Quantum Field Theories with Shadow States. II. Low-Energy Pion-Nucleon Scattering

Abstract

By adapting the methods of the preceding paper, we use the concepts of shadow states and indefinite metric to construct a simple static theory of low-energy pion-nucleon scattering. This theory of $s$- and $p$-wave scattering so constructed is both finite and exactly soluble. Scattering at negative energy also is a well-defined process. The calculated scattering amplitude is found to satisfy the substitution law and to be covariant, unitary, and analytic in almost all neighborhoods of physical scattering energies. When given the masses and coupling constants as input, this theory predicts the scattering phase shifts in agreement with experiment. The present limits on the $s$-wave pion-nucleon scattering total cross sections are compatible with the induced cusps from the opening up of the pseudothreshold of the shadow states.