Dispersion relations at finite temperature and density for nucleons and pions

TL;DR

This paper derives the dispersion relations for nucleons and pions at finite temperature and density using an effective chiral theory, providing insights into their behavior in environments like neutron stars.

Contribution

It presents the first calculation of nucleonic and pionic dispersion relations at finite T and chemical potential within a chiral effective theory framework, including effective mass evaluations.

Findings

Dispersion relations are obtained at leading order in temperature and chemical potential.

Effective masses of quasi-nucleons and quasi-pions are evaluated in thermal and dense conditions.

Results are relevant for understanding matter in neutron stars.

Abstract

We calculate the nucleonic and pionic dispersion relations at finite temperature T and non-vanishing chemical potentials $(\mu_f)$ in the context of an effective chiral theory that describes the strong and electromagnetic interactions for nucleons and pions. The dispersion relations are calculated in the broken chiral symmetry phase, where the nucleons are massive and pions are taken as massless. The calculation is performed at lowest order in the energy expansion, working in the framework of the real time formalism of thermal field theory in the Feynman gauge. These one-loop dispersion relations are obtained at leading order with respect to T and $\mu_f$. We also evaluate the effective masses of the quasi-nucleon and quasi-pion excitations in thermal and chemical conditions as the ones of a neutron star.