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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 $α$, to the process $e^+ e^- -> ν\barν$ 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.