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

Abstract

We propose a new mechanism in which the generation of the supersymmetric $\mu$-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 $\mathcal{R}\times \mathcal{U}(1)$, is presented, where $\mathcal{R}$ ($\mathcal{U}(1)$) denotes a continuous $R$ (flavor) symmetry. In addition to the $\mu$-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 ${\nu }_e-{\nu }_s$ MSW oscillations, where ${\nu }_s$ denotes a sterile state. The atmospheric neutrino puzzle is resolved via maximal mixing angle ${\nu }_{\mu }-{\nu }_{\tau }$ oscillations. The decay of the lightest neutralino (LSP) and leptogenesis are briefly discussed.

Comments: 20 pp. LATEX