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Register a new userA precision calculation of relic neutrino decoupling
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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.
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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 $sin^2theta_{12}$ ($|delta N_{rm eff}| sim10^{-4}$).
We reconsider the problem of the birefringence of electromagnetic (EM) waves in a medium consisting of a plasma and a $ ubar{ u}$-gas within the Standard Model of particle physics. The considered effect arises in such a medium due to the parity violation for the electroweak neutrino-electron interaction. Our recent calculations of the electroweak correction to the photon polarization operator in the electroweak plasma allow us to significantly improve some previous estimates of such effect in astrophysics. We estimate the rotary power for EM waves propagating in a non-relativistic plasma in the intergalactic space and interacting with the gas of relic neutrinos and antineutrinos there. We show that, in presence of a plasma, the EM wave birefringence effect in a $ ubar{ u}$-gas exceeds significantly that effect in a $ ubar{ u}$-gas in empty space considered earlier. These previous treatments of the birefringence relied on the calculations of the refraction index for on-shell photons in vacuum using the forward scattering amplitude $gamma uto gamma u$ with virtual charged leptons in Feynman diagrams. The possibility to observe experimentally the new effect suggested here is discussed.
The cosmic background neutrino of temperature 1.9 K affects rates of radiative emission of neutrino pair (RENP) from metastable excited atoms, since its presence blocks the pair emission by the Pauli exclusion principle. We quantitatively investigate how the Pauli blocking distorts the photon energy spectrum and calculate its sensitivity to cosmic parameters such as the neutrino temperature and its chemical potential. Important quantities for high sensitivities to these parameter measurement are found to be the level spacing of atomic de-excitation and the unknown mass value of lightest neutrino, in particular their mutual relation.
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.
For the small-angle Bhabha-scattering process, we consider the error budget for the calculation of the LEP/SLC luminosity in the Monte Carlo event generator BHLUMI 4.04, from the standpoint of new calculations of exact results for the respective O(alpha**2) photonic corrections in the context of the Yennie-Frautchi-Suura exponentiation. We find that an over-all precision tag for the currently available program BHLUMI 4.04 can be reduced from 0.11% to 0.061% at LEP1 and from 0.25% to 0.122% at LEP2. For the large-angle Bhabha process, we present the Monte Carlo program BHWIDE and compare its predictions with predictions of other Monte Carlo programs as well as semi-analytical calculations.
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