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Neff in the Standard Model at NLO is 3.043
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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.
Forward citations
Cited by 10 Pith papers
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$\nu\bar\nu$ production, annihilation, and scattering at MeV temperatures and NLO accuracy
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Singlet-Doublet fermion origin of dark matter, neutrino mass and inverse first-order electroweak phase transition
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Sensitivity of Next-Generation CMB Surveys to Neutrinos and Other Light Relics
CMB-S4 forecasts: the two-site design reaches sigma(Neff)=0.029 in seven years, the Chile-only revised design reaches 0.030 in nine, and a cosmic-variance-limited survey would reach 0.0073.
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Primordial Black Hole from Tensor-induced Density Fluctuation: First-order Phase Transitions and Domain Walls
Tensor perturbations from FOPT and domain-wall sources are claimed to induce second-order scalar perturbations large enough to form primordial black holes, potentially all of the dark matter.
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Beyond thermal approximations: Precise cosmological bounds on Axion-Like Particles
Solving the momentum-dependent Boltzmann equation and propagating the exact non-thermal ALP spectrum into CMB analyses yields 95% limits f_a>1.63e6 GeV (e), 9.41e6 GeV (mu), 8.06e4 GeV (tau), and g_a_gamma<1.98e-8 GeV^-1.
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The Cosmic Neutrino Background is within Reach of Future Neutrino Telescopes
Including deep-inelastic scattering makes cosmic-ray-boosted relic neutrinos bright enough for IceCube to bound the CνB overdensity to ~100–1000, and future networks could reach the ΛCDM value.
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Neutrino masses from large-scale structures: future sensitivity and theory dependence
Forecasted 1-sigma sensitivity to the sum of neutrino masses is 15 meV for Planck+DESI and 7 meV for CMB-S4+MegaMapper, with the one-loop bispectrum providing 10% and 30% of the constraining power.
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Enlightening dark moments of neutrino with superradiance
Quenched superradiance of dark photon clouds around spinning primordial black holes could turn neutrino electromagnetic moment bounds into observable neutrino fluxes and limits on PBH abundance.
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Cosmologists should compare clustering amplitude with the h-independent statistic sigma_12 instead of sigma_8, because sigma_8's smoothing scale shifts with H0 and artificially worsens the growth tension in high-H0 models.
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ALP production from light primordial black holes: The role of superradiance
Superradiance from spinning light primordial black holes can boost moduli production by about ten orders of magnitude, and the resulting axion-like dark radiation tightens Planck-based limits on these black holes.
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