ON THE DISPERSIVE 2-PHOTON K-L-]MU(-) AMPLITUDE()MU()

We present a full account of the two-loop electroweak, two-photon medi ated short-distance dispersive K-L --> mu(+)mu(-) decay amplitude. QCD corrections change the sign of this amplitude and reduce it by an ord er of magnitude. Thus, the QCD-corrected two-loop amplitude represents only a small fraction (with the central value of 5%) of the one-loop weak short-distance contribution, and has the same sign. In combinatio n with a recent measurement, the standard-model prediction of the shor t-distance amplitude, completed in this paper, provides a constraint o n the otherwise uncertain long-distance dispersive amplitude.