Chiral phase transition in relativistic heavy-ion collisions with weak magnetic fields: ring diagrams in the linear sigma model

TL;DR

This paper investigates how weak magnetic fields influence the chiral phase transition in relativistic heavy-ion collisions using the linear sigma model, highlighting the role of ring diagrams and their impact on the transition.

Contribution

It introduces a detailed calculation of the finite-temperature effective potential including ring diagrams and magnetic field effects within the linear sigma model framework.

Findings

Ring diagrams can prevent the phase transition in certain parameter regions.

Weak magnetic fields have a small but increasingly significant effect at low temperatures.

The study provides insights into the interplay between magnetic fields and chiral symmetry restoration.

Abstract

Working in the linear sigma model with quarks, we compute the finite-temperature effective potential in the presence of a weak magnetic field, including the contribution of the pion ring diagrams and considering the sigma as a classical field. In the approximation where the pion self-energy is computed perturbatively, we show that there is a region of the parameter space where the effect of the ring diagrams is to preclude the phase transition from happening. Inclusion of the magnetic field has small effects that however become more important as the system evolves to the lowest temperatures allowed in the analysis.