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

Abstract

We present in this work a new calculation of the standard-model benchmark value for the effective number of neutrinos, $N_{\mathrm{eff}}^{\mathrm{SM}}$, 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 $\mathcal{O}(e^3)$, 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 $N_{\mathrm{eff}}^{\mathrm{SM}}$ 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 $N_{\mathrm{eff}}^{\mathrm{SM}}=3.0440\pm 0.0002$, where the nominal uncertainty is attributed predominantly to errors incurred in the numerical solution procedure ($|\delta N_{\mathrm{eff}}|\sim 10^{-4}$), augmented by measurement errors in the solar mixing angle ${\sin }^2{\theta }_{12}$ ($|\delta N_{\mathrm{eff}}|\sim 10^{-4}$).

31 pages, 7 figures. Version accepted for publication in JCAP

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