Probing SUSY effects in $K_S^0\to {\mu }^{+}{\mu }^{-}$

We explore supersymmetric contributions to the decay $K_S^0\to {\mu }^{+}{\mu }^{-}$, in light of current experimental data. The Standard Model (SM) predicts $B(K_S^0\to {\mu }^{+}{\mu }^{-})\approx 5\times {10}^{-12}$. We find that contributions arising from flavour violating Higgs penguins can enhance the branching fraction up to $\approx 35\times {10}^{-12}$ within different scenarios of the Minimal Supersymmetric Standard Model (MSSM), as well as suppress it down to $\approx 0.78\times {10}^{-12}$. Regions with fine-tuned parameters can bring the branching fraction up to the current experimental upper bound, $8\times {10}^{-10}$. The mass degeneracy of the heavy Higgs bosons in MSSM induces correlations between $B(K_S^0\to {\mu }^{+}{\mu }^{-})$ and $B(K_L^0\to {\mu }^{+}{\mu }^{-})$. Predictions for the $CP$ asymmetry in $K^0\to {\mu }^{+}{\mu }^{-}$ decays in the context of MSSM are also given, and can be up to eight times bigger than in the SM.