Charm-Quark Contribution to K_L -> mu⁺ mu^- at Next-to-Next-to-Leading

2006/05/31 by Martin Gorbahn, Ulrich Haisch
Physics and Astronomy · #hep-ph

paper · pdf · doi:10.1103/physrevlett.97.122002

published as Phys.Rev.Lett.97:122002,2006 · 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/0508165

arxiv created 2012/09/19 · arxiv updated 2012/09/20

Abstract

We calculate the charm-quark contribution to the decay K_L -> mu⁺ mu^- in next-to-next-to-leading order of QCD. This new contribution reduces the theoretical uncertainty in the relevant parameter P_c from +/-22% down to +/-7%, corresponding to scale uncertainties of +/-3% and +/-6% in the short-distance part of the branching ratio and the determination of the Wolfenstein 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 and the 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 the Cabibbo-Kobayashi-Maskawa matrix element V_td being the dominant individual source in the quoted error.

Citations

• The Rare Decay K⁺ -> pi⁺ nu nubar at the Next-to-Next-to-Leading Order in QCD