Higgs sector andR-parity breaking couplings in models with brokenU(1)B−Lgauge symmetry

Abstract

Four different supersymmetric models based on ${\mathrm{SU}(2)}_{L}\ifmmode\times\else\texttimes\fi{}{U(1)}_{R}\ifmmode\times\else\texttimes\fi{}{U(1)}_{B\ensuremath{-}L}$ and ${\mathrm{SU}(2)}_{L}\ifmmode\times\else\texttimes\fi{}{\mathrm{SU}(2)}_{R}\ifmmode\times\else\texttimes\fi{}{U(1)}_{B\ensuremath{-}L}$ gauge symmetry groups are studied. ${U(1)}_{B\ensuremath{-}L}$ symmetry is broken spontaneously by a vacuum expectation value (VEV) of a sneutrino field. The right-handed gauge bosons may obtain their mass solely by a sneutrino VEV. The physical charged lepton and neutrino are mixtures of gauginos, Higgsinos and lepton interaction eigenstates. Explicit formulas for masses and mixings in the physical lepton fields are found. The spontaneous symmetry-breaking mechanism fixes the trilinear R-parity breaking couplings. Only some special R-parity breaking trilinear couplings are allowed. There is a potentially large trilinear lepton number breaking coupling --- which is unique to left-right models --- that is proportional to the ${\mathrm{SU}(2)}_{R}$ gauge coupling ${g}_{R}.$ The couplings are parametrized by few mixing angles, making spontaneous R-parity breaking a natural ``unification framework'' for R-parity breaking couplings in supersymmetric left-right models.