Criticality of the net-baryon number probability distribution at finite density

Krzysztof Redlich,Bengt Friman,Kenji Morita

doi:10.1016/j.physletb.2014.12.037

Abstract

We compute the probability distribution P(N) of the net-baryon number at finite temperature and quark-chemical potential, μ, at a physical value of the pion mass in the quark-meson model within the functional renormalization group scheme. For μ/T<1, the model exhibits the chiral crossover transition which belongs to the universality class of the O(4) spin system in three dimensions. We explore the influence of the chiral crossover transition on the properties of the net baryon number probability distribution, P(N). By considering ratios of P(N) to the Skellam function, with the same mean and variance, we unravel the characteristic features of the distribution that are related to O(4) criticality at the chiral crossover transition. We explore the corresponding ratios for data obtained at RHIC by the STAR Collaboration and discuss their implications. We also examine O(4) criticality in the context of binomial and negative-binomial distributions for the net proton number.

Highlights

Fluctuations of conserved charges are promising observables for exploring critical phenomena in relativistic heavy ion collisions [1,2,3,4]
We show that the ratio of the net baryon probability distribution to the corresponding Skellam function reveals the critical narrowing of the probability distribution, which is characteristic for the O (4) scaling
We have discussed the properties of the net-baryon number probability distribution P (N) near the chiral crossover transition at vanishing and at finite baryon chemical potential

Summary

Introduction

Fluctuations of conserved charges are promising observables for exploring critical phenomena in relativistic heavy ion collisions [1,2,3,4]. We have argued, that at vanishing chemical potential, the residual O (4) critical fluctuation at physical pion mass leads to narrowing of the probability distribution relative to the Skellam function This corresponds to a negative structure of the sixth order cumulant at the chiral crossover transition [24]. We extend our previous studies to non-zero chemical potential and propose a method for identifying the characteristic properties of the net baryon probability distribution, which are responsible for the critical behavior of the cumulants at the chiral transition We apply this method to the net proton probability Au–Au distributions collisions at o√btsaNinNe≥d by 19 the STAR GeV. We show that the (suitably rescaled) ratio of the net baryon probability distribution to the corresponding Skellam function reveals the critical narrowing of the probability distribution, which is characteristic for the O (4) scaling

The net-baryon number probability distribution

Concluding remarks