Probing lepton flavor triality with Higgs boson decay

Abstract

If neutrino tribimaximal mixing is explained by a non-Abelian discrete symmetry such as ${A}_{4}$, ${T}_{7}$, $\ensuremath{\Delta}(27)$, etc., the charged-lepton Higgs sector has a ${Z}_{3}$ residual symmetry (lepton flavor triality), which may be observed directly in the decay chain ${H}^{0}\ensuremath{\rightarrow}{\ensuremath{\psi}}_{2}^{0}{\overline{\ensuremath{\psi}}}_{2}^{0}$, then ${\ensuremath{\psi}}_{2}^{0}({\overline{\ensuremath{\psi}}}_{2}^{0})\ensuremath{\rightarrow}{l}_{i}^{+}{l}_{j}^{\ensuremath{-}}(i\ensuremath{\ne}j)$, where ${H}^{0}$ is a standard-model--like Higgs boson and ${\ensuremath{\psi}}_{2}^{0}$ is a scalar particle needed for realizing the original discrete symmetry. If kinematically allowed, this unusual and easily detectable decay is observable at the LHC with $1\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ for ${E}_{\mathrm{cm}}=7\text{ }\text{ }\mathrm{TeV}$.