Quark matter 2012
理論の新展開日高義将(理研)

野中さんのスライドより(熱場の量子論2012)

Relativistic Heavy Ion Collisions
thermalization

collisions

Pre-Equilibrium & Initial Statehydrohadronization

freezeout

Global &Collective Flow
Correlations & Fluctuations
QCD at Finite Temperature and Density
QCD Phase Diagram
Hadron Thermodynamics and ChemistryElectro-Weak Probes

Jets

Heavy flavor &Quarkonia
New Theoretical /Experimental Developments板倉さんのスライドより(第19回HIC/第12回HIP)QM2011]A6[5<• _Z ]A6L(0\:=PfT>^)KVTD

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Pc\Cv3]94[8 ^ \ReconstraintgJePlenary talk by H. Song
Uncertainties frominitial quantum
fluc.

(η / s)QGP (visc. hydro)V2

5 /(4π )4 /(4π )3 /(4π )2 /(4π )1 /(4π )(VISHNU)
V2

(visc. hydro)?

V2,V3

2008

early 2011late2011

2012

1 × (1 4 π ) ≤ (η / s )QGP ≤ 2.5 × (1 4 π )Main uncertainties come from initial conditions
MC-KLN, larger ε 2
MC-Glauber, smaller ε 2

HIGHER value of QGP viscosity
LOWER value of QGP viscosity

year

衝突初期の量子ゆらぎ

流体のゆらぎ輸送係数などの理論的精密計算に向けて

Relativistic
H
衝突前
collisions

thermaliz

Pre-Equilibrium & Initial StatePlenary talk by Dusling

The proton pre-collision
Our field has a good understanding of the proton wave-function:NLO DGLAP fits:
http://mstwpdf.hepforge.org/

The proton pre-collision

NLO-BK:
Balitsky, Chirilli PRD 77 014019
Kovchegov, Weigert NPA 784 188
Albacete, Kovchegov PRD 75 125021

understanding of the proton wave-function:
NLO DGLAP fits:
http://mstwpdf.hepforge.org/

Gtr

15 years of HERA data support this picture:

NLO-BK:
Balitsky, Chirilli PRD 77 014019
Kovchegov, Weigert NPA 784 188
Albacete, Kovchegov PRD 75 125021

Albacete, Milhano, Quiroga-Arias ,Rojo,arXiv:1203.1043 (2012).
Quiroga-Arias, Albacete, Armesto, Milhano, Salgado,J.Phys.G G38 (2011) 124124.
Albacete, Armesto, Milhano, Salgado,PRD80 (2009) 034031.

data support this picture:

Albacete, Milhano, Quiroga-Arias ,Rojo,arXiv:1203.1043 (2012).
Quiroga-Arias, Albacete, Armesto, Milhano, Salgado,
J.Phys.G G38 (2011) 124124.
Albacete, Armesto, Milhano, Salgado,PRD80 (2009) 034031.

ilaocPlenary talk by DuslingPower counting in QCD: multiparticle production
Low color charge density (min bias):
Jet graph:

Glasma graph:

High color charge density (central):
Jet graph:ExpectGlasma graph:enhancement of “Glasma” graph! Is this seen in the data?

p+p
In p+p we are seeing the intrinsic
collimation from a single flux tube

Increasing transverse flow in p+p
creates a discrepancy with data.

vsPlenary talk by Dusling

A+A

In A+A there are many such tubes
each with an intrinsic correlation
enhanced by flow

Yet, transverse flow is needed toexplain identical measurements
in Pb+Pb

Are we sure the A+A ridge is probing the nuclear wavefunction?
Dusling, Venugopalan, PRL 108, 262001 (2012).

RelativisticHeavy
衝突直後
collisions

thermalization

Pre-Equilibrium & Initial Statehy

Global &C

Correlation

QCD at Finite TPlenary talk by Dusling

強い場 Tree levelがLeading order
古典Yang-Millsのシミュレーション
QCD: Classical Yang Mills

Romatschke, Venugopalan,
PRL96:062302 (2006),
PRD74:045011 (2006).

