mu^+ mu^- at Next-to-Next-to-Leading Order > 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.