Convergence behaviour in chiral bag models and the pion-nucleon scattering amplitude

Abstract

In typical chiral-bag-model calculations, strong restrictions are imposed on the quark configurations contributing to intermediate-state sums without addressing the question of convergence. In this paper the convergence properties of the sums are examined in connection with the pion-nucleon amplitude evaluated perturbatively to lowest order. Two forms of the interaction are employed: one where the pion-quark coupling is confined to the bag surface and one where it extends throughout the bag volume. The convergence behaviour with respect to intermediate sums is quite different in the two models. Our numerical results for the πN amplitude using the surface interaction exhibit rather poor convergence properties, with large cancellations occurring between intermediate particle and antiparticle contributions. The convergence behaviour obtained with the volume interaction is substantially better. Some implications of our results for future chiral-model calculations are presented.