Perturbative expansion breaks down at
requiring a resummation of all terms likeSee also:
Berges, Scheffler, Sexty, PRD77:034504 (2008),
PLB677 210-213 (2009), PLB681 362-366 (2009).
Berges, Scheffler, Schlichting, Sexty, PRD85:034507 (2012).
Kunihiro, Muller, Ohnishi, Schafer, Takahashi, Yamamoto,
PRD82:114015 (2010). Fukushima, Gelis, NPA874:108 (2012)

Plenary talk by Dusling
Weak coupling: amplification of quantum fluctuations
Consider a homogeneous scalar field:

Background Field

Adding fluctuations to the background field

results in the linearized EoM for small fluctuations:Certain amplitudes grow with time:Whenthese terms need to be resummed.

TimePlenary talk by Dusling
膨張系, スカラー理論
Longitudinally expanding non-linear scalar field
Dusling, Epelbaum, Gelis, Venugopalan,arXiv:1206.3336 (2012).

EoS has developed

Onset of vis. hydroOnset of ideal hydro[Lattice Units]

Have a proof of principle for scalar fields: what about QCD?

Plenary talk by Dusling

Master formula: The first Fermi
Any inclusive observable:

Gauge invariant spectrum of fluctuations:

Dusling, Gelis, Venugopalan,
Nucl. Phys. A872 161-195 (2011).

From solutions of B-JIMWLK

From solution of 3+1Dclassical Yang-Mills Eqs.

Talk by Raju Venugopalan, Wed. 12pm
Berges, Schlichting, 1209.0817

流体におけるゆらぎ

ゆらぎの入った流体
Tµν= Tideal + ΔTµν

+ S , J = nu + Δ J + Iµνµµ

Stochastic sources S=Sand I[(µνµν

S ( x) S ( y ) = 2T η h h + h hµναβµα νβµβ ναµνµµ)+ (ζ − η )h h ]δ ( x − y)23µν

S ( x) I ( y ) = 0µνα' nT $ 2 µν 4I ( x) I ( y ) = 2λ %" h δ ( x − y)& w #µνµαβ4

Talk by Stephanov
Correlations
The equal-(proper)time correlation function at freeze-out time τf :2! ρ(ξ1 , τf ) ρ(ξ2 , τf ) " =AZτfdτ ν
τ3 % + P

Z ∞−∞dξ Gρ (ξ1 − ξ; τf , τ )Gρ (ξ2 − ξ; τf , τ ) .

τ0{z|Gρρ (∆ξ;τf ,τ )}4η/3 + ζConvenient variable ρ ≡ δs/s. Convenient notation: ν ≡.
s[S µν = ∆µν (! + P )f ]Every point ξ, τ is a source of noise, ρ = Gρ ◦ f :
ξ1

ξ2τf

τ
ξ

by Stephanov
Conclusions and Talk
outlook
Disentangling correlation
sources:
Fluctuations of initial conditions
produce ∆η-independent correlation.
Hydrodynamic noise has local
origin and produces characteristic ∆η dependence:

initialgeometry
ﬂuctuationlate times

earlier times

with magnitude proportional toviscosity.
More can be learned from2D ∆φ, ∆η correlations.
Analytical work is in progress(Todd Springer, Saturday).

Hydrodynamic Noise and Bjorken Expansion – p. 11/11

Talk by R. Romatschke

流体モードの自己相互作用によるずれ粘性の熱ゆらぎ補正
A viscosity bound from fluid dynamics

For QCD one finds for ⌘/s in units of ~ = kB = 1

Kovtun, Moore, Romatschke, 1104.1586
cf. for Fermi gas, Chaﬁn, Schafer, 1209.1006[Kovtun, Moore & PR, arXiv:1104.1586]

Talk by Kapusta
T

QCD臨界点でQuark Gluon Plasma

Tc

熱伝導率は発散

Critical point
Hadronic Phase
Color Super Conductivity

0µTalk by Kapusta
quarks & gluons
critical point

Magnitude of proton correlation
baryons & mesons
function depends strongly on
how closely the trajectory
passes by the critical point
2−1
MagnitudedNof( yprotoncorrelation
dNdN2 ) dN ( y1 )−function depends
stronglydy2
dy1
dy on dy
how closely the trajectory
passes by the critical pointdN ( y2 ) dN ( y1 )dN−dy2dy1
dy2dN
dy−1

conventional second-order dissipative hydrodynamics. G(x, y) can be afunctional of the fluid fields in the past, thus this expression
morePostercontainsby Murase
higher-order dissipative terms.

