The rare decay KL → π0μ+μ- within the SM

We present an updated analysis of the rare decay K-L --> pi(0) mu(+)mu(-) within the standard model. In particular, we present the first complete calculation of the two-photon CP-conserving amplitude within chiral perturbation theory, at the lowest non-trivial order. Our results confirm the previous findings that the CP-conserving contribution to the decay rate cannot be neglected. By means of an explicit two-loop calculation, we show that this contribution can be estimated with sufficient accuracy compared to the CP-violating terms. We predict B(K-L --> pi(0) mu(+) mu(-))(SM) = (1.5 +/- 0.3) x 10(-11), with approximately equal contributions from the CP-conserving component, the indirect-CP-violating term, and the interesting direct-CP-violating amplitude. The error of this prediction is mainly of parametric nature and could be substantially reduced with better data on the K-S --> pi(0) l(+)l(-) modes. The standard model predictions for various differential distributions and the sensitivity to possible new-physics effects are also briefly discussed.