The group Σ(36 × 3) with the generalized CP transformation is introduced to predict the mixing pattern of leptons. Various combinations of abelian residual flavor symmetries with CP transformations are surveyed.Six mixing patterns could accommodate the fit data of neutrinos oscillation at 3σ level. Among them, two patterns predict the nontrivial Dirac CP phase, around ±57 • or ±123 • , which is in accordance with the result of the literature and the recent fit data. Furthermore, one pattern could satisfy the experimental constraints at 1σ level.

The modular group PS L 2 (7) with a generalised CP symmetry is used to predict lepton mixing patterns.The residual symmetries in both charged leptons and and neutrinos sector are supposed to be Z 2 ×CP. Seven types of mixing patterns at the 3σ level of the new recent global fit data are obtained. Among them, three types of patterns can give the Dirac CP phase which is in the 1σ range of the global fit data.

The puma model on the basis of the Lorentz and CPT violation may bring an economical interpretation to the conventional neutrinos oscillation and part of the anomalous oscillations. We study the effect of the perturbation to the puma model. In the case of the first-order perturbation which keeps the (23) interchange symmetry, the mixing matrix element Ue3 is always zero. The nonzero mixing matrix element Ue3 is obtained in the second-order perturbation that breaks the (23) interchange symmetry.

Recent data of reactor neutrino experiments set more stringent constraints on leptonic mixing patterns.We examine all possible patterns on the basis of combinations of elementary correlations of elements of leptonic mixing matrix. We obtain 62 viable mixing patters at 3σ level of mixing parameters. Most of these patterns can be paired via the -interchange which changes the octant of θ 23 and the sign of cos δ. All viable patterns can be classified into two groups: the perturbative patterns and nonperturbative patterns. The former can be obtained from perturbing TBM. The latter cannot be obtained from perturbing any mixing pattern whose θ 13 is zero. Different predictions of Dirac CP phase δ of these two types of mixing patterns are discussed. Evolutions of mass matrices of neutrinos with small mixing parameters are discussed via special mixing patterns on the basis of flavor groups. In general cases, a small variation of sin θ 13 may bring about large modifications to alignment of vacuum expectation values in a mixing model. Therefore, small but nonzero sin θ 13 brings a severer challenge to leptonic mixing models on the basis of flavor groups than usual views.

The leptonic mixing parameters of high precision and the next-generation neutrino telescopes make it possible to test new physics in the flavor transition of the high-energy astrophysical neutrinos(HAN). We introduce a nonsymmetric matrix to modify the predictions of the standard flavor transition matrix. It is constructed with the mixing matrix in vacuum and that at the source of the HAN. The mismatch of the mixing matrices results in the new expectation of the flavor ratio of the HAN at Earth. It also leads to a secondary effect called the apparent P violation(APV). The quantitative analyses of the new effects are performed with a moderate setup of the parameters at the source of the HAN. The correlations between the mixing parameters and the new predictions are shown. From the correlations, the dominant parameters determining the new-physics effects are identified.