Net baryon number probability distribution near the chiral phase transition

TL;DR

This paper investigates how the net baryon number probability distribution changes near the chiral phase transition, highlighting the influence of critical fluctuations and different universality classes on the distribution's shape.

Contribution

It introduces a Landau theory-based analysis parametrized to reproduce various scaling behaviors, revealing how critical exponents affect the distribution structure.

Findings

In the mean-field and Z(2) classes, the distribution broadens due to singular thermodynamic contributions.

In the O(4) class, the distribution becomes narrower with a wide tail.

Critical fluctuations significantly alter the probability distribution near the phase transition.

Abstract

We discuss properties of the net baryon number probability distribution near the chiral phase transition to explore the effect of critical fluctuations. Our studies are performed within Landau theory, where the coefficients of the polynomial potential are parametrized, so as to reproduce the mean-field (MF), the $Z(2)$ and $O(4)$ scaling behaviors of the cumulants of the net baryon number. We show, that in the critical region, the structure of the probability distribution changes, dependently on values of the critical exponents. In the MF approach, as well as in the $Z(2)$ universality class, the contribution of the singular part of the thermodynamic potential tends to broaden the distribution. By contrast, in the model with $O(4)$ scaling, the contribution of the singular part results in a narrower net baryon number probability distribution with a wide tail.