Long vs. short distance dispersive two-photon K_L to μ^+ μ^- amplitude

We report on the calculation of the two-loop electroweak, two-photon mediated short-distance dispersive K_L \to \mu^+\mu^- decay amplitude. QCD corrections change the sign of this contribution and reduce it by an order of magnitude. The resulting amplitude enables us to provide a constraint on the otherwise uncertain long-distance dispersive amplitude.