Medium effects on the electrical and Hall conductivities of a hot and magnetized pion gas

TL;DR

This study investigates how magnetic fields influence electrical and Hall conductivities in a hot pion gas, revealing temperature and magnetic field-dependent behaviors using kinetic theory and in-medium scattering cross sections.

Contribution

It introduces a detailed calculation of conductivities incorporating in-medium effects on scattering cross sections within a magnetic field for a pion gas.

Findings

Electrical conductivity increases with temperature at high magnetic fields.

Conductivity decreases with magnetic field at fixed temperature.

In-medium cross sections significantly affect conductivity temperature dependence.

Abstract

The electrical and Hall conductivities in a uniform magnetic field are evaluated for an interacting pion gas using the kinetic theory approach within the ambit of relaxation time approximation (RTA). The in-medium cross sections vis-a-vis the relaxation time for $\pi\pi$ scattering are obtained using a one-loop modified thermal propagator for the exchanged $\rho$ and $\sigma$ mesons using thermal field theoretic techniques. For higher values of the magnetic field, a monotonic increase of the electrical conductivity with the temperature is observed. However, for a given temperature the conductivity is found to decrease steadily with magnetic field. The Hall conductivity, at lower values of the magnetic field, is found to decrease with temperature more rapidly than the electrical conductivity, whereas at higher values of the magnetic field, a linear increase is seen. Use of the in-medium scattering cross-section is found to produce a significant effect on the temperature dependence of both electrical and Hall conductivities compared to the case where vacuum cross-section is used.