Self-consistent thermodynamic potential for magnetized QCD matter

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.

References in corpus (7)

• Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals
• Pion Condensation by Rotation in a Magnetic field
• Recent progresses on QCD phases in a strong magnetic field -- views from Nambu--Jona-Lasinio model
• Chiral condensates and screening masses of neutral pseudoscalar mesons in thermomagnetic QCD medium
• Rotation induced charged pion condensation in a strong magnetic field: A Nambu--Jona-Lasino model study
• Diamagnetic and Paramagnetic Phases in Low-Energy Quantum Chromodynamics
• Thermomagnetic Properties of QCD