ELEMENTARY-PARTICLE POLES IN BETHE-SALPETER EQUATION

An elementary spin-zero particle pole is inserted in the Bethe-Salpeter equation. This gives a non-Regge δl0 term in the potential and the scattering amplitude. We present methods for calculating the l=0 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 Z1 and Z3′ of the elementary particle and show how the vanishing of these constants is related to bootstrap conditions. © 1969 The American Physical Society.