Exploring QCD Phase Diagram in Heavy Ion Collisions

1. Exploring QCD Phase Diagram in Heavy Ion Collisions Krzysztof Redlich University of Wroclaw and EMMI/GSI AA collisions • QCD phase boundary and freezeout in HIC • Cumulants and probability distributions of conserved charges as Probe for the Chiral phase transition: • theoretical expectations and • recent STAR data at RHIC -CEP? Quark-Gluon Plasma Hadronic matter ? Chiral symmetry broken x B

2. Bulk thermodynamics and critical behaviour – probing the response of a thermal medium to an external field, i.e. variation of one of its external control parameters: (generalized) response functions == (generalized) susceptibilities pressure: energy densitynet charge number order parameter thermal fluctuationsdensity fluctuations condensate fluctuations Mean particle yields generalized susceptibilities:

3. Susceptibilities of net charge number – The generalized susceptibilities probing fluctuations of net -charge number in a system and its critical properties pressure: net-charge q susceptibilities particle number density quark number susceptibility 4th order cumulant expressed by and central moment

4. Tests of equlibration of 1st “moments”: particle yields resonance dominance: Rolf Hagedorn partition function Breit-Wigner res. particle yieldthermal densityBRthermal density of resonances Only 3-parameters needed to fix all particle yields

5. Thermal origin of particle production: with respect to HRG partition function • Chemical freezeout and the QCD chiral crossover Chiral crossover O(4) universality A. Andronic et al., Nucl.Phys.A837:65-86,2010. HRG model Chiral crosover Temperature from LGT HotQCD Coll. (QM’12)

6. Is there a memory that the system has passed through a region of QCD chiral transition ? • What is the nature of this transition? • Chemical freezeout and the QCD chiral crossover Chiral crossover O(4) universality A. Andronic et al., Nucl.Phys.A837:65-86,2010. HRG model Chiral crosover Temperature from LGT HotQCD Coll. (QM’12)

7. QCD phase diagram and the O(4) criticality Pisarki & Wilczek conjecture • In QCD the quark masses are finite: the diagram has to be modified TCP Expected phase diagram in the chiral limit, for massless u and d quarks: TCP: Rajagopal, Shuryak, Stephanov Y. Hatta & Y. Ikeda

8. The phase diagram at finite quark masses • The u,d quark masses are small • Is there a remnant of the O(4) criticality at the QCD crossover line? Asakawa-Yazaki Stephanov et al., Hatta & Ikeda CP At the CP: Divergence of Fluctuations, Correlation Length and Specific Heat

9. The phase diagram at finite quark masses Critical region • Can the QCD crossover line appear in the O(4) critical region? It has been confirmed in LQCD calculations TCP CP LQCD results: BNL-Bielefeld Phys. Rev. D83, 014504 (2011) Phys. Rev. D80, 094505 (2009)

10. Bulk Thermodynamics and Critical Behavior Close to the chiral limit, thermodynamics in the vicinity of the QCD transition(s) is controlled by a universal scaling function regular singular • critical behavior controlled by two relevant fields: t, h K. G. Wilson, Nobel prize, 1982 control parameter for amount of chiral symmetry breaking non-universal scales

11. O(4) scaling and magnetic equation of state QCD chiral crossover transition in the critical region of the O(4) 2nd order • Phase transition encoded in • the magnetic equation • of state pseudo-critical line F. Karsch et al universal scaling function common for all models belonging to the O(4) universality class: known from spin models J. Engels & F. Karsch (2012)

12. Quark fluctuations and O(4) universality class • Find a HIC observable which is sensitive to the O(4) criticality • Consider generalized susceptibilities of net-quark number • Search for deviations from the HRG results, which for quantifies the regular part • To probe O(4) crossover consider fluctuations of net-baryon and electric charge: particularly their higher order cumulants with • F. Karsch & K. R. Phys.Lett. B695 (2011) 136 • B. Friman, V. Skokov et al, P. Braun-Munzinger et al. Phys.Lett. B708 (2012) 179 • Nucl.Phys. A880 (2012) 48 • or compare HIC data directly to the LGT results, S. MukherieeQM^12 for BNL lattice group

13. Effective chiral models Renormalisation Group Approach • coupling with meson fileds PQM chiral model • FRG thermodynamics of PQM model: • Nambu-Jona-Lasinio model PNJL chiral model the invariant Polyakov loop potential (Get potential from YM theory, C. Sasaki &K.R. Phys.Rev. D86, (2012); Parametrized LGT data: Pok Man Lo, B. Friman, O. Kaczmarek &K.R.) the SU(2)xSU(2) invariant quark interactions described through: K. Fukushima;C. Ratti & W. Weise; B. Friman , C. Sasaki ., …. fields B.-J. Schaefer, J.M. Pawlowski & J. Wambach; B. Friman, V. Skokov, ... B. Friman, V. Skokov, B. Stokic & K.R.

