A complete solution to neutrino mixing

Abstract

Deviations from expectations have been claimed for solar, atmospheric and high energy prompt neutrinos from charm decay. This information, supplemented only by the existing very good upper limits for oscillations of the $\nu_{\mu}$ at accelerator energies, is used as input to a phenomenological three-flavour analysis of neutrino mixing. The solution found is unique and completely determines the mass eigenstates as well as the mixing matrix relating mass and flavour eigenstates. Assuming the mass eigenstates to follow the hierarchy $m_{1} \ll m_{2} \ll m_{3}$, their values are found to be $m_{1} \ll 10^{-2}$ eV, $m_{2} = (0.18 \pm 0.06)$ eV, $m_{3} = (19.4 \pm 0.7)$ eV. These masses are in agreement with the leptonic quadratic hierarchy of the see-saw model and large enough to render energy-independent any oscillation-induced phenomenon in solar neutrino physics observable on Earth. This possibility is not excluded by the present knowledge of solar neutrino physics. The mixing angles are determined to be $\theta_{12} = 0.55 \pm 0.08$, $\theta_{13} = 0.38 \pm 0.06$, $\theta_{23} < 0.03$. Small values of $\theta_{23}$ are typical of any solution in which $m_{3}$ lies in the cosmological interesting region. The solution found is not in serious contradiction with any of the present limits to the existence of neutrino oscillations. The most relevant implications in particle physics, astrophysics and cosmology are discussed.Comment: 17 pages, 3 figures, to be published in Astroparticle Physic

Neutrino mixing from neutrino oscillation data

“…In first case, the average survival probability of solar ν e 's is constant (this is disfavoured by the data of solar neutrino experiments [20,21]) and the parameters |U e3 | 2 , |U µ3 | 2 satisfy inequalities |U e3 | 2 ≤ a 0 e and |U µ3 | 2 ≤ a 0 µ (that are not compatible with the LSND result, as we have discussed above).…”

Neutrino masses and mixings from an anomaly free SMG×U(1)2 model

“…There is also some variation in the solar neutrino fluxes predicted by different solar models and this theoretical uncertainty means that it is also possible to have an 'energy-independent' vacuum oscillation solution to the solar neutrino problem [13]. By 'energy-independent' we mean that ∆m 2 solar is sufficiently large that many oscillation lengths lie between the sun and the earth, and what we observe is the averaged flux suppression which is the same for solar neutrinos of all energies.…”

“…The analysis of [13] examines the possibility of having an energy-independent solution if the true solar model lies somewhere within the range of currently allowed solar models. Taking the energy-independent flux suppression (F ) as a free parameter they find…”

Neutrino oscillation constraints on neutrinoless double-beta decay

“…The large lower bound for the survival probability P sun νe→νe and its practical independence of the neutrino energy are not compatible with the data of the solar neutrino experiments (see Refs. [44,45]). Therefore, from the results of solar and reactor neutrino experiments we can conclude that |U e3 | 2 is small and satisfies the inequality (3.6).…”