<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>eff</mml:mi></mml:mrow></mml:msub></mml:math> in the Standard Model at NLO is 3.043
Mattia Cielo, Miguel Escudero, G. Mangano, O. Pisanti
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 ${N}_{\mathrm{eff}}$ in the Standard Model is of pivotal importance. In this work, we consider the last ingredient needed to accurately calculate ${N}_{\mathrm{eff}}^{\mathrm{SM}}$: standard zero and finite-temperature QED corrections to ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\leftrightarrow}\ensuremath{\nu}\overline{\ensuremath{\nu}}$ interaction rates during neutrino decoupling at temperatures around $T\ensuremath{\sim}\mathrm{MeV}$. We find that this effect leads to a reduction of $\ensuremath{-}0.0007$ in ${N}_{\mathrm{eff}}^{\mathrm{SM}}$. This next-to-leading-order 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 ${N}_{\mathrm{eff}}^{\mathrm{SM}}=3.043$ with a theoretical uncertainty that is much smaller than any projected observational sensitivity.