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

TL;DR

This paper develops a numerical effective theory for quark-meson systems to study the dynamics of the chiral phase transition, revealing how fluctuations evolve near the critical point and are affected by expansion and dissipation.

Contribution

It introduces a 2PI effective-action formalism for out-of-equilibrium quark-meson systems, capturing fluctuation dynamics during the chiral phase transition.

Findings

Fluctuations of net-baryon number build up near the critical point.

First-order phase transitions show stronger fluctuation signals.

Expansion and dissipation reduce the final fluctuation amplitudes.

Abstract

In this study an effective description in the 2PI effective-action formalism for systems of quarks and mesons in and out of equilibrium within a numerical approach is developed, allowing to approximate the complexity of QCD by taking only the lightest and most relevant degrees of freedom into account. In particular the temporarily building up of fluctuations of the net-baryon number encoded by the fourth-order cumulant (or the rescaled curtosis) for lower momenta is being demonstrated when the phase transition occurs near the critical point, or even stronger when the phase transition is of first order, although the initial system is prepared with purely Gaussian fluctuations in the net baryon number. This is the result of the evolving slow and critical order parameter, i.e., the $\sigma$-field. On the other hand, depending on the speed of the (Hubble-)expansion scale, the final dissipative evolution due to the collisions among the mesons, the quarks and anti-quarks and the order field weakens the final fluctuations considerably.