1. T BB Hadronic matter Quark-Gluon Plasma Chiral symmetry broken Chiral symmetry restored LHC Modelling QCD phase diagram Polyakov loop extended quark-meson model: Including quantum and thermal fluctuations: FRG-approach Probing phase diagram with fluctuations of net baryon number theory & experiment (STAR data) Essential role of higher order moments and their Ratios A-A collisions fixed x 1 st principle calculations: perturbation theory pQCD LGT Probing QCD phase diagram with fluctuations of conserved charges Krzysztof Redlich University of Wroclaw Based on recent work with: B. Friman, V. Skokov; & F. Karsch

2. Sketch of effective chiral models coupled to Polyakov loop coupling with meson fileds PQM chiral model Nambu-Jona-Lasinio model PNJL chiral model the chiral invariant quark interactions described through: K. Fukushima ; C. Ratti & W. Weise; B. Friman, C. Sasaki., …. B.-J. Schaefer, J.M. Pawlowski & J. Wambach; B. Friman, V. Skokov,... the invariant Polyakov loop potential

3. Thermodynamics of PQM model under MF approximation Fermion contribution to thermodynamic potential Entanglement of deconfinement and chiral symmetry Suppresion of thermodynamics due to „statistical confinement” Suppresion suppresion SB limit S

4. The existence and position of CP and transition is model and parameter dependent Introducing di-quarks and their interactions with quark condensate results in CSC phase and dependently on the strength of interactions to new CP’s 4 Generic Phase diagram from effective chiral Lagrangians 1st order Zhang et al, Kitazawa et al., Hatta, Ikeda; Fukushima et al., Ratti et al., Sasaki et al., Blaschke et al., Hell et al., Wambach et al.,.. (Pisarski-Wilczek) O(4)/O(2) univ.; see LGT, Eijri et al 09 crossover Asakawa-Yazaki CP 2 nd order, Z(3) (Stephanov et al.) Hatsuda et al. Alford et al. Shuryak et al. Rajagopal et al.

5. Phase diagram in chiral models with CP at any spinodal points: Singularity at CEP is the remnant of that along spinodals CP spinodals C. Sasaki, B. Friman & K.R. V. Koch et al., I. Mishustin et al., …. fluctuations of net baryon-number

6. Including quantum fluctuations: FRG approach FRG flow equation (C. Wetterich 93) J. Berges, D. Litim, B. Friman, J. Pawlowski, B. J. Schafer, J. Wambach, …. start at classical action and include quantum fluctuations successively by lowering k R egulator function suppresses particle propagation with momentum lower than k k-dependent full propagator

7. FRG at work –O(4) scaling: Near critical properties obtained from the singular part of the free energy density Resulting in the well known scaling behavior of external field Phase transition encoded in the “equation of state” coexistence line pseudo-critical point with

8. FRG-Scaling of an order parameter in QM model The order parameter shows scaling. From the slopes one gets However we have neglected field-dependent wave function renormal. Consequently and. The 3% difference can be attributed to truncation of the Taylor expansion at 3rd order when solving FRG flow equation: see D. Litim analysis for O(4) field Lagrangian

9. The Phase Diagram and EQS Mean-field approximation Function Renormalization Group Mesonic fluctuations shift the CEP to higher temperature The transition is smoother No focusing of isentropes ( see E. Nakano et al. (09) ) (c.f., C. Nonaka & M. Asakawa &. B. Muller) CEP

10. Probing phase diagram with moments of net quark number fluctuations Smooth change of and peak-like structure in as in O(4) Moments probes of the chiral transition MF-results PQM QM FRG-results QM PQM QM model PQM model PQM model QM model SB limit SB

11. Kurtosis of net quark number density in PQM model V. Skokov, B. Friman &K.R. For the assymptotic value due to „ confinement” properties Smooth change with a rather weak dependen- ce on the pion mass For

12. Kurtosis as an excellent probe of deconfinement HRG factorization of pressure: consequently: in HRG In QGP, Kurtosis=Ratio of cumulants excellent probe of deconfinement S. Ejiri, F. Karsch & K.R. Kurtosis F. Karsch, Ch. Schmidt The measures the quark content of particles carrying baryon number

13. Deviations of the ratios of odd and even order cumulants from their asymptotic, low T-value, are increasing with and the cumulant order Properties essential in HIC to discriminate the phase change by measuring baryon number fluctuations ! Ratio of cumulants at finite density

14. QCD phase boundary & Heavy Ion Data QCD phase boundary appears near freezeout line Particle yields and their ratio, well described by the Hadron Resonance Gas

15. QCD phase boundary & Heavy Ion Data Excellent description of LGT EQS by HRG A. Majumder&B. Muller LGT by Z. Fodor et al.. R. Hagedorn Karsch, Tawfik &K.R.

16. Coparison of the Hadron Resonance Gas Model with STAR data Frithjof Karsch & K.R. RHIC data follow generic properties expected within HRG model for different ratios of the first four moments of baryon number fluctuations LGT results for CP see also: R. Gavai &S. Gupta S. Ejiri et al.

17. Deviations of the ratios from their asymptotic, low T-value, are increasing with the order of the cumulant Properties essential in HIC to discriminate the phase change by measuring baryon number fluctuations ! Ratio of higher order cumulants

18. Deviations of the ratios from their asymptotic, low T-value, are increasing with the order of the cumulant order and with increasing chemical potential Properties essential in HIC to discriminate the phase change by measuring baryon number fluctuations ! Ratio of higher order cumulants at finite density

19. Lines of vanishing fluctuations for different moments Broad temperature range of negative values of different moments with n>4 which increases with their orders. Strong deviations from Hadron Resonance Gas result due to collective effects related with chiral symmetry restoration and deconfinement CP cross transition -over CP

20. Conclusions The FRG method is very efficient to include quantum and thermal fluctuations in thermodynamic potential in QM and PQM model The FRG provides correct scaling of physical observables expected in the O(4) universality class To observe fluctuations related with O(4) cross- over in HIC measure higher order fluctuations, N>6 relative to N=2 moments

21. Quark number fluctuations at finite density Strong increase of fluctuations with baryon-chemical potential In the chiral limit the and daverge at the O(4) critical line at finite chemical potential