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K^+ -> pi^+ nu nu-bar and K_L -> pi^0 nu nu-bar Decays in the General MSSM

We reanalyze the rare decays K^+ -> pi^+ nu nu-bar and K_L -> pi^0 nu nu-bar in a general MSSM with conserved R-parity. Working in the mass eigenstate basis and performing adaptive scanning of a large space of supersymmetric parameters, 16 parameters in the constrained scan and 63 in the extended scan, we find that large departures from the Standard Model expectations are possible while satisfying all existing constraints. Both branching ratios can be as large as a few times 10^{-10} with Br(K_L -> pi^0 nu nu-bar) often larger than Br(K^+ -> pi^+ nu nu-bar) and close to its model independent upper bound. We give examples of supersymmetric parameters for which large departures from the SM expectations can be found and emphasize that the present 90% C.L. experimental upper bound on Br(K^+ -> pi^+ nu nu-bar) gives a non trivial constraint on the MSSM parameter space. Unlike previous analyses, we find that chargino box diagrams can give, already for moderately light charged sleptons, a significant contribution. As a byproduct we find that the ranges for the angles beta and gamma in the unitarity triangle are relaxed due to the presence of new CP-violating phases in K^0 - K^0-bar and B^0_d - B^0_d-bar mixing to 12 degrees <= beta <= 27 degrees and 20 degrees <= gamma <= 110 degrees.