$\nu\bar\nu$ production, annihilation, and scattering at MeV temperatures and NLO accuracy

Abstract

Interaction rates of neutrinos and antineutrinos within a QED plasma determine the dynamics of their decoupling in the early universe. We show how to define the relevant double-differential production, annihilation, and scattering rates at NLO. Integrating over these rates with specific weights, other quantities from the literature can be obtained, such as energy transfer rates, or a neutrino interaction rate. In the limit of massless electrons, we show that NLO corrections to the energy transfer rates are as small as those that enter the previously determined neutrino interaction rate, and only have a small influence on the neutrino decoupling parameter, $N_{\rm eff}\,$. For comparison, the influence of a finite electron mass is quantified at LO. Finally we provide a tabulation and fast interpolation routine for all double-differential rates, in order to allow for their use in non-approximate kinetic equations, which may further reduce the systematic uncertainties of the Standard Model prediction for $N_{\rm eff}\,$.