Three neutrinoΔm2scales and the singular seesaw mechanism

Abstract

It is shown that the singular seesaw mechanism can simultaneously explain all the existing data supporting nonzero neutrino masses and mixing. The three mass-squared differences that are needed to accommodate the atmospheric neutrino data (through νµ −νs oscillation), the solar neutrino data via MSW mechanism (through νe − ντ oscillation), and the positive result of νµ − νe oscillation from LSND can be generated by this mechanism, whereas the vacuum oscillation solution to the solar neutrino problem is disfavored. We find that the electron and tau neutrino masses are of order 10 −3 eV, and the muon neutrino and a sterile neutrino are almost maximally mixed to give a mass of order 1 eV. Two heavy sterile neutrinos have a mass of order 1 keV which can be obtained by the double seesaw mechanism with an intermediate mass scale ∼ 10 5 GeV. A possible origin of such a scale is discussed.

A 4-neutrino model with a Higgs triplet

“…This model, described in Section 3, is completely analoguous to the model of Ref. [14] which invokes the singular see-saw mechanism. However, in this case the heavy scale of the see-saw mechanism is quite low of the order of keV.…”

“…[14], which were also noticed in Ref. [16], are that one still has to resort to fine-tuning in order to specify the large active -sterile neutrino mixing to large ν µ -ν s mixing and also to get the correct small ν e -ν µ mixing as required by the result of the LSND experiment [10].…”

“…In particular, it seems difficult to reconcile the mass spectra (2) and the large mixing observed in atmospheric neutrino oscillations with the original see-saw mechanism [12]. However, models have been proposed exploiting the "singular see-saw mechanism" [13] which naturally achieve a large active -sterile neutrino mixing [14,15,16]. Since a large mixing angle ν e → ν s transition as a solution of the solar neutrino puzzle is not compatible with the solar neutrino data [17], the "singular see-saw mechanism" offers the possibility to explain the atmospheric neutrino anomaly by ν µ → ν s oscillations.…”

“…Nevertheless, we will see that one can arrive at a scenario equivalent to the one obtained in Ref. [14]. The possible scalar multiplets extending the Standard Model are simply obtained by studying the representations of SU(2)×U(1) contained in all the fermionic bilinears which can be formed.…”

“…With the two scales v and v T we will show that at this stage we have a model equivalent to the one described in Ref. [14]. Finally, we will introduce a discrete symmetry to achieve maximal ν µ -ν s mixing, to some extent without fine-tuning.…”