Probing Lepton Flavor Triality with Higgs Boson Decay

If neutrino tribimaximal mixing is explained by a non-Abelian discrete symmetry such as $A_4$, $T_7$, $\Delta(27)$, etc., the charged-lepton Higgs sector has a $Z_3$ residual symmetry (lepton flavor triality), which may be observed directly in the decay chain $H^0 \to \psi_2^0 \bar\psi_2^0$, then $\psi_2^0 (\bar\psi_2^0) \to l_i^+ l_j^- ~(i \neq j)$, where $H^0$ is a standard-model-like Higgs boson and $\psi_2^0$ 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 fb$^{-1}$ for E_{cm} = 7 TeV.