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Critical Fluctuation s in the Polyakov L oop -Quark-Meson model and HIC

Critical Fluctuation s in the Polyakov L oop -Quark-Meson model and HIC. Role of q uantum and t hermal fluctuations near chiral phase transition Functional Renormalization Group (FRG) in PQM model FRG in P QM model at work:

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Critical Fluctuation s in the Polyakov L oop -Quark-Meson model and HIC

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  1. Critical Fluctuations in the Polyakov Loop -Quark-Meson model and HIC Role of quantum and thermal fluctuations near chiral phasetransition Functional Renormalization Group (FRG) in PQM model FRG in PQM model at work: O(4) scaling of an order parameter and itssusceptibilities Fluctuations of net quark number density beyond MF Work done with: B. Friman, K. Morita, E. Nakano&V. Skokov Net Quarknumberfluctuationsin HIC experiment STAR Coll. RHIC data and theirinterpreations Work done with: FrithjofKarsch Krzysztof Redlich, University of Wroclaw & CERN

  2. Effective QCD-like models K. Fukushima, C. Ratti & W. Weise, B. Friman & C. Sasaki , ., ..... B.-J. Schaefer, J.M. Pawlowski & J. Wambach; B. Friman et al. Polyakov loop

  3. Phase diagram in chiral models with CP at any spinodal points: spinodals CP Singularity at CEP are the remnant of that along the spinodals spinodals C. Sasaki, B. Friman & K.R., Phys.Rev.Lett.99:232301,2007.

  4. Including quantum fluctuations: FRG approach k-dependent full propagator start at classical action and include quantum fluctuations successively by lowering k FRG flow equation (C. Wetterich 93) J. Berges, D. Litim, B. Friman, J. Pawlowski, B. J. Schafer, J. Wambach, …. Regulator function suppresses particle propagation with momentum Lower than k

  5. Renormalization Group equations in PQM model Flow equation for the thermodynamic potential density in the PQM model with Quarks Coupled to the Background Gluonic Fields • Quark densities modify by the background gluon fields • The FRG flow equation has to be solved together with • Put and => B.-J. Schaefer, JWambach. WambachWambach

  6. Removing cut-off dependence in FRG • Matching of flow equations • We integrate the flow equation bellow from • and switch at to discussed • previously

  7. FRG at work –O(4) scaling: • Near critical properties obtained from the singular part of the free energy density external field • Phase transition encoded in the “equation of state” • Resulting in the well known scaling behavior of coexistence line pseudo-critical point

  8. FRG-Scaling of an order parameter in QM model • The order parameter shows scaling. From the one slope one gets • However we have neglected field-dependent wave function renormal. Consequently and . The 3% difference can be • attributed to truncation of the Taylor expansion at 3th order when solving FRG flow equation: • see D. Litim analysis for O(4) field Lagrangian

  9. Effective critical exponents • Approaching from the side of the symmetric phase, t >0, with small but finite h : from Widom-Griffiths form of the equation of state • For and , thus Define:

  10. Fluctuations & susceptibilities • Two type of susceptibility related with order parameter 1. longitudinal 2. transverse • Scaling properties • at t=0 and

  11. Extracting delta from chiral susceptibilities • Within the scaling region and at t=0 the ratio is independent on h FRG in QM model consitent with expected O(4) scaling

  12. The order parameter in PQM model in FRG approach Mean Field dynamics FRG results • For a physical pion mass, model has crossover transition • Essential modification due to coupling to Polyakov loop • The quantum fluctuations makes transition smother PQM PQM QM <L> <L> QM

  13. Fluctuations of an order parameter Mean Field dynamics FRG results • Deconfinement and chiral transition approximately same • Within FRG broadening of fluctuations and their strength: essential modifications compare with MF

  14. Net quark number density fluctuations FRG results • Coupling to Polykov loops suppresses fluctuations in broken phase • Large influence of quantum fluctuations. • Probes of chiral trans. FRG-results QM PQM QM MF-results PQM

