Neutrinoless double beta decay with R-parity violation

We consider recently observed neutrinoless double beta decay in the context of the minimal supersymmetric standard model with R-parity violating couplings λ′. We observe that most of the current experimental bounds on the R-parity violating couplings do not exclude the possibility that the neutrinoless double beta decay is caused by R-parity violation. But if we consider K–K oscillation, we observe that we have to make the R-parity violating couplings generation-dependent to accommodate with the observed neutrinoless double beta decay. And furthermore, we need some mechanism to cancel the contribution to K–K mixing from a large R-parity violating coupling. We realized this cancellation by assuming that the first- and the second-generation of quark sector do not couple with the first-generation lepton sector by R-parity violating couplings except the term W=λ111′L1Q1D1c, which is responsible for the observed neutrinoless double beta decay.