Neutrino dispersion relations at finite temperature and density in the Left-Right Symmetric Model

TL;DR

This paper derives a comprehensive formula for left-handed neutrino thermal masses at finite temperature and density within the Left-Right Symmetric Model, considering various symmetry phases and medium conditions.

Contribution

It introduces a novel general expression for neutrino effective thermal mass incorporating lepton and boson masses, chemical potential, and temperature, applied to different symmetry phases.

Findings

Calculated neutrino dispersion relations in different symmetry phases.

Obtained effective thermal masses depending on medium parameters.

Provided a general formula applicable to finite temperature and density environments.

Abstract

In this work we calculate the most general left-handed neutrino thermal self-energy at one-loop order in perturbation theory using the Mellin summation technique. We perform this calculation in the real-time formalism of quantum field theory at finite temperature and density assuming that there exists an excess of leptons over antileptons in the medium. Thus, we obtain a novel general expression for the left-handed neutrino effective thermal mass which depends on lepton masses, boson masses, leptonic chemical potential and temperature. As an application of these results into the context of the Left-Right Symmetric Model, we calculate the left-handed neutrino dispersion relations and we obtain the corresponding effective thermal masses for the unbroken, parity-broken and fully-broken symmetry phases.