Pions in magnetic field at finite temperature

TL;DR

This paper investigates the behavior of pions in an external magnetic field at finite temperature using a regularized Nambu--Jona-Lasinio model, deriving meson propagators and analyzing mass transitions at the Mott point.

Contribution

It provides analytical derivations of meson propagators in magnetic fields and numerical calculations of pion masses, highlighting mass jumps at the Mott transition.

Findings

Neutral pions exhibit one mass jump at the Mott transition.

Charged pions exhibit three mass jumps at the Mott transition.

Pion masses are affected by magnetic field and temperature, showing discrete energy level effects.

Abstract

Pions in external magnetic field are investigated in the frame of a Pauli-Villars regularized Nambu--Jona-Lasinio model. The meson propagators in terms of quark bubbles in Ritus and Schwinger schemes are analytically derived, and pion masses are numerically calculated in the Ritus scheme. For neutral and charged pions at finite temperature, there exist respectively one and three mass jumps at the corresponding Mott transition points, due to the discrete energy levels of the two constituent quarks in magnetic field.