1. 1 Recent LGT results and their implications in Heavy Ion Phenomenology quark-gluon plasma hadron gas color superconductor Equation of state in LGT and freeze-out critical conditons Charge fluctuations below and at chiral phase transition : LGT and Chiral Effective Model results how to surch for TCP in hevy ion collisions? T K. Redlich m=0 O(4) 2nd order TCP Z(2), 2nd order 1st order Crossover m=0

2. 2 Chemical freeze-out and its characteristics measures of the effective number of degrees of freedom :expected for if there are leading quasiparticles since Cleymans et al.., A.Tawfik with J. Cleymans & K.R

3. 3 Deconfinement is density driven - ( percolation) lines of constant energy density in HRG Hadron resonance gas partition function provides a good description of m and depen. of deconfinement temperature A. Peikert, et al.. LGT result shows: strong dependence of on and, however for and for all hadrons + gluballs hadrons condition for deconfinement percolation deconfinement H. Satz

4. 4 Phase boundary of the fixed energy density versus chemical freezeout Splitting of the chemical freeze- out and the phase boundary surface appears when the densities of mesons and baryons are comparable? particles production processes LGT ( Allton et al..) Meson Dominated Baryon Dominated Z. Fodor et al.. : QGP hadronization : Hadronic rescattering R. Gavai, S. Gupta

5. 5 Scaling properties of particle production yields H. Oeschler, et al.., A. Andronic, P. Braun-Munzinger &K.R. RHIC SPS Scalings appear due to the strangeness exchange production processes in the hadronic fireball,

6. 6 Scaling relations of production However, thus and P. Koch, B. Muller & J. Rafelski C. M. Ko H. Oeschler et al.. A. Andronic, P.Braun-Munzinger & K.R..

7. 7 EQS and evolution path of fixed entropy/baryon V.D. ToneevV.D. Toneev, J. Cleymans, E.G. Nikonov,J. CleymansE.G. Nikonov K. RedlichK. Redlich, A.A. Shanenko, (2001,2006)A.A. Shanenko Mixed phase model L. Bravina et al.. (2001) UrQMD S. Ejiri, F. Karsch, E. Laermann & C. Schmidt, (2006) LGT 2-flavor

8. 8 QCD at non-vanishing chemical potential C. Allton, M.Doring,S. Ejiri, S.Hands, O. Kaczmarek, F. Karsch, E. Laermann & K. Redlich (2005) Taylor expansion of complex fermion determinant Expansion valid for : interesting region for heavy ions SPS RHIC LHC Problem: (0.18)

9. 9 Quark-fluctuations and chiral symmetery restoration Free energy: expected 2-order transition in 3-d, O(4) universality class: Net Quark Fluctuations 1st order

10. 10 Derivatives of pressure and susceptibilities Difference between and is small at  =0. As pQCD Large spike in : for as in pQCD Interesting in Heavy Ion Collisions

11. 11 Ratios of cumulants reflect carriers of the net-quark and charge S. Ejiri, F. Karsch & K.R. (2006) HRG

12. 12 The Hadron Resonance Gas model and net-quark fluctuations Allton et al.. O(4) S. Ejiri, F. Karsch & K.R, O(6) HRG provides good description of LGT charge fluctuations in confined phase

13. 13 factorization on the Lattice as in HRG HRG-partition function: fixed ratios of baryonic observables independent of

14. 14 Charge Fluctuations in the NJL model Ch. Sasaki, B. Friman & K.R. Generic structure of the phase diagram as expecetd in different chiral models: see eg. Y. Hatta & T. Ikeda; M. Stephanov, K. Rajagopal,.. : quark and isovector chemical potentials /

15. 15 Quark and isovector susceptibilities along the critical curve Non-monotonic behavior of the net quark susceptibility in the vicinity to TCP Crude estimate of the critical region in using chemical freeze-out condition gives: Ch. Sasaki et al..

16. 16 Conclusions For the chemical freeze-out appears in the near vicinity to deconfinement Phenomenological partition function of the Hadron Resonance Gas provides a good approximation of the reqular part of the QCD partition function in the hadronic phase To identify the chiral end-point experimentally one needs to search for non-monotonic in dependence of charge fluctuations