Neff in the Standard Model at NLO is 3.043

TL;DR

This paper refines the Standard Model prediction of the effective number of neutrino species, $N_{eff}$, by calculating next-to-leading order QED corrections during neutrino decoupling, achieving a highly precise value of 3.043.

Contribution

It provides the first detailed NLO QED correction to $N_{eff}$ in the Standard Model, reducing theoretical uncertainty for cosmological measurements.

Findings

$N_{eff}^{SM}$ = 3.043 with minimal uncertainty

NLO QED corrections decrease $N_{eff}$ by 0.0007

Theoretical predictions now surpass observational sensitivity

Abstract

The effective number of relativistic neutrino species is a fundamental probe of the early Universe and its measurement represents a key constraint on many scenarios beyond the Standard Model of Particle Physics. In light of this, an accurate prediction of $N_{\rm eff}$ in the Standard Model is of pivotal importance. In this work, we consider the last ingredient needed to accurately calculate $N_{\rm eff}^{\rm SM}$: standard zero and finite temperature QED corrections to $e^+e^- \leftrightarrow \nu\bar{\nu}$ interaction rates during neutrino decoupling at temperatures around $T\sim {\rm MeV}$. We find that this effect leads to a reduction of $-0.0007$ in $N_{\rm eff}^{\rm SM}$. This NLO QED correction to the interaction rates, together with finite temperature QED corrections to the electromagnetic density of the plasma, and the effect of neutrino oscillations, implies that $N_{\rm eff}^{\rm SM} = 3.043$ with a theoretical uncertainty that is much smaller than any projected observational sensitivity.