Light-cone structure of vertex functions for composite fields

Abstract

Vertex functions for composite fields are defined in a model field theory both on and off mass shell. Light-cone dominance at large momentum transfer is shown to hold, by the compositeness assumption, for the off-shell vertex function. On the other hand, it is in general untrue that the elastic form factor probes light-like distances between the constituents inside the nucleon. The relevant light-cone singularity (in the relative space-time separation x) is less important in this case than the large x 0 behaviour of the wave function at fixed x 2. It is found however that, under some conditions, the light-cone singularity determines the large x 0 behaviour of the wave function, and therefore the large q 2 behaviour of the form factor. For composite particles described by a Bethe-Salpeter equation, this result is equivalent to the known fact that at large q 2 the form factor depends on the binding interaction at small distances. A relation similar to that of Drell-Yan-West is finally established between the asymptotic behaviour of the elastic form factor and the threshold behaviour of the absorptive part of the vertex scaling function.