Hot 1-2 Loop QCD*** B. Kämpfer Research Center Dresden-Rossendorf Technical University Dresden ***: M. Bluhm, R. Schulze, D. Seipt real, purely imaginary G^2 HTL QPM  eQPM vs. lattice QCD 100 MeV – 100 GeV

hadrons quarks & gluons LHCRHIC SPS AGS SIS universe Andronic, PBM, Stachel: *

HTL QPM symmetry preserving appoximations: CJT

2-Loop Approximation  1-loop self-energies + HTL self-energies  gauge invariance

Karsch et al. Λ

Non-Zero Mu flow equation now forbidden p = 0 R. Schulze

Rapidly Rotating Quark Stars with R. Meinel, D. Petroff, C. Teichmuller (Univ. Jena) exact (numerical) solution of Einstein equation (axisymmetry & stationarity)  free boundary problem shedding limit: kinky edge Tc matters Down to T = 0

HTL QPM  eQPM neglect small contributions  eQPM collect. modes + Landau + asympt. disp. relations, 2+1

Purely Imaginary Mu M.P. Lombardo et al. polyn. cont. Roberge-Weiss Z3 symmetry T=3.5,2.5,1.5,1.1 Tc Nf = 4 cont. to real mu: M.Bluhm

Going to High Temperatures Boyd et al. Fodor et al. Aoki et al. region of fit M.Bluhm

Susceptibilities: Test of Mu Dependence data: Allton et al., Nf = 2  10% problem

data: Allton et al., Nf = 2

also good agreement with Gavai-Gupta data for sensible test of flow eq. & baryon charge carriers (no di-quarks etc. needed)

Examples of Side Conditions T = 1.1 Tc solid: pure Nf=2 quark matter, electr.neutr. dashed: Nf=2 quark matter + electrons in beta equilibrium d u e

Naive chiral extrapolation Cheng et al. Karsch et al. not really supported by 1-loop self-energies Pisarski formula for plasma frequency CFT 

Quark mass dependence of 1-loop self-energies dispersion relation gluonsplasmons Feynman gauge g = 0.3 g = 1 g = 3 G

quarksplasmino (2) dispersion relations g = 0.3 g = 1 g = 3

D. Seipt 2007: 1-loop self-energies with finite m_q HTL 1-loop asymptotic dispersion relations gauge dependence: Feynman = Coulomb asymptotically

Aoki Karsch Bernard 0.1 Bernard 0.2 RHIC Init.conds. Using the EoS Nf = 2 +1

A Family of EoS‘s QPM lin.interpol. * fix interpolation is better than extrapolation sound waves

Hydro for RHIC Using the EoS Family within Kolb-Heinz Hydro Package sensitivity to EoS near Tc (cf. Huovinen)

LHC Predictions smaller v2

Towards FAIR: CEP 3 D Ising model

Conclusions 2-loop Γ+ HTL + g  G: - good fits of EoS - small contributions of plasmon, plasmino, Landau damp. effective QPM: only T gluons + quarks, simpl. disp. rel. - imaginary mu - high T - susceptibilities - useable EoS for RHIC + LHC elementary excitations in QGP = ? lattice QCD  spectral functions, propagators (transport coefficients)