A Compromise between Neutrino Masses and Collider Signatures in the Type-II Seesaw Model

Abstract

A natural extension of the standard $SU(2{)}_{\mathrm{L}}\times U(1{)}_{\mathrm{Y}}$ gauge model to accommodate massive neutrinos is to introduce one Higgs triplet and three right-handed Majorana neutrinos, leading to a $6\times 6$ neutrino mass matrix which contains three $3\times 3$ sub-matrices $M_{\mathrm{L}}$, $M_{\mathrm{D}}$ and $M_{\mathrm{R}}$. We show that three light Majorana neutrinos (i.e., the mass eigenstates of ${\nu }_e$, ${\nu }_{\mu }$ and ${\nu }_{\tau }$) are exactly massless in this model, if and only if $M_{\mathrm{L}}=M_{\mathrm{D}}{M}_{\mathrm{R}}^{-1}{M}_{\mathrm{D}}^T$ exactly holds. This no-go theorem implies that small but non-vanishing neutrino masses may result from a significant but incomplete cancellation between $M_{\mathrm{L}}$ and $M_{\mathrm{D}}{M}_{\mathrm{R}}^{-1}{M}_{\mathrm{D}}^T$ terms in the Type-II seesaw formula, provided three right-handed Majorana neutrinos are of $\mathcal{O}(1)$ TeV and experimentally detectable at the LHC. We propose three simple Type-II seesaw scenarios with the $A_4\times U(1{)}_{\mathrm{X}}$ 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 $3\times 3$ neutrino mixing matrix in the future long-baseline neutrino oscillation experiments.

RevTeX 19 pages, no figures

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