1 Chemical freezeout curve from heavy ion data coincides with freezeout T at RHIC and SPC J. Stachel & P. Braun- Munzinger

2 QCD Thermodynamics of confined phase Heavy Ion Phenomenology through Lattice Gauge Theory at finite and ? Based on common work with Bielefeld-Swansea LGT Coll. C.R. Allton, M. Doring, S. Ejiri, S.J. Hands, O. Kaczmarek, F. Karsch, E. Laermann, K.R. & Shinji Ejiri, Frithjof Karsch Critical and Freezeout Conditions in Heavy Ion Collisions Krzysztof Redlich Thermodynamic pressure Charges Fluctuation & Chiral Condensate Quark mass dependence of QCD thermodynamics below deconfinement critical & chemical freezout conditions

3 Taylor expansion of resonance pressure Factorization of the net baryonic pressure baryon mass spectrum Compare with LGT results: Consequences: For fixed any ratio of these observables is T-independent the ratio of the O(2), O(4) and O(6) coefficients:

4 factorization on the Lattice HRG= ratios consistent with the expansion of cosh(x) expected in HRG partition function Ratios of all baryonic observables independent of temperature for fixed

5 quark condensate at finite density Baryon contribution: Net baryon pressure In 2-flavour LGT calculations:

6 Isovector and electric charge fluctuations related with space-like screening limit of the retarded photon self-energy =0 for In LGT: obtained from,however requires independent Monte-Carlo calculations ;

7 Isovector susceptibility in LGT and resonances gas on the lattice: expanding cosh(x) one expects: LGT result supports decomposition of meson baryon contribution in confined phase

8 From LGT to HRG Phenomenology: quantitative analysis of T-dependence of thermodynamics In HRG the pressure can be appr. obtained from the Taylor coefficients of LGT results from Integral method provides good T-dependence of LGT pressure use c’s from LGT check P?

9 LGT results for pion mass dependence of and their parity partners 2 QCDSF Coll., M. Göckeler, et al.. To check T-dependence of the EQS requires

10 Hadron resonance gas model and LGT susceptibilities At only ~10% is due to pions contribution Including interactions e.g. actually reduces fluctuations (R. Rapp & J. Wambach)

11 Isospin multiplets contribution to QCD thermodynamics Diferent Isospin states contribution to the thermodynamic pressure: Connected with LGT coefficient in the Taylor expansion of susceptibilities:

12 Quark mass dependence of QCD thermodynamics below deconfinement Linear dependence of on the quark mass in LGT

13 Deconfinement is density driven - ( percolation) lines of constant energy density in HG Hadron resonance gas partition function provides a good description of m and Nf depen. Of deconfinement temperature A. Peikert, et al.. LGT result shows: dependence of on and, however for and for all hadrons + glubols hadrons condition for deconfinement percolation deconfinement H. Satz

14 Phase boundary of fixed energy density versus chemical freezeout SPS 40 AGeV Spliting of chemical freezeout and phase boundary surface most likely appearswhen the densities of mesons and baryons are comparable For E<30 AGeV strong collective effects in hadronic medium are to be expected LGT J. Cleymans et al.. Mesons Baryons

15 QCD Thermodynamics Heavy Ion Phenomenology Lattice Gauge Theory ? YES: Phenomenological partition function of Hadron Resonance Gas provides satisfactory description of LGT thermodynamics at finite, and

16 Taylor coefficients of isovetor susceptibility from LGT and resonance gas model As expected in resonance gas model LGT results support decomposition expected in HRG-model

17 Hadron resonance gas model and LGT thermodynamics

18 factorization on the Lattice

19 QCD at non-vanishing chemical potential Bielefeld-Swansea approach Taylor expansion of :, complex fermion determinant From dependence of chiral susceptibilities Up to O(6) order in

20 Hadron Mass Spectrum versus quark mass chiral limit quenched limit from LGT or Bag Model

21 Bag Model and Hadron Masses B : surface boundary conditions Hadron Masses from: for and : q q g g q

22 Isovector susceptibility in LGT and resonances gas on the lattice: expanding cosh(x) one expects: thus