Soft modes in hot QCD matter

TL;DR

This paper investigates the critical behavior of the QCD phase transition at finite temperature, showing that the physical point is far from the critical region and that soft modes dominate the physics even beyond criticality.

Contribution

It quantifies the size of the critical region in QCD using functional methods and provides a parametrisation of the order parameter potential for practical use.

Findings

The physical point is far from the critical region.

Soft modes dominate the physics beyond the critical region.

The order parameter potential can be parametrized for phenomenology.

Abstract

The chiral crossover of QCD at finite temperature and vanishing baryon density turns into a second order phase transition if lighter than physical quark masses are considered. If this transition occurs sufficiently close to the physical point, its universal critical behaviour would largely control the physics of the QCD phase transition. We quantify the size of this region in QCD using functional approaches, both Dyson-Schwinger equations and the functional renormalisation group. The latter allows us to study both critical and non-critical effects on equal footing, facilitating a precise determination of the scaling regime. We find that the physical point is far away from the critical region. Importantly, we show that the physics of the chiral crossover is dominated by soft modes even far beyond the critical region. While scaling functions determine all thermodynamic properties of the system in the critical region, the order parameter potential is the relevant quantity away from it. We compute this potential in QCD using the functional renormalisation group and Dyson-Schwinger equations and provide a simple parametrisation for phenomenological applications.