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Charge fluctuations in heavy ion collisions and QCD phase diagram K. Redlich, Uni Wroclaw & EMMI

Charge fluctuations in heavy ion collisions and QCD phase diagram K. Redlich, Uni Wroclaw & EMMI. 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) criticality in QCD

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Charge fluctuations in heavy ion collisions and QCD phase diagram K. Redlich, Uni Wroclaw & EMMI

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  1. Charge fluctuations in heavy ion collisions and QCD phase diagram K. Redlich, Uni Wroclaw & EMMI • QCD phaseboundary, its O(4) „scaling” & relation to freezeoutin HIC • Moments and probablilitydistributions of conservedcharges as probes of the O(4) criticalityin QCD • XuNu -STAR data & expectations HIC crossover CP orTriple Point Qarkyonic Matter with: P. Braun-Munzinger, B. Friman F. Karsch, V. Skokov

  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 . O(4) universality A. Andronic et al., Nucl.Phys.A837:65-86,2010. HRG model Thermal and chemical equilibrium: H. Barz, B. Friman, J Knoll & H.Schultz P. Braun-Munzinger, J. Stachel, Ch. Wetterich C. Greiner & J. Noronha-Hostler, ……..

  3. 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

  4. 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

  5. Effective chiral models and their non-perturbative thermodynamics: 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 the SU(2)xSU(2) invariant quark interactions described through: K. Fukushima;C. Ratti & W. Weise; B. Friman , C. Sasaki ., …. B.-J. Schaefer, J.M. Pawlowski & J. Wambach; B. Friman, V. Skokov, ... B. Friman, V. Skokov, B. Stokic & K.R.

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

  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. 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

  9. Ratio of higher order cumulants Deviations of theratiosfromtheirasymptotic, lowT-value, areincreasingwiththe order of thecumulant Propertiesessentialin HIC to discriminatethephasechange by measuringbaryonnumberfluctuations !

  10. Fluctuations of 6th and 8th order momentsexhibitstrongvariationsfrom HRG predictions: Theirnegativevalues near chiraltransition to be seenin heavy ioncollisionsat LHC & RHIC Range of deviationsfrom HRG Therange of negativefluctuations near chiralcross-over: PNJL model resultswith quantum fluctuationsbeingincluded : Thesepropertiesaredue to O(4) scaling , thusshould be alsotherein QCD.

  11. Theoreticalpredictions 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!!??

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

  13. 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

  14. Comparing HRG Model withPreliminary STAR data: efficiencyuncorrected Data presented at QM’11 Data described by Skellam distribution: No sign for criticality

  15. 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 At the critical point (CP) the width of P(N) should be largerthanexpected in the HRG due to divergence of in 3d Ising model universalityclass

  16. Conclusions: • Probabilitydistributions and higher order cumulantsareexcellentprobes of O(4) criticalityin HIC • Hadron resonance gas providesreference for O(4) criticalbehaviorin HIC and LGT results • Observeddeviations of the from the HRG • value as expectedat the O(4) pseudo-criticalline • Deviation of P(N) from HRG seems to • set in at

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