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 $\delta \sim 0.1$ compared to the previous one. In order to reproduce the mass hierarchy, $m_\tau$ and $\sqrt{ \Delta m_{ atm}^2}$, $m_\mu$ and $\sqrt{ \Delta m_{ sol}^2}$ 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, $\theta_{ 12}, \theta_{ 23}, \theta_{ 13}$ 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 $\theta_{ 12}$ and $\theta_{ 13}$ originate from the same contribution, there is a relation predicted for them $\sin{ \theta_{ 13}}=\displaystyle \frac{ 1-\tan{ \theta_{ 12}}}{ 1+\tan{ \theta_{ 12}}}$. Besides, deviation from $\displaystyle \frac{ \pi}{ 4}$ for $\theta_{ 23}$ should have been as large as deviation from 0 for $\theta_{ 13}$ if it were not the former is suppressed by a factor 4 compared to the latter.
Categories: hep-ph