1. 1 Debye screened QGP QCD : confined Chiral Condensate Quark Potential Deconfinement and Chiral Symmetry restoration expected within QCD mm symmetryChiral symmetry HG Global symmetries

2. 2 Phases of QCD and charge fluctuations quark-gluon plasma hadron gas color superconductor Effective Chiral Models and QCD phase diagram: Charge fluctuations - probe of chiral phase transition : how to possibly search for TCP in heavy ion collisions? T K. Redlich m=0 O(4) 2nd order TCP Z(2), 2nd order 1st order Crossover m=0 (B. Friman, Ch. Sasaki &K.R)

3. 3 Chiral Transformations of QCD-Langrangian Chiral transformations: Decompose: Breaks chiral symmetry: invariant under In QCD vacuum chiral symm. spontaneously broken

4. 4 Order parameter of chiral symmetry restoration Consider chiral susceptibility: to determine the position of the chiral phase transition: { Measures dynamically generated „constituent” quark mass: T=0 quarks „dress” with gluons in hot medium dressing „melts” effective quark mass shift

5. 5 Extendet PNJL model and its mean field dynamics Thermodynamic potential: mean-field approximation : Strength of quarks interactions in scalar and vector sector Polyakov loop dynamical (u,d)-quark masses, shifted chemical potentials and thermal averages of Polyakov loops obtained from the stationary conditions:

6. 6 Chiral Symmetry Restoration – Order Parameter discontinuity Divergence of the chiral susceptibility at the 2nd order transition and at the TCP Discontinuity of the chiral susceptibility: at the 1st order transition discontinuity Fixed Different Slopes

7. 7 Generic Phase diagram for effective chiral Lagrangians Generic structure of the phase diagram as expected in different chiral models: see eg. Y. Hatta & T. Ikeda; M. Stephanov, K. Rajagopal, Fuji,.. Quantitative properties of the phase diagram and the position of TCP are strongly model dependent Large no TCP at finite temperature ! TCP 2nd order transition 1st order transition

8. 8 Effective Thermodynamic Potentials Flattening of the potential at TCP: indeed expanding thermodynamic near at TCP Landau – Ginzburg potential finds: 2nd order TCP 2nd order 1st order

9. 9 Susceptibilities of conserved charges Net quark-number,isovector and electric charge fluctuations No mixing of isospin density with the sigma field due to isospin conservation Hatta & Stephanov TCP 1st order 2nd order

10. 10 Critical structure of the quark susceptibility Quark number susceptibility at Divergence of quark susc. at TCP is directly related with the flattening ( ) of the thermodynamic potential Scalar susceptibility vector-scalar susc. { = finite at 2nd order at TCP Change of the universality class

11. 11 The universality class and T-dependence of M Criticality of directly related with the scalling of and with { at TCP at 2nd The critical exponents of determined by the slope of the order parameter as a function of near TCP 2nd

12. 12 Critical exponents near TCP The strength of singularity at TCP depends on direction in plane along 1st order line any direction not parallel along 2nd order line Ising Model Going beyond mean field: B.-J. Schaefer & J. Wambach Z(2) univer. class

13. 13 Free energy: expected 2-order transition in 3-d, O(4) universality class: Net Quark Fluctuations 1st order Quark fluctuation and O(4) universality

14. 14 How to search for TCP LGT-Bielefeld An increase of is only necessary but not sufficient condition to verify the existence of TCP PNJL model, Sasaki et al..

15. 15 Quark and isovector fluctuations along critical line sensitive probes of TCP Non-singular behavior at TCP of Non-monotonic behavior of the net quark susceptibility in the vicinity to TCP

16. 16 Critical region near TCP The critical window near TCP is elongated on the critical line This window is quite narrow in the direction of fixed T and corresponds to In heavy ion collisions the corresponds to change in

17. 17 Finite quark mass and QCD phase diagram surface of 1st order transitions line of end point CEP TCP crossover line 2nd acts as an external magnetic field and destroys the 2nd order transition preserving the 1st order below CEP changes the effective thermodynamic potential consequently the modification of the critical properties is to be expected:

18. 18 Conclusions The effective chiral Lagrangians provide a powerful tool (due to universality) to study the critical consequences of chiral symmetry restoration in QCD, however The quantitative verification of the phase diagram and the existence of the CEP/TCP in QCD requires the first principle LGT calculations and CBM experiment

19. 19 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

20. 20 Charge Fluctuations Near Deconfinement S.N Jeon & V. Koch E. Shuryak & M. Stephanov M. Asakawa. U. Heinz & B. Muller …. Mass and quantum number gap between confined and deconfined phase