B_{s,d} -> l^+ l^- and K_L -> l^+ l^- in SUSY models with non-minimal sources of flavour mixing

We present a general analysis of B_{s,d}-> l^+ l^- and K_L -> l^+ l^- decays in supersymmetric models with non-minimal sources of flavour mixing. In spite of the existing constraints on off-diagonal squark mass terms, these modes could still receive sizeable corrections, mainly because of Higgs-mediated FCNCs arising at large tan(beta). The severe limits on scenarios with large tan(beta) and non-negligible {tilde d}^i_{R(L)}-{d-tilde}^j_{R(L)} mixing imposed by the present experimental bounds on these modes and Delta B=2 observables are discussed in detail. In particular, we show that scalar-current contributions to K_L -> l^+ l^- and B-{bar B} mixing set non-trivial constraints on the possibility that B_s -> l^+ l^- and B_d -> l^+ l^- receive large corrections.