Phenomenological Description of the Quark-Gluon-Plasma

1. Phenomenological Description of the Quark-Gluon-Plasma B. Kämpfer Helmholtz-Zentrum Dresden-Rossendorf Technische Universität Dresden M. Bluhm, R. Schulze, R. Yaresko, F. Wunderlich, M. Viebach K. Rajagopal, T. Schafer, U. Wiedemann ...: sQGP has no quasi-particle description • QGP parametrization: EoS, viscosities • (obituary or revival of QPM?) • 2. bottom-up approach within AdS/QCD

2. universe quarks & gluons SPS LHC RHIC AGS SIS hadrons Andronic, PBM, Stachel: *

3. Scales Confinement in Early Universe no specific relics (unless p + n) (contrary to BBN: 25% He) Milne coordinates HICs puzzle = entropy production (thermal.) proto-star in core collapse: t ~ 1 sec, T < 50 MeV quark cores? Neutron Stars Steiner et al., 1205.6871 - bursting NSs + photosperic expansion - transiently accreting NSs in quiescence

4. Quasi-Particle Model Landau & Fermi liquids: adiabaticity & Pauli‘s exclusion principle Fermi gas  Fermi liquid no interaction interaction keeps spin, charge, momenta ... but modifies masses ... does not apply always: Luttinger fluid, ... in this spirit: QGP = Bose + Fermi gases masses = self-energies m(T) ~ T G(T), large T: G  g(pQCD)

5. 2-Loop Approximation to CJT/Phi Funct.  1-loop self-energies + HTL self-energies  gauge invariance finite widths: Peshier-Cassing, Bratkovskaya

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

7. Peshier‘s Flow Equation given form Cauchy problem: initial values

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

9. data: Allton et al., Nf = 2

10. also good agreement with Gavai-Gupta data for data: Allton et al., Nf = 2 sensible test of flow eq. & baryon charge carriers (no di-quarks etc. needed) F. Karsch: cumulants & fluctuations  HRG & QPM

11. Purely Imaginary mu Nf = 4 M.P. Lombardo et al. QPM T=3.5,2.5,1.5,1.1 Tc cont. to real mu: polyn. cont. Roberge-Weiss Z3 symmetry I = II, I‘ = inflected I‘‘

12. adjust QPM parameterization at to get 1. phase border line (= characteristic trought Tc) 2. p(T) data: Engels et al. PLB 1997 tests Peshier‘s flow eq. (chem. pot. degree of freedom), at least for Nf = 4 deg. quarks

13. Viscous Fluids Intro: V. Greco water: Gluon Plasma AMY 2003 data: Meyer Nakamura, Sakai QPM

14. QPM Viscosities Decomposition: EoS transp. Kinetic eq.: e.m. tensor: Relaxation time approx.:

15. EoS pQCD: ad hoc strong coupling: Gubser, Buchel further details: Bluhm, BK, Redlich, PLB 2012, PRC 2011 2 Vosresensky et al. (2011): ambiguity of rel. time ansatz

16. data: Boyd et al. Okoamoto et al. KSS

17. instead of QCD AdS/YM Maldacena 1998 Witten 1998 Gubser et al. 1998 AdS5/CFT4 common symmetry group SO(2,d) super YM holography gravity5 QCD4 large-Nc YM Einstein + scalar field bottom-up approach: adjust V(phi) to EoS for free: drag & jet quentching, chir. symm. spectra of glueballs, hadrons ... quantitytive matching to QCD is difficult

18. Panero: mild/no dependence non-pert. EoS SU(3) YM4 I/T4 = T (p/T4)‘ e = I + 3p s = (I + 4p)/T cs2 = p‘ / (T p‘‘)

19. Einstein4 Riemann space-time: glk;n = 0 Rij + gij R/2 = k Tij gravity/geometry gravity/geometry matter matter Gubser, Kajantie, Kiritsis Li et al. maximally symmetric AdS: , constant curvature negative L in Lorentz inv. vacuum: Tij = (e + p) uiuj + p gij -> - L gij (e < 0, p > 0) = 0 Einstein‘s GRG is well tested (PPN coefficients fit observations)

20. Black Holes, e.g. Schwarzschild ds2 = f(r)-1 dr2 + r2 dO22 – f(r) dt2 f(r) = 1 – 2M/r: r H = 2M  horizon (simple zero) Hawking temperature Hawking-Bekenstein entropy Hawking‘s hairless theorem: M, Q, J s(T)  EoS Schwarzschild vacuole in Friedmann-Walker-Lemaitre universe BH Schwarzschild

21. boundary conds.: z = 1/r zH horizon, IR z = 0 AdS, UV t, x 1st ansatz: 2nd ansatz: 3rd ansatz: AdS BH

25. Transport Coefficients: Gubser 2008 fluctuations: linearize Einstein eqs. with phi as holographic coordinate (instead of r or z) Kubo formulae  shear mode: bulk mode:

26. mimicks EoS

27. Summary QPM parametrization of EoS: YM + QGP: mu = 0  T dep. susceptibilities: mu > 0, mu_u,d imaginary mu T  0, mu > 0: quark stars? AdS/YM: holographic improvement needed (EoS vs. V(phi) or As(z); pert. regime? eta = s / 4 pi vs. pert. Regime zeta(T), zeta/eta vs. (1/3 – vs^2) ) No specific relicts of cosmic confinement (memory loss) contrary to BBN next steps: fine tuning of V or As  robustness of zeta? spectral functions (no transport peaks) quarks, mu > 0 Kajantie et al. ... et al.

28. Quark Matter in Neutron Stars? 1054 AD: supernova  radio pulsar X ray source

29. p e, n Neutron Stars & White Dwarfs M / M_sun 2.0 Chandrasekhar stable 1.4 unstable n, (p, e-) e-, nuclei R [km] 10 20 10,000

30. Neutron Stars with Quark Cores (1) M / M_sun 2.0 q Chandrasekhar stable 1.4 unstable n, (p, e-) e-, nuclei q p e, n R [km] 10 20 10,000

31. T CEP q p mix Nf = 3 mix e, n n e1 e2 Neutron Stars with Quark Cores (2) M / M_sun • density jump e2/e1 is • very small: 1) • < 1.5: 2) • > 1.5: 3) 2.0 1) 2) 1.4 unstable 3) R [km] 10 20 10,000

32. T CEP q p mix Nf = 3 mix e, n n e1 e2 The Third Island BK, PLB 1982 Stocker, Schaffner-B. 2000 M / M_sun 2.0 • density jump is • small and EoS(q) stiff: 1) • larger and/or EoS(q) soft: 2) 1) 1.4 2) R [km] 10 20 10,000

33. Pure Quark Stars fit to Bielefeld & WuppertalBp data hybrid stars: sensitive to matching of EoS

34. 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

36. Gubser: V Li: As(z)

38. mild increase (Gubser, Kiritsis) strong increase (Kharzeev, Tuchin Karsch et al.)