Vacuum Alignment in SUSY A4 Models

Abstract

In this note we discuss the vacuum alignment in supersymmetric models with spontaneously broken flavour symmetries in the presence of soft supersymmetry (SUSY) breaking terms. We show that the inclusion of soft SUSY breaking terms can give rise to non-vanishing vacuum expectation values (VEVs) for the auxiliary components of the flavon fields. These non-zero VEVs can have an important impact on the phenomenology of this class of models, since they can induce an additional flavour violating contribution to the sfermion soft mass matrix of right-left (RL) type. We carry out an explicit computation in a class of SUSY A4 models predicting tri-bimaximal mixing in the lepton sector. The flavour symmetry breaking sector is described in terms of flavon and driving supermultiplets. We find non-vanishing VEVs for the auxiliary components of the flavon fields and for the scalar components of the driving fields which are of order m_{SUSY} x and m_{SUSY}, respectively. Thereby, m_{SUSY} is the generic soft SUSY breaking scale which is expected to be around 1 TeV and is the VEV of scalar components of the flavon fields. Another effect of these VEVs can be the generation of a mu term.