Crossing and Unitarity in a Multichannel Static Model. I

Abstract

The infinite multichannel-scattering process of the two-particle scattering of mesons of arbitrary isospin off an isospin-½ target, inelastic two-particle channels being admitted, is considered in the static limit. The restrictions on the S matrix arising from crossing under SU(2) and two-particle unitarity are expressed in terms of three equations alone in the limit of degenerate meson masses. These equations are solved by a perturbative technique, the expansion parameter being a measure of the strength of the inelastic scattering. The principal result of this paper is that the inelastic amplitudes are all related, so that if one is zero all must be zero. Comparisons are made with strong-coupling theory, which also requires an infinite number of channels.