Probing SUSY effects in $K_S^0\rightarrowμ^+μ^-$
We explore supersymmetric contributions to the decay $K_S^0\rightarrowμ^+μ^-$, in light of current experimental data. The Standard Model (SM) predicts $\mathcal{B}(K_S^0\rightarrowμ^+μ^-)\approx5\times 10^{-12}$. 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 $\mathcal{B}(K_S^0\rightarrowμ^+μ^-)$ and $\mathcal{B}(K_L^0\rightarrowμ^+μ^-)$. Predictions for the $CP$ asymmetry in $K^0\rightarrowμ^+μ^-$ decays in the context of MSSM are also given, and can be up to eight times bigger than in the SM.