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

15. FRG for quark-meson model • LO derivative expansion (J. Berges, D. Jungnicket, C. Wetterich) (η small) • Optimized regulators (D. Litim, J.P. Blaizot et al., B. Stokic, V. Skokov et al.) • Thermodynamic potential: B.J. Schaefer, J. Wambach, B. Friman et al. Non-linearity through self-consistent determination of disp. rel. with and with

16. Solving the flow equation with approximations: • Employed Taylor expansion around minim • Get Potential • Ignore flow of mesonic field get Mean Field result Essential to include fermionic vacuum fluctuations: E. Nakano et al.

17. Ratios of cumulantsatfinitedensity: PQM +FRG B. Friman, F. Karsch, V. Skokov &K.R. Eur.Phys.J. C71 (2011) 1694 HRG HRG HRG 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 !

18. STAR data on the first four moments of net baryon number Deviations from the HRG Data qualitatively consistent with the change of these ratios due to the contribution of the O(4) singular part to the free energy HRG

19. Kurtosis saturates near the O(4) phase boundary B. Friman, et al. EPJC 71, (2011) • The energy dependence of measured kurtosis consistent with expectations due to contribution of the O(4) criticality. Can that be also seen in the higher moments?

20. Ratio of higher order cumulants in PQM model B. Friman, V. Skokov &K.R. Phys.Rev. C83 (2011) 054904 Negative ratio! Deviations of the ratios from their asymptotic, low T-value, are increasing with the order of the cumulant

21. STAR DATA Presented at QM’12 Lizhu Chen for STAR Coll. V. Skokov, B. Friman & K.R., F. Karsch et al. HRG The HRG reference predicts: O(4) singular part contribution: strong deviations from HRG: negative structure already at vanishing baryon density

22. Moments of the net conserved charges • Obtained as susceptibilities from Pressure • or since they are expressed as polynomials in the central moment

23. Moments obtained from probability distributions • Moments obtained from probability distribution • Probability quantified by all cumulants • In statistical physics Cumulants generating function:

24. Probability distribution of the net baryon number P. Braun-Munzinger, B. Friman, F. Karsch, V Skokov &K.R. Phys .Rev. C84 (2011) 064911 Nucl. Phys. A880 (2012) 48) • For the net baryon number P(N) is described as Skellam distribution • P(N) for net baryon number N entirely given by measured mean number of baryons and antibaryons • In Skellam distribution all cummulants expressed by the net mean and variance

25. Probability distribution of net proton number STAR Coll. data at RHIC Thanks to Nu Xu and Xiofeng Luo STAR data Do we also see the O(4) critical structure in these probability distributions ?

26. Influence of O(4) criticality on P(N) Consider Landau model: Scaling properties: Mean Field O(4) scaling

27. Contribution of a sigular part to P(N) Get numerically from: For O(4) narrower P(N) For MF broadening of P(N)

28. The influence of O(4) criticality on P(N) for K. Morita, B. Friman et al. • Take the ratio of which contains O(4) dynamics to Skellam distribution with the same Mean and Variance at different • Ratios less than unity near the chiral critical point, indicating the contribution of the O(4) singular part to the thermodynamic pressure

29. The influence of O(4) criticality on P(N) for K. Morita, B. Friman et al. • Take the ratio of which contains O(4) dynamics to Skellam distribution with the same Mean and Variance near • Asymmetric P(N) • Near the ratios less than unity for • For sufficiently large the for

30. The influence of O(4) criticality on P(N) for K. Morita, B. Friman & K.R. • In central collisions the probability behaves as being influenced by the chiral transition

31. Centrality dependence of probability ratio STAR analysis of freezeout K. Morita et al. Non- critical behavior O(4) critical Cleymans & Redlich Andronic, Braun- Munzinger & Stachel • For less central collisions, the freezeout appears away the pseudocritical line, resulting in an absence of the O(4) critical structure in the probability ratio.

32. Energy dependence for different centralities • Ratios at central collisions show properties expected near O(4) chiral pseudocritical line • For less central collisions the critical structure is lost

33. Conclusions: • Hadron resonancegasprovidesreference for O(4) criticalbehavior in HIC and LGT results • Probabilitydistributions and higher order cumulantsareexcellentprobes of O(4) criticality in HIC • Observeddeviations of the and by STAR from the HRG qualitatively expecteddue to the O(4) criticality • Deviations of the P(N) from the HRG Skellam distribution follows expectations of the O(4) criticality • Present STAR data are consistent with expectations, that in central collisions the chemical freezeout appears near the O(4) pseudocritical line in QCD phase diagram