Large $R$-parity Violating Couplings and Grand Unification

We consider a possibility that $R$-parity violating interactions of particles which do not involve the first generation have large (up to 1) coupling constants, $Λ$. Such couplings, if exist, could have a number of phenomenological consequences: renormalization of $b-τ$ mass ratio, generation of $ν_τ$ mass in MeV region, {\em etc.}. In Grand Unified models, where $B$- and $L$-violating couplings appear simultaneously, the proton decay can be forbidden in virtue of hierarchical flavor structure of $Λ.$ However, due to Cabibbo-Kobayashi-Maskawa mixing this decay is induced already in one-loop. Present experimental data give the upper bound $Λ\ltap 10^{-8}$ (or $|λ' λ''| \ltap 7\cdot 10^{-16},$ on products of certain $L$- and $B$-violating coupling constants, in more general context). The bound can be avoided, if there is an asymmetry between the $L$- and $B$-violating couplings of usual matter fields. In the $SU(5)$ model the asymmetry can be related to the doublet-triplet splitting.

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