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

Abstract. 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 $\mu \rightarrow e \gamma, \mu$–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 $K^0 \rightarrow \mu^\pm e^\mp$ and $K^{\pm,0} \rightarrow \pi^{\pm,0} \mu^\pm e^\mp$ decays. We also note the possibility of like-sign lepton decays $K^\pm \rightarrow \pi^\mp \ell^\pm \ell^\pm$ in the presence of non-zero $\tilde{b}_{\mathrm{L}}$–$\tilde{b}_{\mathrm{R}}$ mixing. We conclude that rare kaon decays violating charged-lepton flavour conservation could be an interesting signature of R violation.