Exploring QCD Phase Diagram in Heavy Ion Collisions

1. Exploring QCD Phase Diagram in Heavy Ion Collisions Krzysztof Redlich University of Wroclaw 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 Quark-Gluon Plasma -CEP? Hadronic matter ? Chiral symmetry broken x B

2. Bulk thermodynamics and critical behaviour – probing the response of a thermal medium to an external fields, i.e. variation of one of its external control parameters: (generalized) response functions == (generalized) susceptibilities pressure: energy densityorder 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. A. Andronic et al., Nucl.Phys.A837:65-86,2010. • 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 P. Braun-Munzinger et al. QM (2012)

6. Chiral crossover • 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 O(4) universality A. Andronic et al., Nucl.Phys.A837:65-86,2010. HRG model Chiral crosover Temperature from LGT HotQCD Coll. (QM’12) Chemical Freezeout LHC (ALICE) P. Braun-Munzinger (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 Critical region • The u,d quark masses are small • There is a remnant of the O(4) criticality at the QCD crossover line: Asakawa-Yazaki Stephanov et al., Hatta & Ikeda CP LQCD results: BNL-Bielefeld group Phys. Rev. D83, 014504 (2011) At the CP: Divergence of Fluctuations, Correlation Length and Specific Heat Phys. Rev. D80, 094505 (2009)

9. 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

10. 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 O(4) 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)

11. 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

12. 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.

13. Ratios of cumulantsatfinitedensity: LGT and PQM with FRG B. Friman, F. Karsch, V. Skokov &K.R. Eur.Phys.J. C71 (2011) 1694 HRG HRG HRG value Ch. Schmidt et al. S. Ejiri et al. Deviations from low T HRG value: are increasing with and the cumulant order

14. 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

15. 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?

16. 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

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

18. 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

19. 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

20. 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

21. 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 For preliminary STAR data QM 2012

22. 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.

23. 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 (check for the influence of : efficiency , volume fluctuations and baryon number conservation!!!) • 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 on QCD phase diagram