QCD Equation of State - Impact on elliptic flow and transverse

momentum spectra

Marcus BluhmForschungszentrum Dresden-Rossendorf

• Comparison with lattice QCD• Chiral extrapolation• RHIC & LHC – v2, transverse momentum spectra

with B. Kämpfer, R. Schulze, D. Seipt & U. Heinzsupported by BMBF, GSI

T

µB

Motivation

early universe: µB <<< T

WIMP‘s: Tf.o. ~ MX / 25

RHICLHC-ALICE

µB < T

quark starsµB >> Tp(e,nB)

Quasi-Particle Model

MB et al., Eur. Phys. J. C 2007MB et al., Eur. Phys. J. C 2007

Σ 2-part. irred. diagr.

CJT

2-loop QCDthermodynamics

k/mg

finite widths Im ΠT ≠ 0

k

asymptotic dispersion relations:

chiral expansion in mq/T:

replace g G

gluons

2+1

Equation of State

Nf=2+1

2000 … 2007

sensible chiral extrapolation

not testable: dependence on Nσ, Nτ, action, …

Tc is external information

cs2

mq

Tc = 170 MeV

Πq = mq2 + 2mf

2 h(mq/T)

T/Tc

Isospin susceptibility

diagonal and non-diagonal susceptibilities

c2I

c4I

Sensible µB - extrapolation

EoS for RHIC + LHC – Family of EoS‘s

QPM

lin.interpol.

*fix

+

+

+

high energy density region fixed

baryon density effectstiny

low density region fixed

µB = 0

RHIC top energy

strange baryons

P.Kolb

directly emitted hadrons

S0 = 110 fm-3

n0 = 0.4 fm-3

τ0 = 0.6 fm/c

e0 = 29.8 GeV fm-3

p0 = 9.4 GeV fm-3

T0 = 357 MeV

EoS favored with soft region around Tc and rapid increase above Tc

LHC estimates

conservative guess: s0 = 330 fm-3 , τ0 = 0.6 fm/ce0 = 127 GeV fm-3

p0 = 42 GeV fm-3

T0 = 515 MeV

pT spectra flatterv2 at fixed pT smaller

Summary & Outlook

• Quasi-particle model based on 2-loop QCD Φ • Comparison with lattice QCD• Family of EoS‘s for RHIC & LHC – chiral extrapolation• Application: v2, p┴-spectra

• soft EoS near Tc with rapid rise in cs2 above Tc favored

• LHC: pT-spectra flatter, v2(pT) smaller

• variation of EoS, initial & final conditions• event-by-event fluctuations, viscous effects

Light hadrons

Bielefeld-Swansea data

c0

c2

c4

c6

„phase transition“

D=1.15

neglect strong interaction

QPM

lQCD

MB et al., PLB 2005