A natural extension of the standard SU(2)LβΓU(1)Yβ gauge
model to accommodate massive neutrinos is to introduce one Higgs triplet and
three right-handed Majorana neutrinos, leading to a 6Γ6 neutrino mass
matrix which contains three 3Γ3 sub-matrices MLβ, MDβ
and MRβ. We show that three light Majorana neutrinos (i.e., the mass
eigenstates of Ξ½eβ, Ξ½ΞΌβ and Ξ½Οβ) are exactly massless in this
model, if and only if MLβ=MDβMRβ1βMDTβ
exactly holds. This no-go theorem implies that small but non-vanishing neutrino
masses may result from a significant but incomplete cancellation between
MLβ and MDβMRβ1βMDTβ terms in the Type-II
seesaw formula, provided three right-handed Majorana neutrinos are of O(1) TeV and experimentally detectable at the LHC. We propose three simple
Type-II seesaw scenarios with the A4βΓU(1)Xβ flavor symmetry to
interpret the observed neutrino mass spectrum and neutrino mixing pattern. Such
a TeV-scale neutrino model can be tested in two complementary ways: (1)
searching for possible collider signatures of lepton number violation induced
by the right-handed Majorana neutrinos and doubly-charged Higgs particles; and
(2) searching for possible consequences of unitarity violation of the 3Γ3 neutrino mixing matrix in the future long-baseline neutrino oscillation
experiments.Comment: RevTeX 19 pages, no figure