Inverse magnetic catalysis effect and current quark mass effect on mass spectra and Mott transitions of pions under external magnetic field

TL;DR

This study investigates how external magnetic fields and current quark mass influence pion mass spectra and Mott transitions using a two-flavor NJL model, highlighting the inverse magnetic catalysis effect and quark mass variations.

Contribution

It introduces a magnetic-dependent coupling constant to model inverse magnetic catalysis and analyzes its impact on pion Mott transition temperatures and mass spectra.

Findings

Mott transition temperatures decrease with magnetic field when IMC is considered.

Charged pions show oscillatory Mott transition temperature behavior in weak magnetic fields.

Current quark mass significantly affects the monotonicity and magnitude of Mott transition temperatures.

Abstract

Mass spectra and Mott transition of pions $(\pi^0,\ \pi^\pm)$ at finite temperature and magnetic field are investigated in a two-flavor NJL model, and we focus on the inverse magnetic catalysis (IMC) effect and current quark mass (CQM) effect. Due to the dimension reduction of the constituent quarks, the pion masses jump at their Mott transitions, which is independent of the IMC effect and CQM effect. We consider the IMC effect by using a magnetic dependent coupling constant, which is a monotonic decreasing function of magnetic field. With IMC effect, the Mott transition temperature of $\pi^0$ meson $T_m^0$ is a monotonic decreasing function of magnetic field. For charged pions $\pi^{\pm}$, the Mott transition temperature $T_m^+$ fast increases in weak magnetic field region and then decreases with magnetic field, which are accompanied with some oscillations. Comparing with the case without IMC effect, $T_m^0$ and $T_m^+$ are lower when including IMC effect. CQM effect are considered by varying parameter $m_0$ in non-chiral limit. For $\pi^0$ meson, $T_m^0$ is not a monotonic function of magnetic field with low $m_0$, but it is a monotonic decreasing function with larger $m_0$. In the weak magnetic field region, $T_m^0$ is higher for larger $m_0$, but in the strong magnetic field region, it is lower for larger $m_0$. For $\pi^+$ meson, $T^+_m$ is only quantitatively modifies by current quark mass effect, and it becomes higher with larger $m_0$.