Charged-lepton-flavour violation in kaon decays in supersymmetric theories

We discuss rare kaon decays that violate charged-lepton flavour conservation in supersymmetric theories with and without R parity, in view of possible experiments using an intense proton source as envisaged for a neutrino factory. In the minimal supersymmetric standard model, such decays are generated by box diagrams involving charginos and neutralinos, but the limits from mu - egamma, mu-e conversion and Deltam(K) constrain the branching ratios to challengingly small values. However, this is no longer the case in R-violating theories, where such decays may occur at tree level at rates close to the present experimental limits. Within this framework, we obtain bounds on products of LL (E) over bar and LQ (D) over bar operators from the experimental upper limits on K-0 --> and mu(+/-)e(-/+) and K-+/-,K-0 --> pi(+/-),(0)mu(+/-)e(-/+) decays. We also note the possibility of like-sign lepton decays K+/- --> pi(-/+)l(+/-)l(+/-) in the presence of non-zero (b) over tildeL-(b) over tildeR mixing. We conclude that rare kaon decays violating charged-lepton flavour conservation could be an interesting signature of R violation.