$\Delta$ self-energy at finite temperature and density and the $\pi N$ cross-section

TL;DR

This paper calculates the $$-baryon self-energy at finite temperature and density, analyzing its impact on the $$-nucleon scattering cross-section and related transport properties in a hot, dense medium.

Contribution

It provides a detailed evaluation of the $$ self-energy using thermal field theory and explores medium modifications of the $$-nucleon cross-section with implications for transport coefficients.

Findings

Significant suppression of the $$-nucleon cross-section peak at high temperature and density.

Medium modifications lead to changes in nucleon relaxation times.

Temperature dependence of shear viscosity is affected by medium effects.

Abstract

The self energy of $\Delta$-baryon is evaluated at finite temperature and density using the real time formalism of thermal field theory. The Dyson-Schwinger equation is used to get the exact thermal propagator followed by the spectral function of $\Delta$. The $\pi N$ scattering cross section obtained using explicit $\Delta$ exchange is normalized to the experimental data in vacuum and its medium modification is implemented by means of the exact thermal propagator. A significant suppression of the peak of the cross-section is observed at higher temperature and baryon density. Effects on the mean relaxation time of nucleons and the temperature dependence of the shear viscosity of a pion nucleon gas are demonstrated.