Theory of S-Wave Pion Scattering and Photoproduction at Low Energies

Abstract

A fixed-source analysis of the s-wave pion-nucleon interaction is constructed along the lines of the Chew-Low-Wick formalism. A bilinear s-wave interaction of the form λ0ϕ·ϕ+λτ·(ϕ×π) is added to the usual p-wave coupling (4π)1/2(f/μ)σ·∇τ·ϕ. Scattering equations are developed and solved in the one-meson approximation. Values for the renormalized coupling parameters λ0 and λ are determined which give reasonable agreement with the s-wave phase shifts up to ∼100-Mev pion kinetic energy. This s-wave interaction with the parameters fixed by the scattering analysis is then applied to the discussion of the π+ and π0 photo-production cross sections. A Kroll-Ruderman theorem is proved for the above nonlocal interaction and it is shown that the contributions to s-wave neutral and charged photoproduction are consistent with experiment. Other experimental implications, in particular as to the possible role of π-π forces, are discussed.