Light Unstable Sterile Neutrino

The three massless active (doublet) neutrinos may mix with two heavy and one light sterile (singlet) neutrinos so that the induced masses and mixings among the former are able to explain the present data on atmospheric and solar neutrino oscillations. If the LSND result is also to be explained, one active neutrino mass eigenstate must mix with the light sterile neutrino. A specific model is proposed with the spontaneous and soft explicit breaking of a new global U(1)S symmetry so that a sterile neutrino will decay into an active antineutrino and a nearly massless pseudo-Majoron. Present experimental data [1, 2, 3] indicate that neutrinos oscillate. Hence they should have small nonzero masses and mix with one another. This may be achieved without additional fermions beyond those of the minimal standard model by a heavy Higgs triplet [4, 5]. On the other hand, most theoretical approaches assume the addition of 3 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, thus yielding the famous mass matrix MνN =   0 mD mD M   . (1) At this point, one may impose the conservation of lepton number as an additive global symmetry, i.e. U(1)L, so that M = 0; but then mD would have to be extremely small, which is considered rather unnatural. The conventional solution of this problem is to not consider U(1)L at all so that M is naturally very large and since mD cannot be larger than the electroweak breaking scale v = (2 √ 2GF ) −1/2 = 174 GeV, a small mass mν = mD/M is obtained [6]. This of course requires M to be many orders of magnitude greater than v and renders it totally undetectable experimentally. Recently, it has been pointed out [7] that if mD comes from a different Higgs doublet with a suppressed vacuum expectation value (VEV), then M may in fact be only a few TeV or less and become observable at future colliders. In this note we consider the case where both mD and M are small for one (call it S) of the three singlets, but mD is still less than M by perhaps an order of magnitude. This is in contrast to the pseudo-Dirac scenario [8], i.e. M << mD, in which case neutrino oscillations would be maximal between active and sterile species, in disfavor with the most recent data [1, 2]. Before discussing the theoretical reasons for mD and M to be small, consider first the phenomenology of such a possibility. The 3 active neutrinos νe, νμ, ντ are now each a linear combination of 4 light neutrino mass eigenstates. With mD less than M by an order of