Electric conductivity of hot pion matter

TL;DR

This paper calculates the electric conductivity of hot pion matter using the electromagnetic spectral function within the Vector Dominance Model, addressing discrepancies in previous theoretical estimates.

Contribution

It introduces a novel calculation of the electric conductivity by incorporating the $ ho$ meson's self-energy with thermal loops and vertex corrections, improving the understanding of transport properties in hot hadronic matter.

Findings

The spectral function's low-energy peak varies with temperature.

The calculated conductivity differs from previous models, highlighting model dependencies.

Results provide insights into electromagnetic responses of hot pion matter.

Abstract

The determination of transport coefficients plays a central role in characterizing hot and dense nuclear matter. Currently, there are significant discrepancies between various calculations of the electric conductivity of hot hadronic matter. In the present work we calculate the electric conductivity of hot pion matter by extracting it from the electromagnetic spectral function, via its zero energy limit at vanishing 3-momentum, within the Vector Dominance Model (VDM). Since within the VDM the photon couples to the hadronic currents primarily through the $\rho$ meson, we use hadronic many-body theory to calculate the $\rho$-meson's self-energy in hot pion matter, by dressing its pion cloud with thermal $\pi$-$\rho$ and $\pi$-$\sigma$ loops including vertex corrections to maintain gauge invariance. In particular, we analyze the low-energy transport peak of the spectral function, extract its behavior with temperature and compare to (the results of) existing approaches in the literature.