Charge Breaking Minima in the Broken R-parity Minimal Supersymmetric Standard Model

We reconsider the possible presence of charge and colour breaking minima inthe scalar potential of the minimal supersymmetric standard model (MSSM) andits minimal generalization with R-parity explicitly broken by bilinear terms(RMSSM). First we generalize some results previously derived for the MSSM case.Next we investigate how robust is the MSSM against its RMSSM extension. Weexamine the constraints on the RMSSM parameter space that follow from therequired absence of charge breaking minima in the scalar potential. We pointout the possibility of generating non--zero vacuum expectation values for thecharged Higgs field which is not present in the MSSM. However, given thesmallness of neutrino masses indicated by neutrino oscillation data, we showthat the RMSSM represents only a slight perturbation of the MSSM and is thus assafe (or unsafe) as the MSSM itself from unwanted minima in the scalarpotential.Comment: Latex 16 pages, 2 figure