  15. 4th order quark number density fluctuations FRG results MF results • Peak structure might appear due to chiral dynamics. In GL-theory FRG results QM PQM model PQM PQM model QM model QM model Kink-like structure Dicontinuity

  16. Kurtosis as excellent probe of deconfinement S. Ejiri, F. Karsch & K.R. Phs. Lett. Phys. Lett. B633 (2006) 275 • HRG factorization of pressure: consequently: in HRG • In QGP, • Kurtosis=Ratio of cumulants excellent probe of deconfinement Kurtosis F. Karsch, Ch. Schmidt Observed quark mass dependence of kurtosis, remnant of chiral O(4) dynamics?

  17. Kurtosis of net quark number density in PQM model V. Skokov, B. Friman &K.R. FRG results MF results • Strong dependence on pion mass, remnant of O(4) dynamics!? • Smooth change with a rather weak dependen- ce on the pion mass

  18. The Phase Diagram Function Renormalization Group Mean-field approximation The shaded regions are defined by 5% deviation of temperature derivative of the chiral condensate from its maximal value. The dashed curves denote the isentropes. The solid lines are the lines of the fixed μ/T, along which thermodynamic properties is to be considered. ● Mesonic fluctuations shifts CEP to higher temperatures ● The transition is smoother ● No focusing of isentropes (see detailed analysis in E. Nakano et al, 2009 )

  19. Finite chemical potential: the second-order cumulant c2 Mean-field approximation Function Renormalization Group ● The shrinkage of the critical region in FRG calculations (before indicated by B.-J. Schaefer and J. Wambach). In the MF vacuum fluctuations are found to be Important: E. Nakano, B.-J. Schaefer, B. Stokicc, B. Frimanc, & K. R.

  20. Finite chemical potential: the fourth-order cumulant c4 Mean-field approximation Function Renormalization Group

  21. Finite chemical potential: the third-order cumulant c3 Function Renormalization Group Group Mean-field approximation Strong fluctuations in third order cumulant and its negative values in the critical region are modified due to quantum fluctuations.

  22. FRG: Finite chemical potential: cumulants ratios Deviations of theratios of odd and even order cummulantsfromtheirassymptotic, lowT-value, areincreasingwith and thecumulat order Propertiesessentialin HIC to discriminatethephasechange by measuringbaryonnumberfluctuations !

  23. STAR DATA ON MOMENTS of FLUCTUATIONS Phys. Rev. Lett. 105, 022302 (2010) • Mean • Variance • Skewness • Kurtosis

  24. Is there memory that system have passed through a region of QCD phase transition ? • Particle yields and their ratio, as well as LGT results for well described by the Hadron Resonance Gas Partition Function . Is that the case with moments of fluctuations? A. Andronic, P. Braun-Munzinger & J. Stachel Acta Phys.Polon.B40:1005-1012,2009. A. Andronic et al., Nucl.Phys.A837:65-86,2010.

  25. Properties of fluctuationsin HRG Calculate generalized susceptibilities: from Hadron Resonance Gas (HRG) partition function: then, and resulting in: Compare this HRG model predictions with STAR data at RHIC:

  26. 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 Can we also quantify the energy dependence of each moment separately using thermal parameters along the chemical freezeout curve?

  27. 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

  28. LGT and phenomenological HRG model C. Allton et al., S. Ejiri, F. Karsch & K.R. • Smooth change of and peak in at expected from O(4) universality argument and HRG • For fluctuations as expected in the Hadron Resonance Gas

  29. Conclusions • The FRG method is very efficient to include quantum and thermal fluctuations in thermodynamic potential in QM and PQM models • The FRG provide correct scaling of physical obesrvables expected in the O(4) universality class • The quantum fluctuations modified the mean field results leading to smearing of the chiral cross over transition • The RHIC data on the first four moments of net- proton fluctuations consitent with expectations from HRG: particle indeed produced from thermal source • To observe large fluctuations related with O(4) cross-over, mesure higher order fluctuations, N>6

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