetic dynamics: KфMPфSTBasic assumptions: linear response, conformality, (extrapolation of) weak coupling
・Initially energy density only, recently extended to include conserved (U(1), strangeness, baryon) charges (ICCING)[Carzon, Martinez, Noronha-Hostler, Plaschke, Schlichting, Sievert, 2301.04572]

Lesson: Now we have a numerical code to include the pre-equilibrium dynamics !

2. Numerical code: KфMPфST (2/2)
Idea: Use KфMPфST as an actual hydro input, and test how it works (or not)・ Can reproduce some observables like flow and multiplicity well

[Gale, Paquet, Schenke, Shen, 2106.11216]= IP glasma + KфMPфst + MUSIC + UrQMD[Nunes da Silva, Chinellato, Hippert, Serenone,Takahashi, Denicol, Luzum, Noronha, 2211.10561]= Trento + KфMPфst + MUSIC + UrQMD・ Significant changes in some observables due to conformality⇒ No bulk stress in KфMPфST phase ⇒ More radial flow & less entropy production

Lessons: ・ Conformality seems a problem ⇒ Needs further sophistication
・ Even so, clearly demonstrating that the pre-equilib. dynamics does affect when extracting
the QGP properties

0 fm/ccollision

1/Qs ~ O(0.1) fm/c

TimeO(1) fm/c

“Hydrodynamize”

Diluted by expansion

Developments in hydrodynamization/attractor

Gluon saturation➡ pQCD (CGC)

1. Weak vs strong coupling

Strong color flux tube (Glasma)

2. Two origins of attractor:
time attractors➡ Classicalearly/late
YM (+ fluctuation)
3. Attractors beyond TμνParton matter

4. Lower symmetries (e.g. non-conformal case)➡ kinetic theory
5. Implications to QCD-phase-diagram study in HIC

Quark-gluon plasma➡ Hydrodynamics

1. Weak vs strong couplings
Idea: Compare with the strong-coupling result of AdS/CFT・ Actual QCD coupling is not so small
・ Q: Are there any differences ?
A: Basically consistent with the weak-coupling result after rescaling of time (though there do exist diffs.)(I will mention later)

Bjorken expansion with conformal symmetry[Keegan, Kurkela Romatschke, van der Schee, Zhu, 1512.05347][Giacalone, Mazeliauskas, Schlichting, 1908.02866](effective) relaxation time

Lessons: ・ Hydrodynamization seems universal, independent of coupling strength & micro. theories⇒ imply the weak-coupling scenario is still valid at intermediate couplings
・ Rescaling of time may enable us to study hydro attractor in a universal manner(・ At least when the symmetry is high enough. May be OK in HIC …)

2. Two origins of attractor: early/late time attractors
Idea: Carefully check the “speed” of attraction to discriminate the origin of attractors
Power-law “slow” early-time attractor

Exponentially-fast late-time attractor[Kurkela, van der Schee, Wiedemann, Wu, arXiv:1907.08101]

・ Origin of attractor = How to forget initial information
・ Two ways to forget:
Expansion (effective at early-times)

vs[Blaizot, Yan, 1712.03856] [Brewer, Ke, Yan, Yin, 2212.00820][Heller, Jefferson, Spalinski, Svensson, 2003.07368]

Collisions (effective at late-times)

・ Which is dominant depends on microscopic theory. cf. Collision effect win in the strong-coupling limit

Lesson: There are in general two origins of the hydrodynamic attractor in HIC

3. Attractors beyond Tμν
Idea: Check attractor behaviors of distribution function and higher moments with kinetics
Bjorken expansion with RTA kernel [Strickland, 1809.01200]

124・Attractor for distribution function exists ⇒ Faster convergence for lower momentum (pT)⇒ Momentum dependence of hydro behavior
・Similar attractor behaviors for higher moments
cf. recent study with AMY kinetics

Talk by Monnai, Mon. 13:50~[Almaalol, Kurkela, Strickland, 2004.05195]

Lesson: Attractor does exist beyond Tμν,
though the time-scale depends on momentum scale or the order of moments

4. Lower symmetries (non-conformal case)Idea: Break the conformality by, e.g., finite mass, non-conformal EoS
MIS under Bjorken flow with non-conformal EoS:
[Chen, Yan, 2109.06658]

Non-equilibrium evolution
w/ various initial cond.

・ Attractor does exist for non-conformal case as well

[Chattopadhyay, Jaiswal, Du, Heinz, Pal, 2107.05500 & 2107.10248][Alalawi, Strickland, Pal, 2210.00658]

・ Details of attraction can change, e.g., disappearance of early-time attractor in shear
early attractor ≈ free streaming of total⇒

has an early-time attractor, but(in the conformal limit,

andhas an early-attractor, as

do not necessarily to have separately

and thus behaves essentially the same as)

Lessons: ・Hydrodynamization does occur with lower symmetries,

cf. for other symmetry consideration, see, e.g., with transverse profile: [1907.08101. 2020.135901, 2102.11785]
other flows: Gubser [1711.01745, 1804.04771, 1911.06406, 2020.135481]
Hubble [2104.12534]

・The degree of symmetry can affect hydrodynamization ⇒ Needs further study5. Implications to QCD-phase-diagram study in HIC
Idea: That hydrodynamics is applicable does NOT mean equilibrium
・ Only out-of-equilibrium QCD phase diagram can be explored in HIC[Du, Schlichting, 2012.09068 & 2012.09079][Romatchke, 1609.02820]= func. ofBefore
After hydrodynamization⇒ Isotropization (and thus thermalization)never achieved in HIC⇒ low energy collisions may not even hydrodynamize

・ Non-equilibrium effects can modify matter propertiesexample) “Non-equilibrium” correction to viscosityNon-equil.
correction !

⇐ determined by matching hydro attractor to viscous hydro[Romatchke, 1704.08699]

equilibrium

Lessons: ・ Open question: need to think what we are really measuring in HIC・ In any case, interesting opportunity to study non-equilibrium QCD

Nonequilibrium

I. Progress ~2015
II. Progress after 2015
III. Summary

Summary: Our understanding as of 2023

Significant progress over the past 10 years ⇒ No longer a black box
・ Establishment of the weak coupling picture & proposal of hydrodynamization ~2015
・ Many progresses after 2015

- Classical YM: 3D glasma simulation, quark production, …
- Kinetic theory: inclusion of quarks, KфMPфST, …
- Hydrodynamization: weak vs strong coup., early/late-time attractors, attractors beyond Tμν,

non-conformal case, implication to QCD-phase-diagram study in HIC, …

・ Have rich connection to others: In HIC ⇒ corr./fluc. observables, intense fields, small system, …
Plenary by Sakai, Tue. 10:00~

Plenary by Yang, Tue. 11:40~

Plenary by Kanakubo, Wed. 10:00~

Other area ⇒ cold atom, early Universe, intense lasers, …

See reviews: [Berges, Heller, Mazeliauskas, Venugopalan, 2005.12299][Fedotov, Ilderton, Karbstein, King, Seipt, HT, Torgrimsson, 2203.00019]

・ But still lots of open questions ⇒ Needs your insights !