Compromise between neutrino masses and collider signatures in the type-II seesaw model

Abstract

A natural extension of the standard $\mathrm{SU}(2{)}_{\mathrm{L}}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1{)}_{\mathrm{Y}}$ gauge model to accommodate massive neutrinos is to introduce one Higgs triplet and three right-handed Majorana neutrinos, leading to a $6\ifmmode\times\else\texttimes\fi{}6$ neutrino mass matrix which contains three $3\ifmmode\times\else\texttimes\fi{}3$ submatrices, ${M}_{\mathrm{L}}$, ${M}_{\mathrm{D}}$ and ${M}_{\mathrm{R}}$. We show that three light Majorana neutrinos (i.e., the mass eigenstates of ${\ensuremath{\nu}}_{e}$, ${\ensuremath{\nu}}_{\ensuremath{\mu}}$, and ${\ensuremath{\nu}}_{\ensuremath{\tau}}$) are exactly massless in this model, if and only if ${M}_{\mathrm{L}}={M}_{\mathrm{D}}{M}_{\mathrm{R}}^{\ensuremath{-}1}{M}_{\mathrm{D}}^{T}$ exactly holds. This no-go theorem implies that small but nonvanishing neutrino masses may result from a significant but incomplete cancellation between ${M}_{\mathrm{L}}$ and ${M}_{\mathrm{D}}{M}_{\mathrm{R}}^{\ensuremath{-}1}{M}_{\mathrm{D}}^{T}$ terms in the Type-II seesaw formula, provided three right-handed Majorana neutrinos are of $\mathcal{O}(1)\text{ }\text{ }\mathrm{TeV}$ and experimentally detectable at the LHC. We propose three simple Type-II seesaw scenarios with the ${A}_{4}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1{)}_{\mathrm{X}}$ flavor symmetry and its explicit breaking 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 $3\ifmmode\times\else\texttimes\fi{}3$ neutrino mixing matrix in the future long-baseline neutrino oscillation experiments.