Light quark loops in \( {K}^{\pm}\to {\pi}^{\pm}\nu \overline{\nu} \) from vector meson dominance and update on the Kaon Unitarity Triangle

Abstract

We use vector meson dominance to calculate non-perturbative contributions to the branching ratio of the rare decay \( {K}^{\pm}\to {\pi}^{\pm}\nu \overline{\nu} \) stemming from matrix elements involving up-quark loops. The importance of this observable as well as of K⁰ → π⁰l⁺l⁻ and of the direct CP violation parameter \( {\epsilon}_K^{\prime } \) is then discussed in the context of a Unitarity Triangle sqtudy based on Kaon sector observables only.