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Article
Report number	arXiv:2306.05460 ; CERN-TH-2023-103
Title	$N_{\mathrm{eff}}$ in the Standard Model at NLO is 3.043
Related title	Neff in the Standard Model at NLO is 3.043
Author(s)	Cielo, Mattia (INFN, Naples ; Naples U.) ; Escudero, Miguel (CERN) ; Mangano, Gianpiero (INFN, Naples ; Naples U.) ; Pisanti, Ofelia (INFN, Naples ; Naples U.)
Publication	2023-12-13
Imprint	2023-06-08
Number of pages	6
Note	4 pages, 2 figures. v2: Added a paragraph discussing electroweak corrections and other processes at O(alpha). v3: matches published version. References added, typos fixed
In:	Phys. Rev. D 108 (2023) L121301
DOI	10.1103/PhysRevD.108.L121301 (publication)
Subject category	astro-ph.CO ; Astrophysics and Astronomy ; hep-ph ; Particle Physics - Phenomenology
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.
Copyright/License	preprint: (License: arXiv nonexclusive-distrib 1.0) publication: © 2023-2024 authors (License: CC BY 4.0), sponsored by SCOAP³

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