Spontaneous R-Parity Violation, $A_4$ Flavor Symmetry and Tribimaximal Mixing

TL;DR

This paper proposes a model where spontaneous R-parity violation occurs within an $A_4$ flavor symmetry framework, leading to neutrino mixing patterns consistent with tribimaximal mixing, and explores the implications for neutrino mass matrices.

Contribution

The paper introduces a novel model combining spontaneous R-parity violation with $A_4$ flavor symmetry to naturally produce tribimaximal neutrino mixing.

Findings

Neutrino mass matrix can produce tribimaximal mixing under specific VEV constraints.

The model allows for high VEV of singlet sneutrinos even with small or zero VEVs of others.

Extended neutral fermion mass matrix includes mixings with neutrinos, neutralinos, and singlet higgsinos.

Abstract

We explore the possibility of spontaneous R parity violation in the context of $A_4$ flavor symmetry. Our model contains $SU(3)_c \times SU(2)_L \times U(1)_Y$ singlet matter chiral superfields which are arranged as triplet of $A_4$ and as well as few additional Higgs chiral superfields which are singlet under MSSM gauge group and belong to triplet and singlet representation under the $A_4$ flavor symmetry. R parity is broken spontaneously by the vacuum expectation values of the different sneutrino fields and hence we have neutrino-neutralino as well as neutrino-MSSM gauge singlet higgsino mixings in our model, in addition to the standard model neutrino- gauge singlet neutrino, gaugino-higgsino and higgsino-higgsino mixings. Because all of these mixings we have an extended neutral fermion mass matrix. We explore the low energy neutrino mass matrix for our model and point out that with some specific constraints between the sneutrino vacuum expectation values as well as the MSSM gauge singlet Higgs vacuum expectation values, the low energy neutrino mass matrix will lead to a tribimaximal mixing matrix. We also analyze the potential minimization for our model and show that one can realize a higher vacuum expectation value of the $SU(3)_c \times SU(2)_L \times U(1)_Y$ singlet sneutrino fields even when the other sneutrino vacuum expectation values are extremely small or even zero.