$K_{\ell 4}$ Form-Factors and $\pi$-$\pi$ Scattering

Abstract

The $F$ and $G$ form-factors of $K_{\ell4}$ and the quark condensates are calculated to ${\cal O}(p^6)$ in Chiral Perturbation Theory (CHPT). Full formulas are presented as much as possible. A full refit of most of the ${\cal O}(p^4)$ CHPT parameters is done with a discussion of all inputs and underlying assumptions. We discuss the consequences for the vacuum expectation values, decay constants, pseudoscalar masses and $\pi$-$\pi$ scattering.