R-Parity Violation: Origin of $μ$-Term and Other Consequences

Abstract

We propose a new mechanism in which the generation of the supersymmetric $μ$-term as well charged lepton masses is closely tied to R-parity violation involving heavy vector-like families . A realistic example based on $SU(3)_c\times SU(2)_L\times U(1)_Y$, supplemented by the symmetry ${\cal R}\times {\cal U}(1)$, is presented, where ${\cal R}$ (${\cal U}(1)$) denotes a continuous $R$ (flavor) symmetry. In addition to the $μ$-term, the charged fermion mass hierarchies and mixings, as well as baryon number conservation are also nicely explained. Bilinear R-parity violating coupling involving the first generation gives rise to neutrino mass relevant for the small angle $ν_e-ν_s$ MSW oscillations, where $ν_s $ denotes a sterile state. The atmospheric neutrino puzzle is resolved via maximal mixing angle $ν_{μ}-ν_τ$ oscillations. The decay of the lightest neutralino (LSP) and leptogenesis are briefly discussed.