Two-loop large-mtelectroweak corrections toK→πνν¯for an arbitrary Higgs boson mass

We consider for the first time the leading large top quark mass corrections, arising at higher order in electroweak interactions, to the rare decays $\overrightarrow{K}\pi \nu \overline{\nu }$ and the related modes $\overrightarrow{B}{X}_s\nu \overline{\nu }$ and $\overrightarrow{B}{l}^{+}{l}^{-}$. Higher order effects of similar type have previously been calculated in the large-$m_t$ limit for key observables of precision electroweak physics at $Z$ factories. Here we obtain the corresponding corrections of order $\mathcal{O}{(G}_F^2{m}_t^4)$ at the amplitude level for short-distance dominated rare meson decays. This allows us to quantify the importance of higher order electroweak effects for these processes, which can be reliably computed and have very small uncertainties from strong interactions. Simultaneously it becomes possible to remove, to some extent, ambiguities in the definition of electroweak parameters describing the strength of flavor-changing neutral current interactions. The corrections we discuss are at the level of a few percent.