Finite-temperature corrections to the effective potential of neutrinos in a medium.

Abstract

We consider a neutrino of any flavor propagating through a thermal background of charged leptons, nucleons, and neutrinos. The neutrino self-energy is calculated in a general gauge up to terms of order ${\mathit{g}}^{2}$/${\mathit{m}}_{\mathit{W}}^{4}$, and it is shown that, although the self-energy depends on the gauge parameter, the dispersion relation is independent of it. On the basis of this result it is argued that the neutrino effective potential must be defined from the dispersion relation and not directly from the self-energy. Explicit formulas for the effective potential are given.