Elementary-Particle Poles in the Bethe-Salpeter Equation

Abstract

An elementary spin-zero particle pole is inserted in the Bethe-Salpeter equation. This gives a non-Regge ${\delta }_{l0\mathrm{}}$ term in the potential and the scattering amplitude. We present methods for calculating the $l=0\mathrm{}$ partial-wave amplitude with emphasis on finding the pole positions. Our methods are tested with a ladder-approximation example. Finally, this puts us in a position to discuss the renormalization constants $Z_1$ and $Z_{3^{\prime }}$ of the elementary particle and show how the vanishing of these constants is related to bootstrap conditions.