Radiative corrections to neutrino energy loss rate in stellar interiors

We consider radiative electromagnetic corrections, at order \alpha, to the process $e^+ e^- \to \nu \bar{\nu}$ at finite density and temperature. This process represents one of the main contributions to the cooling of stellar environments in the late stages of star evolution. We find that these corrections affect the energy loss rate by a factor $(-4 \div 1) %$ with respect to the tree level estimate, in the temperature and density ranges where the neutrino pair production via e^+ e^- annihilation is the most efficient cooling mechanism.