Dirac Neutrinos with $S_4$ Flavor Symmetry in Warped Extra Dimensions

Abstract

We present a warped extra dimension model with the custodial symmetry $SU(2)_L\times SU(2)_R\times U(1)_X\times P_{LR}$ based on the flavor symmetry $S_4\times Z_2\times Z'_2$, and the neutrinos are taken to be Dirac particles. At leading order, the democratic lepton mixing is derived exactly, and the high dimensional operators introduce corrections of order $\lambda_c$ to all the three lepton mixing angles such that agreement with the experimental data can be achieved. The neutrino mass spectrum is predicted to be of the inverted hierarchy and the second octant of $\theta_{23}$ is preferred. We suggest the modified democratic mixing, which is obtained by permuting the second and the third rows of the democratic mixing matrix, should be a good first order approximation to understanding sizable $\theta_{13}$ and the first octant of $\theta_{23}$. The constraints on the model from the electroweak precision measurements are discussed. Furthermore, we investigate the lepton mixing patterns for all the possible residual symmetries $G_{\nu}$ and $G_{l}$ in the neutrino and charged lepton sectors, respectively.