$K^+\to \pi^+\nu\overline\nu$ and $K^0_L\to\mu^+\mu^-$ Decays within the Minimal Supersymmetric Standard Model

Abstract

We present a detailed calculation of the contributions of charginos, scalar quarks, and charged Higgs boson to the $K^+\rightarrow \pi^+\nu\overline\nu$\ and $K^0_L\rightarrow\mu^+\mu^-$\ decays. We include mixings: that of charginos and that of the scalar partners of the left and right handed top quark. We find that the box contribution to the amplitudes is much smaller than the penguin contribution, which can be $\sim$10\% of the Standard Model contribution, even for relatively large SUSY masses. The charged Higgs contribution can be as large as 25\% of the SM contribution in the first decay and as much as 40\% of the SM contribution in the second decay.