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

Abstract

We present a full account 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 amplitude and reduce it by an order 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 combination with a recent measurement, the standard-model prediction of the short-distance amplitude, completed in this paper, provides a constraint on the otherwise uncertain long-distance dispersive amplitude.

Comments: 7 pages, 6 PS figures, uses psfig, revised version with important numerical error corrected, to appear in Z.f.Phys.C (and one additional reference)