Faddeev Equations for theK→3πAmplitude

Abstract

Integral equations for the three-pion decay amplitude of the $K$ meson are derived in the context of a potential-scattering model. Nonlocal $S$- and $P$-wave separable potentials are used. Some numerical solutions are presented for the $S$-wave case. The shapes of the decay spectra are found to be insensitive to the shape of the potential for the cases investigated. The connection with the integral equations of Khuri and Treiman is discussed. A zero-range approximation requires that ${a_2}^2>{a_0}^2$ in order to fit the experimental data. Some aspects of three-body states in the presence of a resonance are investigated. No observable effects of a triangle singularity are found for the cases considered.