Mass modification of hot pions in magnetized dense medium

TL;DR

This paper investigates how strong magnetic fields affect the mass of hot pions in dense nuclear matter, revealing that charged pion masses increase with magnetic field strength and oscillate with temperature, with implications for pion condensation.

Contribution

It provides a detailed calculation of pion mass modifications in a magnetized medium using thermal field theory, including the effects of Landau quantization and vacuum contributions.

Findings

Charged pion mass increases with magnetic field at fixed temperature and chemical potential.

Charged pion mass remains constant across temperature and chemical potential for a given Landau level.

Large magnetic fields are required for neutral pion condensation.

Abstract

A phenomenological pion-nucleon interaction is used to obtain pionic mass modification in presence of constant homogeneous magnetic field background at finite temperature and chemical potential in the real time formalism of thermal field theory. The magnetically modified propagator in its complete form is used to obtain the one loop self-energy for pions. For charged pions we find that the effective mass increases with the magnetic field at given temperature and chemical potential. Since the transverse momentum of charged pion is quantized and its contribution to Dyson-Schwinger Equation is large compared to the loop correction, the charged pion mass remains constant with both temperature and chemical potential for a given landau level. In order to unveil the role of the real part of the self-energy, we also calculate the effective mass neglecting the trivial shift. The effective mass for charged pions shows an oscillatory behavior which is attributed to the thermal contribution of the self-energy. It is argued that the magnetic field dependent vacuum contribution to the self-energy influences the behavior of the effective mass both qualitatively and quantitatively. We also find that very large field is necessary for neutral pions to condense.