On the short-distance constraints from K_{L,S} -> mu^+ mu^-

Abstract

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 $B(K_L\to {\mu }^{+}{\mu }^{-}{)}_{\mathrm{short}}$, 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.

Comments: 16 pages, 4 figures, latex