Type II seesaw supersymmetric neutrino model for $\theta_{13}\neq0$

Abstract

Using the type II seesaw approach and properties of discrete flavor symmetry group representations, we build a supersymmetric $A_{4}\times A_{3}$\ neutrino model with $\theta_{13}\neq0$. After describing the basis of this model--which is beyond the minimal supersymmetric Standard Model--with a superfield spectrum containing flavons in $A_{4}\times A_{3}$\ representations, we first generate the tribimaximal neutrino mixing which is known to be in agreement with the mixing angles $\theta_{12}$ and $\theta_{23}$. Then, we give the scalar potential of the theory where the $A_{3}$ discrete subsymmetry is used to avoid the so-called sequestering problem. We \textrm{next} study the deviation from the tribimaximal mixing matrix which is produced by perturbing the neutrino mass matrix with a nontrivial $A_{4}$ singlet. Normal and inverted mass hierarchies are discussed numerically. We also study the breaking of $A_{4}$\ down to $Z_{3}$\ in the charged lepton sector, and use the branching ratio of the decay $\tau \rightarrow \mu \mu e$--which is allowed by the residual symmetry $Z_{3}$--to get estimations on the mass of one of the flavons and the cutoff scale $\Lambda$ of the model.