Generalised CP and Trimaximal TM1_1 Lepton Mixing in S4S_4 Family Symmetry

We construct two flavor models based on $S_4$ family symmetry and generalised CP symmetry. In both models, the $S_4$ family symmetry is broken down to the $Z^{SU}_2$ subgroup in the neutrino sector, as a consequence, the trimaximal $\text{TM}_1$ lepton mixing is produced. Depending on the free parameters in the flavon potential, the Dirac CP is predicted to be either conserved or maximally broken, and the Majorana CP phases are trivial. The two models differ in the neutrino sector. The flavon fields are involved in the Dirac mass terms at leading order in the first model, and the neutrino mass matrix contains three real parameters such that the absolute neutrino masses are fixed. Nevertheless, the flavon fields enter into the Majorana mass terms at leading order in the second model. The leading order lepton mixing is of the tri-bimaximal form which is broken down to $\text{TM}_1$ by the next to leading order contributions.Comment: 28 page

Nucleon-antinucleon Interaction from the Modified Skyrme Model

We calculate the static nucleon-antinucleon interaction potential from the modified Skyrme model with additional $B^{\mu}B_{\mu}$ term using the product ansatz. The static properties of single baryon are improved in the modified Skyrme model. State mixing is taken into account by perturbation theory, which substantially increases the strength of the central attraction. We obtain a long and mid range potential which is in qualitative agreement with some phenomenological potentials.Comment: 21 pages, 7 figur

Generalised CP and Δ(96)\Delta (96) Family Symmetry

We perform a comprehensive study of the $\Delta (96)$ family symmetry combined with the generalised CP symmetry $H_{\rm{CP}}$. We investigate the lepton mixing parameters which can be obtained from the original symmetry $\Delta (96)\rtimes H_{\rm{CP}}$ breaking to different remnant symmetries in the neutrino and charged lepton sectors, namely $G_{\nu}$ and $G_l$ subgroups in the neutrino and the charged lepton sector respectively, and the remnant CP symmetries from the breaking of $H_{\rm{CP}}$ are $H^{\nu}_{\rm{CP}}$ and $H^{l}_{\rm{CP}}$, respectively, where all cases correspond to a preserved symmetry smaller than the full Klein symmetry, as in the semi-direct approach, leading to predictions which depend on a single undetermined real parameter, which may be fitted to the reactor angle for example. We discuss 26 possible cases, including a global $\chi^2$ determination of the best fit parameters and the correlations between mixing parameters, in each case.Comment: 71 pages, 10 figure

Deviation from Bimaximal Mixing and Leptonic CP Phases in S4S_4 Family Symmetry and Generalized CP

The lepton flavor mixing matrix having one row or one column in common with the bimaximal mixing up to permutations is still compatible with the present neutrino oscillation data. We provide a thorough exploration of generating such a mixing matrix from $S_4$ family symmetry and generalized CP symmetry $H_{CP}$. Supposing that $S_4\rtimes H_{CP}$ is broken down to $Z^{ST^2SU}_2\times H^{\nu}_{CP}$ in the neutrino sector and $Z^{TST^{2}U}_4\rtimes H^{l}_{CP}$ in the charged lepton sector, one column of the PMNS matrix would be of the form $\left(1/2, 1/\sqrt{2}, 1/2\right)^{T}$ up to permutations, both Dirac CP phase and Majorana CP phases are trivial in order to accommodate the observed lepton mixing angles. The phenomenological implications of the remnant symmetry $K^{(TST^2, T^2U)}_4\rtimes H^{\nu}_{CP}$ in the neutrino sector and $Z^{SU}_{2}\times H^{l}_{CP}$ in the charged lepton sector are studied. One row of PMNS matrix is determined to be $\left(1/2, 1/2, -i/\sqrt{2}\right)$, and all the three leptonic CP phases can only be trivial to fit the measured values of the mixing angles. Two models based on $S_4$ family symmetry and generalized CP are constructed to implement these model independent predictions enforced by remnant symmetry. The correct mass hierarchy among the charged leptons is achieved. The vacuum alignment and higher order corrections are discussed.Comment: 44 pages, 7 figure