Meson-exchange $πN$ Models in Three-Dimensional Bethe-Salpeter Formulation
The pion-nucleon scattering is investigated by using several three-dimensional reduction schemes of the Bethe-Salpeter equation for a model Lagrangian involving $π$, $N$, $Δ$, $ρ$, and $σ$ fields. It is found that all of the resulting meson-exchange models can give similar good descriptions of the $πN$ scattering data up to 400 MeV. However they have significant differences in describing the $πNN$ and $πNΔ$ form factors and the $πN$ off-shell t-matrix elements. We point out that these differences can be best distinguished by investigating the near threshold pion production from nucleon-nucleon collisions and pion photoproduction on the nucleon. The consequences of using these models to investigate various pion-nucleus reactions are also discussed.