Inverse magnetic catalysis and confinement within a contact interaction model for quarks

TL;DR

This paper investigates how external magnetic fields influence chiral symmetry breaking and confinement-deconfinement transitions in quark matter using a contact interaction model, revealing phenomena like magnetic catalysis and inverse magnetic catalysis.

Contribution

It introduces a contact interaction model that includes an explicit confining scale and studies the effects of magnetic fields on transition temperatures, aligning with lattice and effective model predictions.

Findings

Magnetic catalysis observed with increasing transition temperatures under strong magnetic fields.

Inverse magnetic catalysis occurs when a decreasing coupling with magnetic field is considered.

Model results agree with lattice QCD and effective models predictions.

Abstract

We evaluate the impact of an external magnetic field on the chiral symmetry and confinement-deconfinement transition temperatures by using a vector-vector contact interaction model for quarks regularized so as to include an explicit confining scale in the corresponding gap equation. Exploring the evolution of the chiral condensate and the confining scale with temperature $T$ and magnetic field strength $eB$ ($e$ represents the fundamental electric charge), we determine the pseudo-critical temperatures for the chiral ($T_c^\chi$) and deconfinement ($T_c^c$) transitions from their inflection points, respectively. By construction, $T_c^\chi= T_c^c$ in the chiral limit. Within a mean field approximation, we observe the magnetic catalysis phenomenon, characterized by a rising behavior of $T_c^\chi$ and $T_c^c$ with growing $eB$. Considering a lattice inspired running coupling which monotonically decreases with $eB$, inverse magnetic catalysis takes place in our model. We explore the role of the magnetic field in the traits of the confinement-deconfinement transition described by the model. Our findings are also in agreement with predictions derived from effective models of strong interactions.