Two-loop electroweak corrections for the K → πν(ν)over-bar decays

The rare K -> pi nu(nu) over bar decays play a central role in testing the standard model and its extensions. Upcoming experiments plan to measure the decay rates with high accuracy. Yet, unknown higher-order electroweak corrections result in a sizeable theory error. We remove this uncertainty by computing the full two-loop electroweak corrections to the top-quark contribution X-t to the rare decays K-L -> pi(0) nu(nu) over bar, K+ -> pi(+) nu(nu) over bar, and B -> X-d,X-s nu(nu) over bar in the standard model. The remaining theoretical uncertainty related to electroweak effects is now far below 1%. Finally we update the branching ratios to find Br(K-L -> pi(0)nu(nu) over bar) = 2.43(39)(6) x 10(-11) and Br(K+ -> pi(+)nu(nu) over bar) = 7.81(75)(29) x 10(-11). The first error summarizes the parametric, the second the remaining theoretical uncertainties.