On the short-distance constraints from K_(L,S) -> mu^+ mu^-

Motivated by new precise results on several $K_L$ decays, sensitive to the ${K_L \to \gamma \gamma}$ form factor, we present a new analysis of the $K_L\to \mu^+\mu^-$ long-distance amplitude based on a semi-phenomenological approach. Particular attention is devoted to the evaluation of the uncertainties of this method and to the comparison with alternative approaches. Our main result is a conservative upper bound of $2.5 \times 10^{-9}$ on $B(K_L \to \mu^+ \mu^-)_{\rm short}$, which is compatible with the SM expectation and which provides significant constraints on new-physics scenarios. The possibility to extract an independent short-distance information from future searches on $K_S \to \mu^+ \mu^-$ is also briefly discussed.