Towards a precision calculation of Neff in the Standard Model 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 Neff 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 NeffSM 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 NeffSM = 3.0440 ± 0.0002. We therefore conclude that aforementioned number remains to be the state-of-the-art benchmark for NeffSM in the standard model of particle physics.