Double Threefold Degeneracies for Active and Sterile Neutrinos

We explore the possibility that the 3 active (doublet) neutrinos have nearly degenerate masses which are split only by the usual seesaw mechanism from 3 sterile (singlet) neutrinos in the presence of a softly broken A4 symmetry. We take the unconventional view that the sterile neutrinos may be light, i.e. less than 1 keV, and discuss some very interesting and novel phenomenology, including a connection between the LSND neutrino data and solar neutrino oscillations. Present experimental data [1, 2, 3] indicate that neutrinos oscillate. Hence they should have small nonzero masses and mix with one another. On the other hand, since neutrino oscillations only measure the difference of mass squares, the possibility that all 3 active neutrinos are nearly degenerate in mass should not be overlooked [4]. There are two canonical ways of making mν nonzero. One is through the small vacuum expectation value (VEV) of a Higgs triplet [5, 6]. The other is through the addition of 3 heavy singlet neutral fermions (usually considered as right-handed neutrinos NR). In that case, a Dirac mass mD linking the left-handed doublet neutrinos νL with NR as well as a Majorana mass M for NR are allowed. Combining the two mechanisms, the following mass matrix MνN = 