Towards a precision calculation of N eff in the Standard Model. Part III. Improved estimate of NLO contributions to the collision integral

We compute the dominant QED correction to the neutrino-electron interaction rate in the vicinity of neutrino decoupling in the early universe, and estimate its impact on the effective number of neutrino species N eff in cosmic microwave background anisotropy observations. We find that the correction to the interaction rate is at the sub-percent level, consistent with a recent estimate by Jackson and Laine. Relative to that work we include the electron mass in our computations, but restrict our analysis to the enhanced t -channel contributions. The fractional change in N eff SM due to the rate correction is of order 10 -5 or below, i.e., about a factor of 30 smaller than that recently claimed by Cielo et al., and below the nominal computational uncertainties of the current benchmark value of N eff SM = 3.0440 ± 0.0002. We therefore conclude that aforementioned number remains to be the state-of-the-art benchmark for N eff SM in the standard model of particle physics.