Understanding for flavor physics in the lepton sector

Abstract

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 $S4\ast U(1)$. 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 $\sin {\theta }_{13}=\frac{1-\tan {\theta }_{12}}{1+\tan {\theta }_{12}}$. Besides, deviation from $\frac{\pi }{4}$ 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.

version to appear in Phys. Rev. D

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