Phase diagram in an external magnetic field beyond a mean-field approximation

TL;DR

This paper investigates the phase diagram of a chiral quark-meson model in a magnetic field beyond mean-field, revealing limitations in current models and implications for the existence of a critical end point.

Contribution

It provides a nonperturbative analysis of the phase structure including meson fluctuations and discusses the impact of magnetic fields on the phase transition, challenging previous model predictions.

Findings

Including meson fluctuations does not resolve discrepancies with lattice results.

The crossover line curvature increases with magnetic field.

A chiral critical end point is excluded at zero baryon chemical potential in large Nc limit.

Abstract

The phase structure of the Polyakov loop-extended chiral quark-meson model is explored in a nonperturbative approach, beyond a mean-field approximation, in the presence of a magnetic field. We show that by including meson fluctuations one cannot resolve the qualitative discrepancy on the dependence of the crossover transition temperature in a non-zero magnetic field between effective model predictions and recent lattice results (arXiv:1111.4956).We compute the curvature of the crossover line in the T - {\mu}_B plane at a non-zero magnetic field and show that the curvature increases with increasing magnetic field. On the basis of QCD inequalities, we also argue that, at least in the large Nc limit, a chiral critical end point and, consequently, a change from crossover to a first-order chiral phase transition are excluded at zero baryon chemical potential and non-zero magnetic field.