Tri-Bimaximal Neutrino Mixing and the T13T_{13} Flavor Symmetry

We present a supersymmetric $T_{13}$ model for the tri-bimaximal neutrino mixing, and the complete flavor group is $T_{13}\times Z_{4}\times Z_2$. At leading order, the residual symmetry of the charged lepton sector is $Z_3$, and the $T_{13}$ symmetry is broken completely in the neutrino sector. The charged lepton mass hierarchies are determined by the spontaneous breaking of the flavor symmetry, both the type I see-saw mechanism and the Weinberg operator contribute to generating the light neutrino masses. Tri-bimaximal mixing is exact at leading order while subleading contributions introduce corrections of order $\lambda^2_c$ to the three lepton mixing angles. The vacuum alignment and subleading corrections are studied in detail, a moderate hierarchy of order $\lambda_c$ between the vacuum expectation values of the flavon fields in the charged lepton and neutrino sectors can be accommodated.Comment: 32 pages, 2 figure

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

Leptogenesis and residual CP symmetry

We discuss flavour dependent leptogenesis in the framework of lepton flavour models based on discrete flavour and CP symmetries applied to the type-I seesaw model. Working in the flavour basis, we analyse the case of two general residual CP symmetries in the neutrino sector, which corresponds to all possible semi-direct models based on a preserved $Z_2$ in the neutrino sector, together with a CP symmetry, which constrains the PMNS matrix up to a single free parameter which may be fixed by the reactor angle. We systematically study and classify this case for all possible residual CP symmetries, and show that the $R$-matrix is tightly constrained up to a single free parameter, with only certain forms being consistent with successful leptogenesis, leading to possible connections between leptogenesis and PMNS parameters. The formalism is completely general in the sense that the two residual CP symmetries could result from any high energy discrete flavour theory which respects any CP symmetry. As a simple example, we apply the formalism to a high energy $S_4$ flavour symmetry with a generalized CP symmetry, broken to two residual CP symmetries in the neutrino sector, recovering familiar results for PMNS predictions, together with new results for flavour dependent leptogenesis.Comment: 35 pages, 8 figure