Chiral transition with magnetic fields

TL;DR

This paper investigates how external magnetic fields influence the chiral phase transition in an effective field theory, revealing that magnetic fields raise the critical temperature for symmetry restoration and addressing boson mass instabilities at high temperatures.

Contribution

It introduces a method to compute magnetic and thermal corrections up to ring order in high-temperature regimes, analyzing the transition's dependence on magnetic field strength and other parameters.

Findings

Critical temperature increases with magnetic field strength.

Magnetic fields always raise the chiral symmetry restoration temperature.

Resummation of ring diagrams stabilizes boson masses at high temperature.

Abstract

We study the nature of the chiral transition for an effective theory with spontaneous breaking of symmetry, where charged bosons and fermions are subject to the effects of a constant external magnetic field. The problem is studied in terms of the relative intensity of the magnetic field with respect to the mass and the temperature. When the former is the smallest of the scales, we present a suitable method to obtain magnetic and thermal corrections up to ring order at high temperature. By these means, we solve the problem of the instability in the boson sector for these theories, where the squared masses, taken as functions of the order parameter, can vanish and even become negative. The solution is found by considering the screening properties of the plasma, encoded in the resummation of the ring diagrams at high temperature. We also study the case where the magnetic field is the intermediate of the three scales and explore the nature of the chiral transition as we vary the field strength, the coupling constants and the number of fermions. We show that the critical temperature for the restoration of chiral symmetry monotonically increases from small to intermediate values of the magnetic fields and that this temperature is always above the critical temperature for the case when the magnetic field is absent.