Kinetics of the chiral phase transition in a quark-meson $\sigma$ model

TL;DR

This paper investigates the dynamics of the chiral phase transition in a quark-meson model using a self-consistent kinetic theory approach, focusing on fluctuation build-up and dissipation during fireball evolution.

Contribution

It introduces a novel kinetic framework combining the 2PI formalism with a linear-$\sigma$ model to study out-of-equilibrium fluctuations in chiral phase transitions.

Findings

A transient increase in net-baryon number fluctuations occurs during evolution.

Dissipative effects from collisions counteract fluctuation build-up.

The fluctuation dynamics depend on the fireball's expansion speed.

Abstract

Using the two-particle irreducible (2PI) $\Phi$-functional formalism for self-consistent approximations of a linear-$\sigma$ model for quarks and mesons in and out of equilibrium, the build-up of fluctuations of net-baryon number during the time evolution of an expanding fireball is studied within a kinetic theory for the order parameter ($\sigma$ field) and quark distribution functions. Initializing the system with purely Gaussian fluctuations a fourth-order cumulant is temporarily built up due to the evolution of the $\sigma$-field. This is counterbalanced, however, by the dissipative evolution due to collisions between quarks, anti-quarks, mesons, and the mean field, depending on the speed of the fireball expansion.