Net quark number probability distribution near the chiral crossover transition

TL;DR

This paper analyzes how the probability distribution of net quark number is affected by the chiral crossover transition using the quark-meson model, revealing significant deviations from non-critical distributions.

Contribution

It demonstrates the impact of chiral phase transition effects on net quark number distribution, including mesonic fluctuations, within the quark-meson model.

Findings

Distribution narrows near the chiral crossover transition.

Mesonic fluctuations cause significant deviations from mean-field and Skellam distributions.

Volume dependence and scaling properties of cumulants are characterized.

Abstract

We investigate properties of the probability distribution of the net quark number near the chiral crossover transition in the quark-meson model. The calculations are performed within the functional renormalization group approach, as well as in the mean-field approximation. We find, that there is a substantial influence of the underlying chiral phase transition on the properties of the probability distribution. In particular, for a physical pion mass, the distribution which includes the effect of mesonic fluctuations, differs considerably from both, the mean-field and Skellam distributions. The latter is considered as a reference for a non-critical behavior. A characteristic feature of the net quark number probability distribution is that, in the vicinity of the chiral crossover transition in the O(4) universality class, it is narrower than the corresponding mean-field and Skellam function. We study the volume dependence of the probability distribution, as well as the resulting cumulants, and discuss their approximate scaling properties.