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

TL;DR

This paper calculates neutrino interaction rates at next-to-leading order in a QED plasma, improving the precision of early universe neutrino decoupling models and providing tools for more accurate cosmological predictions.

Contribution

It introduces a method to define and compute double-differential neutrino rates at NLO, including tabulated data and interpolation routines for use in kinetic equations.

Findings

NLO corrections to energy transfer rates are small.

Finite electron mass effects are quantified at leading order.

Provided data enables more precise modeling of neutrino decoupling.

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 $N_{\rm eff}\,$.