# Electrical conductivity and Hall conductivity of hot and dense hadron gas in a magnetic field: a relaxation time approach

## TL;DR

This paper calculates the electrical and Hall conductivities of hot, dense hadron gas under magnetic fields using the relaxation time approximation, revealing their dependence on temperature, chemical potential, and magnetic field.

## Contribution

It introduces a detailed analysis of transport coefficients in hadron gas with magnetic fields using the relaxation time approach within the hadron resonance gas model, including energy dependence.

## Key findings

- Electrical conductivity decreases with magnetic field.
- Hall conductivity exhibits non-monotonic behavior with magnetic field.
- Hall conductivity vanishes at zero baryon chemical potential.

## Abstract

We estimate the electrical conductivity and the Hall conductivity of hot and dense hadron gas using the relaxation time approximation of the Boltzmann transport equation in the presence of electromagnetic field. We have investigated the temperature and the baryon chemical potential dependence of these transport coefficients in presence of magnetic field. The explicit calculation is performed within the ambit of the hadron resonance gas model. We find that the electrical conductivity decreases in the presence of magnetic field. The Hall conductivity on the other hand shows a non monotonic behavior with respect to the dependence on magnetic field. We argue that for a pair plasma (particle-anti particle plasma) where $\mu_B=0$, Hall conductivity vanishes. Only for non vanishing baryon chemical potential Hall conductivity has non zero value. We also estimate the electrical conductivity and the Hall conductivity as a function of the center of mass energy along the freeze out curve as may be relevant for relativistic heavy ion collision experiments.