Probing QCD Phase Diagram with Fluctuations of conserved charges

1. Probing QCD Phase Diagram with Fluctuations of conserved charges HIC • QCD phase boundary and • its O(4) „scaling” • Higher order moments of conserved • charges as probe of QCD criticality • in HIC • STAR data & expectations K. Fukushima Krzysztof Redlich University of Wroclaw & EMMI/GSI

2. Budapest-Wuppertal LGT data • Particle yields and their ratio, as well as LGT results at are well described by the Hadron Resonance Gas Partition Function (F. Karsch, A. Tawfik & K.R.). O(4) universality A. Andronic et al., Nucl.Phys.A837:65-86,2010. HRG model Chiral crosover Temperature from LGT Chemical Freezeout LHC (ALICE) HotQCD Coll. (QM’12) P. Braun-Munzinger (QM’12)

3. S. Ejiri, F. Karsch & K.R. • Particleyields and their ratio, as well as LGT resultsare welldescribed by the Hadron ResonanceGas PartitionFunction . O(4) universality HRG model

4. O(4) scaling and critical behavior • Near critical properties obtained from the singular part of the free energy density with with • Phase transition encoded in • the “equation of state” pseudo-critical line F. Karsch et al

5. O(4) scaling of net-baryon number fluctuations with • The fluctuations are quantified by susceptibilities • From freeenergy and scalingfunction one gets • Resulting in singularstructures in n-th order momentswhichappear for and for • since in O(4) univ. class

6. Kurtosis as an excellent probe of deconfinement S. Ejiri, F. Karsch & K.R.: Phys.Lett. B633 (2006) 275 • HRG factorization of pressure: consequently: in HRG • In QGP, • Kurtosis=Ratio of cumulants with is an excellent probe of deconfinement Kurtosis F. Karsch, Ch. Schmidt The measures the quark content of particles carrying baryon number

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

8. Kurtosis as an excellent probe of deconfinement Ch. Schmidt at QM’12 • HRG factorization of pressure: consequently: in HRG • In QGP, • Kurtosis=Ratio of cumulants excellent probe of deconfinement Kurtosis F. Karsch, Ch. Schmidt The measures the quark content of particles carrying baryon number

9. Ratios of cumulantsatfinitedensity: PQM +FRG B. Friman, V. Skokov &K.R. HRG HRG Deviations of the ratios of odd and even order cumulants from theirasymptotic, lowT-value, areincreasing with and the cumulant order Propertiesessential in HIC to discriminate the phasechange by measuringbaryonnumberfluctuations !

10. Comparison of the Hadron ResonanceGas 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 Error Estimation for Moments Analysis: Xiaofeng Luo arXiv:1109.0593v

11. STAR data: Deviations from HRG • Critical behavior? • Conservationlaws? A. Bzdak, V. Koch, V.Skokov ARXIV:1203.4529 • Volume fluctuations? B. Friman, V.Skokov &K.R.

12. Ratio of higher order cumulants B. Friman, V. Skokov &K.R. Deviations of the ratios from theirasymptotic, lowT-value, areincreasing with the order of the cumulant

13. Fluctuations of the 6th and 8th order moments exhibit strong deviations from the HRG predictions: => Such deviations are to be expected in HIC already at LHC and RHIC energies B. Friman, V. Skokov &K.R. Range of deviationsfrom HRG The range of negativefluctuationsnearchiral cross-over: PNJL model results with quantum fluctuationsbeingincluded : Thesepropertiesaredue to O(4) scaling , thusshould be alsothere in QCD.

14. Theoretical predictions and STAR data Deviation from HRG if freeze-out curve close to Phase Boundary/Cross over line L. Chen, BNL workshop, CPOD 2011 STAR Data Polyakov loop extended Quark Meson Model Lattice QCD STAR Preliminary Strong deviations of data from the HRG model (regular part of QCD partition function) results: Remnant of O(4) criticality!!??

15. STAR DATA Presented at QM’12 Lizhu Chen for STAR Coll. V. Skokov

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

17. Probability distribution of the net baryon number • 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 HRG the means are functions of thermal parameters at Chemical Freezeout

18. Influence of criticality on the shape of P(N) In the first approximation the quantifies the width of P(N) HRG LGT hotQCD Coll. Similar: Budapest-Wuppertal Coll Shrinking of the probability distribution already expected due to deconfinement properties of QCD At the critical point (CP) the width of P(N) should be larger than that expected in the HRG due to divergence of in 3d Ising model universality class

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

20. Contribution of a singular part to P(N) K. Morita, B. Friman, V. Skokov &K.R. Got numerically from: For O(4) narrower P(N) For MF broadening of P(N)

21. 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 from the HRG • as expectedat the O(4) pseudo-criticalline • Shrinking of P(N) from the HRG follows expectations of the O(4) criticality

22. Influence of volume fluctuations on cumulants Probability distribution at fixed V V Moments of net charge Cumulants central moment

23. Volume fluctuations and higher order cumulants in PQM model in FRG approach General expression for any P(N): - Bell polynomials V. Skokov, B. Friman & K.R.