On the short-distance dispersive two-photon K_L -> mu^+ mu^- amplitude

We present a full account of the two-loop, two-photon mediated short-distance dispersive $K_L \rightarrow\mu^+\mu^-$ decay amplitude. We clarify the dynamical mechanism due to QCD corrections which suppresses this amplitude to such a degree that it cannot compete with the two-photon mediated absorptive counterpart. We disprove some far-reaching conclusions inferred from earlier two-loop considerations. Finally, we point out that according to the present experimental status of the process, there is no room for a long distance dispersive amplitude comparable in size to the absorptive part.