Minimalistic Neutrino Mass Model

We consider the simplest model which solves the solar and atmospheric neutrino puzzles, in the sense that it contains the smallest amount of beyond the Standard Model ingredients. The solar neutrino data is accounted for by Planck-mass effects while the atmospheric neutrino anomaly is due to the existence of a single righthanded neutrino at an intermediate mass scale between 109 GeV and 1014 GeV. Even though the neutrino mixing angles are not exactly predicted, they can be naturally large, which agrees well with the current experimental situation. Furthermore, the amount of lepton asymmetry produced in the early universe by the decay of the right-handed neutrino is very predictive and may be enough to explain the current baryon-to-photon ratio if the right-handed neutrinos are produced out of thermal equilibrium. One definitive test for the model is the search for anomalous seasonal effects at Borexino. 1 Neutrino Puzzles and Masses The SuperKamiokande atmospheric neutrino data [1], provide very strong evidence for neutrino conversion, i.e. that neutrinos produced in well defined flavour eigenstates partially convert to different flavour eigenstates at the detection point. A similar conclusion follows from the long standing solar neutrino puzzle [2] and a number of other atmospheric neutrino experiments [3]. Altogether, solar and atmospheric data indicate the need for νe and νμ conversions, respectively. There are a number of neutrino flavour conversion mechanisms [4, 5, 6], and the simplest one is that of neutrino oscillations [7]. Although in some circumstances neutrino oscillations do not imply neutrino masses [8], typically they do. Due to the fact that neutrino mass and flavour eigenstates should, in general, differ, quantum interference effects can lead to sizeable neutrino conversion rates either from large mixing angles or from resonant matter effects. In this scenario, the solar and atmospheric neutrino puzzles are interpreted as strong evidence for nonzero neutrino masses. The present data can be summarised as follows: the atmospheric neutrino puzzle is best solved by νμ → ντ with close to maximal mixing (sin θ ≃ 0.5) and ∆matm ≃ 10−3 − 10−2 (eV) [9]. On the other hand the solar neutrino puzzle requires νe → νx oscillations, where νx is some linear combination of νμ and ντ . While the atmospheric neutrino data indicate large mixing angles, the current solar neutrino data do not indicate a unique solution. The mixing is either very small (sin ω ≃ 10−3) or quite large (0.1 < ∼ sin ω < ∼ 0.5), while the value of ∆m⊙ varies from 10−4 eV to 10−10 eV [9]. The neutrino oscillation interpretation of the solar and atmospheric data only fixes the mass-squared splittings amongst the the neutrinos, not the overall mass scale. In fact, the data are equally well explained if all neutrino masses were almost degenerate at some arbitrarily large value. There are, however, constraints on neutrino masses from tritium beta decay experiments at the level of 3 eV [10], while cosmological considerations impose limits on the sum of all stable neutrino species, namely ∑ im i ν < ∼ 30 eV. There are also a number of results from the non-observation of neutrinoless double beta decay [11], which imply that Mee = ∑ i U 2 eimνi <∼ 0.2 eV where νi, i = 1, 2, 3 are the neutrino mass eigenstates, with masses mνi , and Uei are the components of νe in the νi basis (νe = ∑ i Ueiνi). Barring the possibility of quasi-degenerate neutrinos an/or exotic neutrino conversion