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Understanding for flavor physics in the lepton sector

In this paper, we give a model for understanding flavor physics in the lepton sector--mass hierarchy among different generations and neutrino mixing pattern. The model is constructed in the framework of supersymmetry, with a family symmetry $S4*U(1)$. There are two right-handed neutrinos introduced for seesaw mechanism, while some standard model(SM) gauge group singlet fields are included which transforms non-trivially under family symmetry. In the model, each order of contributions are suppressed by $δ\sim 0.1$ compared to the previous one. In order to reproduce the mass hierarchy, $m_τ$ and $\sqrt{Δm_{atm}^2}$, $m_μ$ and $\sqrt{Δm_{sol}^2}$ are obtained at leading-order(LO) and next-to-leading-order(NLO) respectively, while electron can only get its mass through next-to-next-to-next-to-leading-order(NNNLO) contributions. For neutrino mixing angels, $θ_{12}, θ_{23}, θ_{13}$ are $45^\circ, 45^\circ, 0$ i.e. Bi-maximal mixing pattern as first approximation, while higher order contributions can make them consistent with experimental results. As corrections for $θ_{12}$ and $θ_{13}$ originate from the same contribution, there is a relation predicted for them $\sin{θ_{13}}=\displaystyle \frac{1-\tan{θ_{12}}}{1+\tan{θ_{12}}}$. Besides, deviation from $\displaystyle \fracπ{4}$ for $θ_{23}$ should have been as large as deviation from 0 for $θ_{13}$ if it were not the former is suppressed by a factor 4 compared to the latter.