KL→μe: A possible probe of slepton mass splitting?

We make a phenomenological analysis of supersymmetric contributions to ${\mathit{K}}_{\mathit{L}}$→μe¯. Using parameters consistent with the ${\mathit{K}}_{\mathit{L}}$-${\mathit{K}}_{\mathit{S}}$ mass difference, we find that the experiments planned or currently running will be unable to detect slepton mass splittings. An improvement in the measurement of the branching ratio by three orders of magnitude will make it possible to record such contributions if sleptons are at least a few GeV apart in mass.