Probability distribution of conserved charges and the QCD phase transition

1. Probability distribution of conserved charges and the QCD phase transition • QCD phaseboundary, its O(4) „scaling” & relation to freezeoutin HIC • Moments and probablilitydistributions of conservedcharges as probes for proximity to O(4) criticality • STAR data & expectiations With:P. Braun-Munzinger, B. Friman F. Karsch, V. Skokov

2. Chemical freezeout and QCD crtitical line • Relating freezeout and QCD critical line at small chemical potential • Particle yields and their ratios as well as LGT thermodynamics at are well described by the HRG Partition Function ! • QCD crossover line- remnant of the O(4) criticality O(4) universality A. Andronic et al., Nucl.Phys.A837:65-86,2010.

3. LGT and phenomenological HRG model C. Allton et al., S. Ejiri, F. Karsch & K.R. • The HRG partition function provides and excellent approximation of the QCD thermodynamics at See also: C. Ratti et al., P. Huovinen et al., B. Muller et al.,…….

4. Kurtosis as an excellent probe of deconfinement S. Ejiri, F. Karsch & K.R. • 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

5. 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

6. O(4) scaling of net-baryon number fluctuations with • The fluctuations are quantified by susceptibilities • Fromfree energy and scalingfunction one gets • Resulting in singularstructuresinn-th order momentswhichappear for and for • sincein O(4) univ. class

7. Ratio of cumulantsatfinitedensity HRG HRG Deviations of theratios of odd and even order cumulantsfromtheirasymptotic, lowT-value, areincreasingwith and thecumulant order Propertiesessentialin HIC to discriminatethephasechange by measuringbaryonnumberfluctuations !

8. C. Schmidt, HotQCD F. Karsch & K.R. Phys. Rev. D Rap. Com, (2011)

9. Ratio of higher order cumulantsatfinitedensity Deviations of theratiosfromtheirasymptotic, lowT-value, areincreasingwiththe order of thecumulant order and withincreasing chemical potential Propertiesessentialin HIC to discriminatethephasechange by measuringbaryonnumberfluctuations !

10. Properties of fluctuationsin HRG Calculate generalized susceptibilities: from Hadron Resonance Gas (HRG) partition function: and and resulting in: Comparethese HRG model predictionswith STAR data at RHIC:

11. 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 Error Estimation for Moments Analysis: Xiaofeng Luo arXiv:1109.0593v

12. Mean, variance, skewness and kurtosisobtained by STAR and rescaled HRG • STAR Au-Au • STAR Au-Au these data, due to restricted phase space: Account effectively for the above in the HRG model by rescaling the volume parameter by the factor 1.8/8.5

13. Moments obtained from probability distributions • Moments obtained form the probability distribution • Probability quantified by all moments • In statistical physics Moments generating function:

14. conservation on the average exact conservation • Probability quantified by :mean numbers of charged 1,2 and 3 particles & their antiparticles

15. P(N) in the Hadron Resonance Gas for net- proton number Theprobabilitydistribution for net baryonnumber N isgovernedin HRG by theSkellamdistribution The probability distribution for net proton number N is entirely given in terms of (measurable) mean number of protons b and anti-protons

16. Probability distribution obtained form measured particle spectra: STAR data broken lines • Mean proton and anti-protoncalculatedinthe HRG with • takenatfreezeutcurve and Volumeobtained form thenet-mean proton number

17. Comparing HRG Model withPreliminary STAR data: efficiencyuncorrected Data presented at QM’11, H.G. Ritter, GSI Colloquium Data consistent with Skellam distribution: No sign for criticality

18. Centrality dependence at 39 and 200 GeV Preliminary STAR data arXiv:1106.2926 STAR data Phys. Rev. Lett. 105 (2010) Xiaofeng Luo for the STAR Collaboration Data consitent with Skellam distribution: No sign for criticality Data efficiency uncorrected !

19. Centralitydependenceat 39 and 200 GeV STAR data Preliminary STAR data Data consitent with Skellam distributionHRG shows broader distribution

20. Centralitydependenceat 39 and 200 GeV Preliminary STAR data STAR data-efficiency uncorected Data consitentwithSkellamdistributionHRG showsbroaderdistribution

21. Seealso: Claudia Rattifor LGT Data of Budapest-Wuppertal Coll.

22. Data versusUrQMD V. Skokov et al.. • UrQMDprovide much toonarowerprobabilitydistribution of net proton number

23. Probability distributions and their energy dependence for • Themaxima of haveverysimilarvalues for all thusconst. for all

24. Moments energy dependence: Skellamdistribution Weak dependence of even order cummulants on energy!!

25. Higher order moments and probabilitydistributionsareexcellentprobes of criticalityin HIC • The 6th and 8th order momentsnegativealreadyatthe LHC • Deviation of P(N) setsinat and increaseswithcentrality: • remnant of O(4) criticality • Thismightindicatethatcriticallinedecouplesfromthefreezeoutline near • Theaboveneed to be checkedwithefficiencycorrected data Conclusions: ? J. Cleymans &K.R.