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Hot 1-2 Loop QCD*** B. Kämpfer Research Center Dresden-Rossendorf Technical University Dresden real, purely imaginary 100 MeV – 100 GeV G^2 HTL QPM eQPM vs. lattice QCD ***: M. Bluhm, R. Schulze, D. Seipt universe RHIC SPS AGS SIS Andronic, PBM, Stachel: * LHC HTL QPM CJT symmetry preserving appoximations: 2-Loop Approximation 1-loop self-energies + HTL self-energies gauge invariance Λ Karsch et al. Non-Zero Mu flow equation now forbidden p=0 R. Schulze Down to T = 0 Rapidly Rotating Quark Stars with R. Meinel, D. Petroff, C. Teichmuller (Univ. Jena) exact (numerical) solution of Einstein equation (axisymmetry & stationarity) free boundary problem Tc matters shedding limit: kinky edge HTL QPM eQPM , 2+1 neglect small contributions eQPM + asympt. disp. relations collect. modes + Landau Purely Imaginary Mu Nf = 4 M.P. Lombardo et al. T=3.5,2.5,1.5,1.1 Tc cont. to real mu: polyn. cont. Roberge-Weiss Z3 symmetry M.Bluhm Going to High Temperatures Fodor et al. Boyd et al. region of fit Aoki et al. M.Bluhm Susceptibilities: Test of Mu Dependence 10% problem data: Allton et al., Nf = 2 data: Allton et al., Nf = 2 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 d u e solid: pure Nf=2 quark matter, electr.neutr. dashed: Nf=2 quark matter + electrons in beta equilibrium Naive chiral extrapolation Karsch et al. Cheng et al. CFT Pisarski formula for plasma frequency not really supported by 1-loop self-energies Quark mass dependence of 1-loop self-energies gluons G plasmons Feynman gauge dispersion relation g = 0.3 g=1 g=3 quarks plasmino (2) dispersion relations g = 0.3 g=1 g=3 D. Seipt 2007: 1-loop self-energies with finite m_q HTL 1-loop gauge dependence: Feynman = Coulomb asymptotically asymptotic dispersion relations Using the EoS Bernard 0.2 Bernard 0.1 Karsch Aoki Nf = 2 +1 RHIC Init.conds. A Family of EoS‘s QPM + lin.interpol. fix * + + sound waves interpolation is better than extrapolation Hydro for RHIC Using the EoS Family within Kolb-Heinz Hydro Package sensitivity to EoS near Tc (cf. Huovinen) LHC Predictions smaller v2 Towards CBM @ 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)