Recoupling Effects in the Isobar Model. I. General Formalism for Three-Pion Scattering

The consequence of elastic unitarity and analyticity for the isobar model of isocalar three-pion scattering are derived. All recoupling effects are retained and a careful discussion of real pion exchange is presented. In this way we show how the isobar model may be made to satisfy Watson's theorem. We display the common origin of both these phenomena and obtain the modifications they generate in the partial-wave discontinuity equations. In preparation for a forthcoming treatment of one and two-pion exchange forces, the N/D equations are derived for the J=1^- isoscalar amplitude. The effect of recoupling in the narrow width approximation is demonstrated by a calculation of the effective ρ-π phase space and suggests that recoupling is important.