$K_{l4}$ - Decays Beyond One Loop

Abstract

The matrix elements for $K\rightarrow \pi \pi \l \nu$ decays are described by four form factors $F,G,H$ and $R$. We complete previous calculations by evaluating $R$ at next-to-leading order in the low-energy expansion. We then estimate higher order contributions using dispersion relations and determine the low-energy constants $L_1,L_2$ and $L_3$ from data on $K_{e4}$ decays and on elastic pion scattering. Finally, we present predictions for the slope of the form factor $G$ and for total decay rates.