Unitary, relativistic resonance model for πNscattering

Abstract

Pion nucleon scattering up to 600 MeV laboratory kinetic energy is described by a manifestly covariant wave equation in which the pion is restricted to its mass shell. The kernel of the equation includes nucleon (N), Roper (${\mathit{N}}^{\mathrm{*}}$), delta (Δ), and ${\mathit{D}}_{13}$ poles, with their corresponding crossed pole terms approximated by contact interactions, and contact σ- and ρ-like exchange terms. The πNN vertex is treated as a mixture of ${\gamma }^5$ and ${\gamma }^{\mathrm{\mu }}$ ${\gamma }^5$ coupling, with a mixing parameter λ chosen so that the dressed nucleon pole will be unshifted by the interaction. Chiral symmetry is maintained at threshold. The resonance contributions are fully unitarized by the equation, with their widths determined by the dynamics included in the model. The Δ and ${\mathit{D}}_{13}$ are treated as pure spin 3/2 particles, with no spin 1/2 amplitude in the S channel. The complete development of this model, which gives a very good fit to all the data up to 600 MeV, is presented.