1次の流体のゆらぎ:White noise• Consider a simpler case (near the equilibrium):
高次の流体のゆらぎ: Colored noise Fluctuation Dissipation Relation

G(x): Extended for x0<0 aseven functions

Non-zero correlation in different time  Colored Noise

3. A Simple Case for Simulation
 Simple second-order dissipative hydro輸送係数などの精密理論計算へ

Thermal Photon Production at NLO
Talk by Derek Teaney
KHot QGP

3 d2k(2⇡) 3 = Photon emission rate per phase-spaced k

The photon emission rate at weak coupling:• The rate is function of the coupling coupling constant and k/T :hd2k(2⇡)3 3 / e2 T 2 O(g 2 log) + O(g 2 ) +|{z}d k
LO AMYO(g 3 log) + O(g 3 )+...
|{z}
1From soft gT gluons, nB ' T'!
gO(g 3 ) is closely related to open issues in energy loss:• At NLO must include drag, collisions, bremsstrhalung, and kinematic limits

Talk by Derek Teaney
Three rates for photon production at Leading Order

Baier,Kapusta, AMY

1. Hard Collisions – a 2 $ 2 processes

K⇠e

Q~T2

m21|{z}g 2 CF T 2 /4⇥

⇥ nF (k) ⇥ log (T /µ) + C2to2 (k)| {z }
fermi dist.

2. Collinear Bremmstrahlung – a 1 $ 2 processes
KP+KP~gT⇠e2

m21 nF⇥Cbremm (k)| {z }

LPM + AMY and all that stuff!

⇤⇤

Talk by Derek Teaney
3. Quark Conversions – 1 $ 1 processes (analogous to drag)KK~gT~gTorKK= ⇠ e2 m21 nF [log(µ? /m1 ) + Ccnvrt ]Full LO Rate is independent of scale µ? :hi
d2k 3 / e2 m21 nF log (T /m1 ) + Ccnvrt + Cbremm (k) + Ccnvrt|{z}d k⌘ CLO (k)Talk by Derek Teaney

O(g) Corrections to Hard Collisions, Bremm, Conversions:
1. No corrections to Hard Collisions:
2. Corrections to Bremm:(a) Small angle bremm. Corrections to AMY coll. kernel.

(Caron-Huot)✓⇠gQ = (q +, q , q?) = (gT, g 2T, gT )T g 2 m2D
CLO [q? ] = 2 2! A complicated but analytic formula
2q? (q? + mD )(b) Larger angle bremm. Include collisions with energy exchange, q✓⇠pg

Q = (q +, q , q?) = (gT, gT, gT )⇠ gT .

Talk by Derek Teaney
3. Corrections to Conversions:

KK~gTorK• Doable because of HTL sum rules (light cone causality)

K
Simon Caron-Huot• Gives a numerically small and momentum indep. contribution to the NLO rate
Full results depend on all these corrections.
These rates smoothly match onto each other as the kinematics change.

Talk by Derek Teaney
Conclusion
NLO Results: ⇠ g 3 log(1/g) + g 3large-✓ -bremm
conversions
small-✓ -bremmz}|p{ z}|{ z}|{✓◆h m2i
22C Td LO2Tmmg
DA
112 22k/emn(k)log+Clarge ✓ (k) +Csmall ✓ (k)F1322d k
m1
m1mD
2.5m1
Nf=3

• The result again

α=0.30

NLO / LO

2.52

Nf=3NLONLO/ LO / LO

α=0.30uncert. est.

NLO / LO2

1.5uncert. est.

1.5

110.5
0.5

02024466

8 10 12 14 16 18 208 10 12 14 16 18 20

k/Tk/T

Many things can be computed next (e.g. shear viscosity and e-loss)

まとめ
初期の量子ゆらぎの計算可能に．
流体の初期状態へゆらぎの入った流体の粒子相関
Arnold, Moore, and Yaffeの結果を超えたNLOの摂動計算が可能になってきた．
他にも色々な発展
Lattice QCD, Heavy quark, Jet, energy loss, ...