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Register a new userTowards a precision calculation of $N_{rm eff}$ in the Standard Model II: Neutrino decoupling in the presence of flavour oscillations and finite-temperature QED
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We present in this work a new calculation of the standard-model benchmark value for the effective number of neutrinos, $N_{rm eff}^{rm SM}$, 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 ${cal O}(e^3)$, 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 $N_{rm eff}^{rm SM}$ value, through testing the values 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 $N_{rm eff}^{rm SM} = 3.0440 pm 0.0002$, where the nominal uncertainty is attributed predominantly to errors incurred in the numerical solution procedure ($|delta N_{rm eff}| sim10^{-4}$), augmented by measurement errors in the solar mixing angle $sin^2theta_{12}$ ($|delta N_{rm eff}| sim10^{-4}$).
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We discuss Dirac neutrinos whose right-handed component $ u_R$ has new interactions that may lead to a measurable contribution to the effective number of relativistic neutrino species $N_{rm eff}$. We aim at a model-independent and comprehensive study on a variety of possibilities. Processes for $ u_R$-genesis from decay or scattering of thermal species, with spin-0, spin-1/2, or spin-1 initial or final states are all covered. We calculate numerically and analytically the contribution of $ u_R$ to $N_{rm eff}$ primarily in the freeze-in regime, since the freeze-out regime has been studied before. While our approximate analytical results apply only to freeze-in, our numerical calculations work for freeze-out as well, including the transition between the two regimes. Using current and future constraints on $N_{rm eff}$, we obtain limits and sensitivities of CMB experiments on masses and couplings of the new interactions. As a by-product, we obtain the contribution of Higgs-neutrino interactions, $Delta N_{rm eff}^{rm SM} approx 7.5times10^{-12}$, assuming the neutrino mass is 0.1 eV and generated by the standard Higgs mechanism.
If neutrinos are Dirac particles the existence of light right-handed neutrinos $ u_{R}$ is implied. Those would contribute to the effective number of relativistic neutrino species $N_{{rm eff}}$ in the early Universe. With pure standard model interactions, the contribution is negligibly small. In the presence of new interactions, however, the contribution could be significantly enhanced. We consider the most general effective four-fermion interactions for neutrinos (scalar, pseudo-scalar, vector, axial-vector and tensor), and compute the contribution of right-handed neutrinos to $N_{{rm eff}}$. Taking the Planck 2018 measurement of $N_{{rm eff}}$, strong constraints on the effective four-fermion coupling are obtained, corresponding to interaction strengths of $10^{-5}sim10^{-3}$ in units of the Fermi constant. This translates in new physics scales of up to 43 TeV and higher. Future experiments such as CMB-S4 can probe or exclude the existence of effective 4-neutrino operators for Dirac neutrinos. Ways to avoid this conclusion are discussed.
We study the distortions of equilibrium spectra of relic neutrinos due to the interactions with electrons, positrons, and neutrinos in the early Universe. We solve the integro-differential kinetic equations for the neutrino density matrix, including three-flavor oscillations and finite temperature corrections from QED up to the next-to-leading order $mathcal{O}(e^3)$ for the first time. In addition, the equivalent kinetic equations in the mass basis of neutrinos are directly solved, and we numerically evaluate the distortions of the neutrino spectra in the mass basis as well, which can be easily extrapolated into those for non-relativistic neutrinos in the current Universe. In both bases, we find the same value of the effective number of neutrinos, $N_{rm eff} = 3.044$, which parameterizes the total neutrino energy density. The estimated error for the value of $N_{rm eff}$ due to the numerical calculations and the choice of neutrino mixing parameters would be at most 0.0005.
We evaluate the contribution to $N_{rm eff}$ of the extra sterile states in low-scale Type I seesaw models (with three extra sterile states). We explore the full parameter space and find that at least two of the heavy states always reach thermalisation in the Early Universe, while the third one might not thermalise provided the lightest neutrino mass is below ${mathcal O}(10^{-3}$eV). Constraints from cosmology therefore severely restrict the spectra of heavy states in the range 1eV- 100 MeV. The implications for neutrinoless double beta decay are also discussed.
We revisit the decoupling of neutrinos in the early universe with flavour oscillations. We rederive the quantum kinetic equations which determine the neutrino evolution based on a BBGKY-like hierarchy, and include for the first time the full collision term, with both on- and off-diagonal terms for all relevant reactions. We focus on the case of zero chemical potential and solve these equations numerically. We also develop an approximate scheme based on the adiabatic evolution in the matter basis. In fact, the large difference between the oscillations and cosmological time scales allows to consider averaged flavour oscillations which can speed up the numerical integration by two orders of magnitude, when combined with a direct computation of the differential system Jacobian. The approximate numerical scheme is also useful to gain more insight into the physics of neutrino decoupling. Including the most recent results on plasma thermodynamics QED corrections, we update the effective number of neutrinos to $N_{mathrm{eff}} = 3.0440$. Finally we study the impact of flavour oscillations during neutrino decoupling on the subsequent primordial nucleosynthesis.
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