Spontaneous R-parity violation, A 4 flavor symmetry and tribimaximal mixing

Abstract

We explore the possibility of obtaining tribimaximal mixing matrix in the set-up of a spontaneous R parity violating theory and in the presence of A 4 flavor symmetry. Our model contains SU(3) C × SU(2) L × 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 of all these mixings we have an extended 17 × 17 neutral fermion mass matrix. We explore the low energy neutrino mass matrix of 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, despite the non-trivial extension of the neutral fermion mass matrix which comes as an artifact of R-parity violation. We analyze the scalar potential minimization of our model and show that one can realize R-parity violation in this model through large vacuum expectation values of the SU(3) C × SU(2) L × U(1) Y singlet sneutrino fields, even when the other sneutrino vacuum expectation values are extremely small or even zero.