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 -> e
\gamma, \mu-e conversion and \Delta m_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\bar{E} and LQ\bar{D} operators from the experimental upper
limits on K^0 -> \mu^\pm e^\mp and K^{\pm,0} -> \pi^{\pm,0} \mu^\pm e^\mp
decays. We also note the possibility of like-sign lepton decays K^\pm ->
\pi^\mp \ell^\pm \ell^\pm in the presence of non-zero \tilde{b}_L-\tilde{b}_R
mixing. We conclude that rare kaon decays violating charged-lepton flavour
conservation could be an interesting signature of R violation.Comment: 25 pages, 6 figures, Prepared for the Kaon Physics Working Group as
part of the ECFA/CERN study of Neutrino Factory & Muon Storage Rings At CERN.
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