1. QCD Equation of State - Impact on elliptic flow and transverse momentum spectra Marcus Bluhm Forschungszentrum Dresden-Rossendorf Comparison with lattice QCD Chiral extrapolation RHIC & LHC – v 2, transverse momentum spectra with B. Kämpfer, R. Schulze, D. Seipt & U. Heinz supported by BMBF, GSI

2. T µBµB Motivation early universe: µ B <<< T WIMP‘s: T f.o. ~ M X / 25 RHIC LHC-ALICE µ B < T quark stars µ B >> T p(e,n B )

3. Quasi-Particle Model MB et al., Eur. Phys. J. C 2007 Σ 2-part. irred. diagr. CJT 2-loop QCD thermodynamics

4. k/m g finite widths Im Π T ≠ 0 k asymptotic dispersion relations: chiral expansion in m q /T: replace g G gluons 2+1

5. Equation of State N f =2+1 2000 … 2007 sensible chiral extrapolation not testable: dependence on N σ, N τ, action, … T c is external information cs2cs2 mqmq T c = 170 MeV Π q = m q 2 + 2m f 2 h(m q /T)

6. T/T c Isospin susceptibility diagonal and non-diagonal susceptibilities c2Ic2I c4Ic4I Sensible µ B - extrapolation

7. EoS for RHIC + LHC – Family of EoS‘s QPM lin.interpol. * fix + + + high energy density region fixed baryon density effects tiny low density region fixed µ B = 0

8. RHIC top energy strange baryons P.Kolb directly emitted hadrons S 0 = 110 fm -3 n 0 = 0.4 fm -3 τ 0 = 0.6 fm/c e 0 = 29.8 GeV fm -3 p 0 = 9.4 GeV fm -3 T 0 = 357 MeV EoS favored with soft region around T c and rapid increase above T c

9. LHC estimates conservative guess: s 0 = 330 fm -3, τ 0 = 0.6 fm/c e 0 = 127 GeV fm -3 p 0 = 42 GeV fm -3 T 0 = 515 MeV p T spectra flatter v 2 at fixed p T smaller

10. 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: v 2, p ┴ -spectra soft EoS near T c with rapid rise in c s 2 above T c favored LHC: p T -spectra flatter, v 2 (p T ) smaller variation of EoS, initial & final conditions event-by-event fluctuations, viscous effects

11. Light hadrons

12. Bielefeld-Swansea data c0 c2 c4 c6 „phase transition“ D=1.15 neglect strong interaction QPM lQCD MB et al., PLB 2005