Poincaré invariant exchange model of pion-nucleon scattering

Pion-nucleon scattering up to a pion laboratory kinetic energy of 700 MeV is described by a Poincar\'e invariant, instant form model. The model is constructed in a space spanned by single-baryon states $|B〉,$ where B is the nucleon, or any resonance that contributes in the energy range considered; and by meson-baryon states |μB〉, where |μB〉=|πN〉, |πΔ〉, or |ηN〉. The model specifies a mass operator in the form M=M₀+U, where M₀ is a noninteracting mass operator and U contains the interactions. The 〈πN|U|πN〉 potentials are derived from N, Δ, σ, and ρ exchange processes. The vertex interactions 〈μB|U|B^'〉 are derived from field theory interaction Hamiltonians. Coupling to the inelastic channels, |πΔ〉 and |ηN〉, is provided by a 〈πN|U|πΔ〉 transition potential due to nucleon exchange; and by interactions of the form μBB^''μ^'B^'.