Towards a precision calculation of $N_{\rm eff}$ in the Standard Model II: Neutrino decoupling in the presence of flavour oscillations and finite-temperature QED

TL;DR

This paper provides a highly precise calculation of the effective number of neutrinos in the Standard Model, incorporating neutrino oscillations, finite-temperature QED effects, and detailed collision integrals, with a thorough uncertainty analysis.

Contribution

It introduces a new, highly accurate benchmark value for N_eff in the Standard Model, including comprehensive physical effects and uncertainty assessments.

Findings

N_eff^SM = 3.0440 ± 0.0002

Uncertainty mainly from numerical methods and measurement errors

Refined understanding of neutrino energy density in cosmology

Abstract

We present in this work a new calculation of the standard-model benchmark value for the effective number of neutrinos, $N_{\rm eff}^{\rm SM}$, that quantifies the cosmological neutrino-to-photon energy densities. The calculation takes into account neutrino flavour oscillations, finite-temperature effects in the quantum electrodynamics plasma to ${\cal O}(e^3)$, where $e$ is the elementary electric charge, and a full evaluation of the neutrino--neutrino collision integral. We provide furthermore a detailed assessment of the uncertainties in the benchmark $N_{\rm eff}^{\rm SM}$ value, through testing the value's dependence on (i)~optional approximate modelling of the weak collision integrals, (ii)~measurement errors in the physical parameters of the weak sector, and (iii)~numerical convergence, particularly in relation to momentum discretisation. Our new, recommended standard-model benchmark is $N_{\rm eff}^{\rm SM} = 3.0440 \pm 0.0002$, where the nominal uncertainty is attributed predominantly to errors incurred in the numerical solution procedure ($|\delta N_{\rm eff}| \sim10^{-4}$), augmented by measurement errors in the solar mixing angle $\sin^2\theta_{12}$ ($|\delta N_{\rm eff}| \sim10^{-4}$).