Neutrino energy loss rate in a stellar plasma

We review the purely leptonic neutrino emission processes, contributing to the energy loss rate of the stellar plasma. We perform a complete analysis up to the first order in the electromagnetic coupling constant. In particular the radiative electromagnetic corrections, at order alpha, to the process e(+)e(-) --> v (v) over bar at finite density and temperature have been computed. This process gives one of the main contributions to the cooling of stellar interior in the late stages of star evolution. As a result of the analysis we find that the corrections affect the energy loss rate, computed at tree level, by a factor (-4-1)% in the temperature and density region where the pair annihilation is the most efficient cooling mechanism. (C) 2003 Elsevier Science B.V. All rights reserved.