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

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.