The initial conditions for The initial conditions for hydro at RHIC / LHChydro at RHIC / LHC

Eccentricity → elliptic flow: extracting η/s and hydro limit (EoS) Thermalization →

“Parton cascade” w/o cutoffs

Adrian DumitruJ.W. Goethe Univ., Frankfurt

Collaborators: H.-J. Drescher, Y. Nara, J.-Y. Ollitrault, B. Schenke, M. Strickland

Chronological evolution of HIC

● Colliding nuclear wavefunctions

● Thermalization stage

● (Viscous) Hydro expansion

● Transition to confined “vacuum”

● Hadronic freeze­out

Tim

e

Pressure gradients and elliptic flow

Idea : Pressure gradients  convert spatial anisotropy to momentum anisotropy

TargetSpectators Projectile Spectators

Participants

X

Y

Initial

Coordinate space

Momentum space

Later

=⟨ y2

−x2⟩

⟨ x2 y2

⟩v2=

⟨ px2−py

2⟩

⟨ px2py

2⟩

Standard model for the initial transverse density profile

Wounded nucleon model: number of participants scaling

part r⊥ ,b= partA r⊥ ,b part

B r⊥ ,b

= T A r⊥b /2 1−1−NNinelT B r⊥−b /2/BB

T B r⊥−b /2 1−1−NNinelT A r⊥b /2/AA

T A x⊥ =∫dz A x⊥ , z Ar =0

1exp [r−R0/a ]

Dilute Parton Gas→

`Saturated' Color Field →

Gluon Saturation at High EnergyGluon Saturation at High Energy

xG(x,Q2)

Inclusive gluon production K t-factorization:

x , k t2 ; r t ~

1s Qs

2

Qs2 x , r t

max Qs2 , kT

2

Kharzeev, Levin, Nardi model:

Q s

Saturation

perturb. ~ 1/kt

2

Φ

kt(λ≈0.28)

Hydro with CGC vs. Glauber initial conditions

Ideal hydro with CGC initial condition (KLN)and τ0 < 1 fm/c overpredicts elliptic flow!

T. H

irano

at a

l., P

hys.

Let

t. B

636

(20

06)

299

Eccentricity from kt-factorization

nu

cl-t

h/0

6050

12

do not trust:Qs2 ~ nPart

Scaling properties:dN g

d 2 r⊥

dy=

4N c

N c2−1

∫d 2 pt

pt2 ∫ d2 k tsx1, k t

2x2, pt−k t

2

~ Q s min2 log

Q s max2

Q s min2

CGC:

Glauber:

CGCGlauber

dNdy

~ min partA ,part

B

dNdy

~partA part

B

2

BA

Kharzeev, Levin, PLB 523 (2001)Dumitru, McLerran, NPA 700 (2002)

Problems

● uGDF Φ does not factorize, Qs not 'universal'    (Lappi, Venugopalan, nucl-th/0609021)

● Qs → 0 at the surface   (IR sensitivity, unrealiable for periph.    collisions and/or lighter ions)

A

B

B=Q sp2⟨T Br t ⟩ ,

B= pB Q sp2

kt2

Φ

Qsp2

fKLNfKLN nucl-th/0605012nucl-th/0611017

Results: Multiplicity

fKLN reproduces Glauber in peripheral collisions !fKLN reproduces Glauber in peripheral collisions !

Voloshin/Poskanzer plot: scaled flow vs densityVoloshin/Poskanzer plot: scaled flow vs density

Glauber IC

CGC IC

nucl-th/0508009

Drescher, Dumitru, Gombeaud, Ollitrault,arXiv:0704.3553

Consistent with hydro limit: K/K0 ~ 0.4

Saturation seen

Finite X-section σ ~ 7.6 mb (CGC)σ ~ 4.3 mb (Glauber)

Viscosity estimate η/s ~ 0.1 (CGC) η/s ~ 0.2 (Glauber)

Speed of soundcs(CGC) / cs(Gl.) ~ .7

extracted EoS, viscosity depend on IC !extracted EoS, viscosity depend on IC !

Ideal hydro should overshoot flow data: EoS should give (Glauber) (CGC)

Higher eccentricity of CGC-IC: → lower cs (“softer” EoS), not larger η/s

Hydro ok for semi-central Au+Au: dissip. correction ~ 30%

-30% agrees with 2+1d viscous hydro:

but EoS should be harder !but EoS should be harder ! Romatschke & Romatschke, arXiv:0706.1522

Boltzmann­Vlasov­Yang­Mills Theory

Soft exchange (q < π/a) via fields (Lorentz force) Hard exchange (q > π/a) via collision term

See poster by See poster by BjBjöörn Schenke !rn Schenke !

U. Heinz, '83U. Heinz, '83

Summary Initial conditions key element of hydro fits

CGC eccentricity requires softer EoS, lower η/s

theoretical modeling of thermalization stage: cutoff-free Boltzmann-Vlasov-YM approach