Self-consistent thermodynamic potential for magnetized QCD matter

TL;DR

This paper develops a self-consistent thermodynamic potential for magnetized QCD matter within the NJL model, incorporating vacuum effects, a running coupling, and finite chemical potential to study magnetic properties and phase transitions.

Contribution

It introduces a regularized, self-consistent thermodynamic potential for magnetized QCD matter, including vacuum effects and a running coupling to capture inverse magnetic catalysis.

Findings

Reproduces paramagnetic behavior of QCD matter.

Shows suppression of magnetization at large magnetic fields with running coupling.

Identifies de Haas-van Alphen oscillations at small magnetic fields.

Abstract

Within the two-flavor Nambu--Jona-Lasinio model, we derive a self-consistent thermodynamic potential $\Omega$ for a QCD matter in an external magnetic field $B$. To be consistent with Schwinger's renormalization spirit, counter terms with vacuum quark mass are introduced into $\Omega$ and then the explicit $B$-dependent parts can be regularized in a cutoff-free way. Following that, explicit expressions of gap equation and magnetization can be consistently obtained according to the standard thermodynamic relations. The formalism is able to reproduce the paramagnetic feature of a QCD matter without ambiguity. For more realistic study, a running coupling constant is also adopted to account for the inverse magnetic catalysis effect. It turns out that the running coupling would greatly suppress magnetization at large $B$ and is important to reproduce the temperature enhancement effect to magnetization. The case with finite baryon chemical potential is also explored: no sign of first-order transition is found by varying $B$ for the running coupling and the de Haas-van Alphen oscillation shows up in the small $B$ region.