Chiral transition in a magnetic field and at finite baryon density

TL;DR

This paper investigates how a magnetic field and finite baryon density influence chiral symmetry breaking and phase transitions in a quark-meson model, revealing the order of transitions varies with magnetic field strength and quantum fluctuations.

Contribution

It provides a detailed analysis of the chiral phase transition in a magnetic field at finite density using a renormalized effective potential, highlighting the role of vacuum fluctuations.

Findings

Weak magnetic fields induce dynamical chiral symmetry breaking.

Vacuum fluctuations change the order of the phase transition.

At strong magnetic fields, the transition is first order without vacuum fluctuations and second order with them.

Abstract

We consider the quark-meson model with two quark flavors in a constant external magnetic field $B$ at finite temperature $T$ and finite baryon chemical potential $\mu_B$. We calculate the full renormalized effective potential to one-loop order in perturbation theory. We study the system in the large-$N_c$ limit, where we treat the bosonic modes at tree level. It is shown that the system exhibits dynamical chiral symmetry breaking, i. e. that an arbitrarily weak magnetic field breaks chiral symmetry dynamically, in agreement with earlier calculations using the NJL model. We study the influence on the phase transition of the fermionic vacuum fluctuations. For strong magnetic fields, $|qB|\sim5m_{\pi}^2$ and in the chiral limit, the transition is first order in the entire $\mu_B-T$ plane if vacuum fluctuations are not included and second order if they are included. At the physical point, the transition is a crossover for $\mu_B=0$ with and without vacuum fluctuations.