The bjorken-johnson-low limit in perturbation theory

Abstract

The Bjorken-Johnson-Low limit is analysed in perturbation theory with currents constructed from fermion fields with a neutral gluon interaction. Diagrams with many loops can be treated. For those which are not divergent it is shown that the limit is violated in well-defined circumstances by terms involving powers of logarithms. The maximum power of ln (−q02), and its numerical coefficient, are directly related to the degree of divergence, and its coefficient, of an associated vertex part. The terms of orderq0−1 are shown to correspond to renormalized vertex parts with the vertex given by the canonical commutator together with a series of dynamical corrections to it. Some simple diagrams requiring renormalization are also analysed. Coefficients of ln (−q02) can again be related to those of divergencies in self-energy and vertex parts except that there is now a minus sign multiplying them.