On the dispersive two-photon ${K_L\rightarrow \mu^+ \mu^-}$ amplitude

J.O. Eeg; K. Kumerički; I. Picek

doi:doi:10.1007/s100520050102

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2018 Impact factor 4.843

Particles and Fields

Eur. Phys. J. C 1, 531-537

On the dispersive two-photon ${K_L\rightarrow \mu^+ \mu^-}$ amplitude

J.O. Eeg¹ - K. Kumericki² - I. Picek²

¹ Department of Physics, University of Oslo, N-0316 Oslo, Norway (e-mail: j.o.eeg@fys.uio.no)
² Department of Physics, Faculty of Science, University of Zagreb, POB 162, HR-10001 Zagreb, Croatia
(e-mail: kkumer@phy.hr, picek@phy.hr)

Received: 30 April 1997

Abstract
We present a full account of the two-loop electroweak, two-photon mediated short-distance dispersive K_L $\rightarrow\mu^+\mu^-$ 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.