Thermo-magnetic properties of the strong coupling in the local Nambu--Jona-Lasinio model

TL;DR

This study investigates how the strong coupling constant and quark mass in the Nambu-Jona-Lasinio model depend on temperature and magnetic field, aligning these findings with lattice QCD results to understand magnetic catalysis phenomena.

Contribution

It introduces a temperature and magnetic field dependent strong coupling and quark mass in the NJL model, matching lattice QCD results and explaining inverse magnetic catalysis.

Findings

G remains constant at zero temperature with increasing magnetic field.

Both G and M decrease at high temperatures with increasing magnetic field.

Pressure behaviors align with lattice QCD, showing negative transverse pressure below transition temperature.

Abstract

We study the thermo-magnetic properties of the strong coupling constant G and quark mass M entering the Nambu-Jona-Lasinio model. For this purpose, we compute the quark condensate and compare it to lattice QCD (LQCD) results to extract the behavior of G and M as functions of the magnetic field strength and temperature. We find that at zero temperature, where the LQCD condensate is found to monotonically increase with the field strength, M also increases whereas G remains approximately constant. However, for temperatures above the chiral/deconfinement phase transitions, where the LQCD condensate is found to monotonically decrease with increasing field, M and G also decrease monotonically. For finite temperatures, below the transition temperature, we find that both G and M initially grow and then decrease with increasing field strength. To study possible consequences of the extracted temperature and magnetic field dependence of G and M, we compute the pressure and compare to LQCD results, finding an excellent qualitative agreement. In particular, we show that the transverse pressure, as a function of the field strength, is always negative for temperatures below the transition temperature whereas it starts off being positive and then becomes negative for temperatures above the transition temperature, also in agreement with LQCD results. We also show that for the longitudinal pressure to agree with LQCD calculations, the system should be described as a diamagnet. We argue that the turnover of M and G as functions of temperature and field strength is a key element that drives the behavior of the quark condensate going across the transition temperature and provides clues for a better understanding of the inverse magnetic catalysis phenomenon.