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We explore supersymmetric contributions to the decay K_S^0→μ^+μ^-, in light of current experimental data. The Standard Model (SM) predicts B(K_S^0→μ^+μ^-)≈5× 10^-12. We find that contributions arising from flavour violating Higgs penguins can enhance the branching fraction up to ≈ 35× 10^-12 within different scenarios of the Minimal Supersymmetric Standard Model (MSSM), as well as suppress it down to ≈ 0.78× 10^-12. Regions with fine-tuned parameters can bring the branching fraction up to thedoi:10.1007/jhep05(2018)024 fatcat:d5a2mlbyp5hhtkxturqbhr6lge