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We calculate the charm-quark contribution to the decay K_L -> mu^+ mu^- innext-to-next-to-leading order of QCD. This new contribution reduces thetheoretical uncertainty in the relevant parameter P_c from +/-22% down to+/-7%, corresponding to scale uncertainties of +/-3% and +/-6% in theshort-distance part of the branching ratio and the determination of theWolfenstein parameter rhobar from K_L -> mu^+ mu^-. The error in P_c = 0.115+/- 0.018 is now in equal shares due to the combined scale uncertainties andthe current uncertainty in the charm-quark mass. We find BR (K_L -> mu^+mu^-)_SD = (0.79 +/- 0.12) x 10^-9, with the present uncertainty in theCabibbo-Kobayashi-Maskawa matrix element V_td being the dominant individualsource in the quoted error.Comment: 5 pages, 2 figures; Note added concerning the erroneous treatment of  anomalous triangle diagrams. The associated numerical effect is negligible.  arXiv admin note: substantial text overlap with arXiv:hep-ph/050816

physical review letters

Charm-Quark Contribution to<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>K</mml:mi><mml:mi>L</mml:mi></mml:msub><mml:mo>→</mml:mo><mml:msup><mml:mi>μ</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>μ</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:math>at Next-to-Next-to-Leading Order

Charm-Quark Contribution toKL→μ+μ−at Next-to-Next-to-Leading Order