If neutrino tribimaximal mixing is explained by a non-Abelian discrete symmetry such as A 4 , T 7 , ∆(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, where H 0 is a standard-model-like Higgs boson and ψ 0 2 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.

We construct a neutrino mass matrix M ν via a seesaw mechanism with perturbed invariant under a cyclic permutation by introducing one parameter δ into the diagonal elements of M ν with assumption that trace of the perturbed M ν is equal to trace of the unperturbed M ν . We found that the perturbed neutrino mass matrices M ν can predicts the mass-squared difference ∆m 2 ij = 0 with the possible hierarchy of neutrino mass is normal or inverted hierarchy. By using the advantages of the masssquared differences and mixing parameters data from neutrino oscillation experiments, we then have neutrino masses in inverted hierarchy with masses: |m 1 | = 0.101023 eV, |m 2 | = 0.101428 eV, and |m 3 | = 0.084413 eV.

Abstract. We study and formulate the Lagrangian for the LC, RC, RL, and RLC circuits by using the analogy concept with the mechanical problem in classical mechanics formulations. We found that the Lagrangian for the LC and RLC circuits are governed by two terms i. e. kinetic energy-like and potential energy-like terms. The Lagrangian for the RC circuit is only a contribution from the potential energy-like term and the Lagrangian for the RL circuit is only from the kinetic energy-like term.

In order to accommodate nonzero and relatively large of mixing angle θ 13 , we modified the tribimaximal mixing(TBM) matrix by introducing a simple perturbation matrix to perturb TBM matrix. The modified TBM can reproduce nonzero mixing angle θ 13 = 7.9 0 which is in agreement with the present experimental results. By imposing two zeros texture into the obtained neutrino mass matrix from modified TBM, we then have the neutrino mass spectrum in normal hierarchy. Some phenomenological implications are also discussed. *

We evaluate the predictive power of the neutrino mass matrices arising from seesaw mechanism with heavy Majorana mass matrices subject to texture zero and satisfy a cyclic permutation invariant form to the solar neutrino mixing phenomena. From eight possible patterns of heavy Majorana neutrino mass matrix, we found that there is no heavy Majorana neutrino mass matrix to be invariant in form under a cyclic permutation. But, by imposing an additional assumption that at least one of the 2 × 2 sub-matrices of heavy Majorana neutrino mass matrix inverse having zero determinant, we found that only two of the eight possible patterns for heavy Majorana neutrino mass matrices to be invariant under a cyclic permutation. One of the two invariant heavy Majorana neutrino mass matrices could produces neutrino mass matrix M ν that can be used to explain the neutrino mixing phenomena for both solar and atmospheric neutrinos qualitatively.