Two-loop electroweak corrections for the K→πνν decays

The rare K→πνν 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 Xt to the rare decays KL→π0νν, K+→π+νν, and B→Xd,sνν 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(KL→π0νν)=2.43(39)(6)x10-11 and Br(K+→π+νν)=7.81(75)(29)x10-11. The first error summarizes the parametric, the second the remaining theoretical uncertainties.