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

A bstract We use vector meson dominance to calculate non-perturbative contributions to the branching ratio of the rare decay $$ {K}^{\pm}\to {\pi}^{\pm}\nu \overline{\nu} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>K</mml:mi> <mml:mo>±</mml:mo> </mml:msup> <mml:mo>→</mml:mo> <mml:msup> <mml:mi>π</mml:mi> <mml:mo>±</mml:mo> </mml:msup> <mml:mi>ν</mml:mi> <mml:mover> <mml:mi>ν</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> stemming from matrix elements involving up-quark loops. The importance of this observable as well as of K 0 → π 0 l + l − and of the direct CP violation parameter $$ {\epsilon}_K^{\prime } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>ϵ</mml:mi> <mml:mi>K</mml:mi> <mml:mo>′</mml:mo> </mml:msubsup> </mml:math> is then discussed in the context of a Unitarity Triangle sqtudy based on Kaon sector observables only.