Kurtosis and compressibility near the chiral phase transition

TL;DR

This paper investigates how net quark number fluctuations, specifically kurtosis and compressibility, behave near the QCD chiral phase transition, highlighting their dependence on pion mass and comparing effective model results with lattice QCD data.

Contribution

It provides a detailed analysis of fluctuation observables near the chiral transition using an effective chiral model, emphasizing pion mass effects and coupling to the Polyakov loop.

Findings

Kurtosis peaks and inverse compressibility dips at pseudocritical temperature for physical pion mass.

These features diminish as pion mass increases.

Results align qualitatively with recent lattice QCD findings.

Abstract

The properties of net quark number fluctuations in the vicinity of the QCD chiral phase transition are discussed in terms of an effective chiral model in the mean-field approximation. We focus on the ratio of the fourth- to second- order cumulants (kurtosis) and the compressibility of the system and discuss their dependence on the pion mass. It is shown that near the chiral phase transition, both observables are sensitive to the value of $m_\pi$. For physical $m_\pi$, the kurtosis exhibits a peak whereas the inverse compressibility shows a dip at the pseudocritical temperature. These structures disappear for large $m_\pi$. Our results, obtained in an effective model with two flavors, are qualitatively consistent with recent results of 2+1 flavor lattice gauge theory. We also discuss the high- and low-temperature properties of these observables and the role of the coupling of the quark degrees of freedom to the Polyakov loop.