Radiative corrections to pion-nucleon coupling constants

Abstract

The electromagnetic corrections to the π- N coupling constants have been calculated by four methods. Feynman graphs, sidewise dispersion relations, sum rules, and current commutation relations. The results are explicitly shown to be gauge invariant. Only the nucleon intermediate state is considered in the Feynman approach and the dispersion relation approach, but the effect of the N ∗ (1238) intermediate state is estimated in the commutation relation approach. The elastic electromagnetic form factors are used to cut off the integrals for the Feynman graphs and sum rules, and an ultraviolet cutoff is used in the dispersion integrals. The uses of PCAC and quark model current-current commutators for calculating the coupling constant shifts are shown to be model dependent and to lead to a logarithmic divergence. Comparisons of the various methods are made; although numerical results do not agree, they are generally in the direction required to understand charge dependent effects in N-N scattering.