Static Model Using Crossing-Symmetric Off-Shell Equations Satisfying Two-Particle Unitarity

Abstract

Off-shell equations for the ${\ensuremath{\pi}}^{\ensuremath{-}}p$ and ${\ensuremath{\pi}}^{+}p$ elastic scattering amplitudes are derived for a static model, based on charged scalar theory. These amplitudes satisfy elastic unitarity below the three-particle cut and are related by crossing symmetry. The equations are solved numerically in the bound-state region for the entire range of coupling, and the results compared with the known results of charged scalar theory. In particular, calculations of the bound-state ${N}^{++}$ are reasonable. Possible extensions to more realistic models are discussed.