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Probability distribution of conserved charges and the QCD phase transition K. Redlic h

Probability distribution of conserved charges and the QCD phase transition K. Redlic h. QCD phase boundary , its O(4) „ scaling ” & relation to freezeout in HIC Moments and probablility distributions of conserved charges as probes of the O(4) crossover criticality

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Probability distribution of conserved charges and the QCD phase transition K. Redlic h

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  1. Probability distribution of conserved charges and the QCD phase transitionK. Redlich • QCD phaseboundary, its O(4) „scaling” & relation to freezeoutin HIC • Moments and probablilitydistributions of conservedcharges as probes of the O(4) crossovercriticality • STAR data & expectiations HIC crossover CP orTriple Point ? Qarkyonic Matter ? 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 baryon 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 PQM -RG See talk of Vladimir Skokov HRG HRG Deviations of theratios of odd and even order cumulantsfromtheirasymptotic, lowT-value, areincreasingwith and thecumulant order Propertiesessentialin HIC to discriminatethephasechange by measuringbaryonnumberfluctuations !

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

  9. 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:

  10. 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

  11. Mean, variance, skewness and kurtosisobtained by STAR and rescaled HRG • STAR Au-Au • STAR Au-Au these data, due to transverse momentum cut. Account effectively for the above in the HRG model by rescaling the volume parameter by the factor 1.8/8.5

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

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

  14. 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

  15. 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

  16. 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

  17. HRG energy dependence versus STAR data arXiv:1106.2926 Data presented at QM’11, H.G. Ritter, GSI Colloquium Xiaofeng Luo for the STAR Collaboration Data consitentwithSkellamdistributionHRG showsbroaderdistribution

  18. Observed schrinking of the probability distribution already expected due to deconfinement properties of QCD In the first approximation the quantifies the width of P(N) HRG LGT hotQCD Coll. Similar: Budapest-Wuppertal Coll

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

  20. Centrality dependence of O(4) criticality? Weakdependence of chemcial Freezeout on centrality In thechiral limit decrease of volumereducecriticlity Decrease of chemical potentil J. Engels Decrease of centralityshiftsthe chemical line out of chiral O(4) cross over Influence of volume on criticalityrequiresdetaileknowlege of FiniteSizeScaling Function for free energy in O(4) universalityclass

  21. Centralitydependenceat 62 and 200 GeV Preliminary STAR data H.G. Ritter, GSI Colloquium Published STAR data-efficiency uncorected HRG showsincreasingbroadening of distributionswithcentrality

  22. Centralitydependence of HRG model deviationsfrom data: Thanks to Xu Nu

  23. Criticalityincreaseswithcentrality: seenintheprobabilitydistributions and momentscompared to data

  24. O(4) criticality Hadronic freezout Based on therelationbetween HRG model and presentlyaveliable data we couldconcludethat: schematic diagram • Theseparationbetween chemical freezeoutline and the O(4) chirallinemightappearin HIC atcollisionenergieslargerthan 39 GeV?? O(4) criticality HRG freezeout

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

  26. Conclusions: • Probabilitydistributionsand higher order cumulantsareexcellentprobes of O(4) criticalityin HIC • Hadron resonance gas providesreference for O(4) criticalbehaviorin HIC and LGT results • In the HRG the P(N) isuniquallydetermined by • themeasuremultiplicities of chargedparticles. Thisavoidsambiguityindeterminingfreezeoutparameters and volume of the system • Deviationof P(N) form HRG setsinat and increaseswithcentrality: • Thismightindicatedremnantsof O(4) criticality • in STAR data on net proton probabilitydistribution • in central Au-Au collisionsat

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