Light quark loops in $K^\pm \to \pi^\pm \nu\bar\nu$ 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 $K^\pm \to \pi^\pm \nu\bar \nu$ stemming from matrix elements involving up-quark loops. The importance of this observable as well as of $K^0 \to \pi^0 l^+ l^-$ 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.