# Quark Matter 2012

12-18 August 2012
US/Eastern timezone

## Baryon number probability distribution in the presence of the chiral phase transition

16 Aug 2012, 16:00
2h

Poster Correlations and fluctuations

### Speaker

Dr Kenji Morita (Kyoto University)

### Description

We discuss the influence of the chiral phase transition on the properties of the probability distribution of conserved charges based on effective chiral models and on the Landau theory of phase transition [1]. Statistical fluctuations of the net baryon number have been regarded as a diagnostic tool of the chiral phase transition in QCD and in heavy ion collisions. Normally, they are discussed by calculating cumulants of the net baryon number in the grand canonical ensemble. Lattice QCD and effective model calculations have revealed their critical behaviors in the vicinity of the chiral phase transition. The purpose of this work is to characterize the critical behavior in terms of the baryon number probability distribution which is a measurable observable in heavy ion collisions. We show the influence of the chiral crossover transition on the net baryon number probability distribution within the Polyakov loop extended quark-meson model, in a non-perturbative approach, based on the functional renormalization group method [1]. We construct an analytically solvable model which respects relevant symmetries, based on the Landau theory, and discuss properties of the baryon number probability distribution in the presence of the phase transition. We emphasize the relationship of the probability distribution to the analytic structure of the grand canonical partition function in a complex chemical potential [2-4]. We show, through both numerical and analytic considerations, that the singular structure, which gives the divergent cumulants, leads to an interesting anomalous oscillatory behavior in the probability distribution. Our theoretical studies are relevant in heavy ion phenomenology to possibly identify the QCD phase transition and its order by measuring probability distributions of conserved charges. [1] K. Morita, V. Skokov, B. Friman and K. Redlich, to appear. [2] V. Skokov, K. Morita, B. Friman, Phys. Rev. D83, (2011) 071502(R). [3] K. Morita, V. Skokov, B. Friman and K. Redlich, Probing deconfinement in the Polyakov-loop extended Nambu-Jona-Lasinio model at imaginary chemical potential,'' arXiv:1111.3446 [hep-ph]. [4] K. Morita, V. Skokov, B. Friman and K. Redlich, Phys. Rev. D84 (2011) 074020. [5] K. Morita, V. Skokov, B. Friman and K. Redlich, Phys. Rev. D84 (2011) 076009.

### Primary author

Dr Kenji Morita (Kyoto University)

### Co-authors

Prof. Bengt Friman (GSI) Prof. Krzysztof Redlich (University of Wroclaw) Dr Vladimir Skokov (Brookhaven national laboratory)

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