Current Commutators near the Light Cone

Abstract

The behavior of nonforward matrix elements of current commutators near the light cone is discussed. In momentum space this is equivalent to an investigation of the absorptive part of nonforward Compton scattering in the scaling (Bjorken) limit. Starting from the assumption that the forward absorptive part scales, as indicated by the experiments on inelastic lepton-proton scattering, it is shown that all nonforward helicity amplitudes are bounded by functions which approach finite limits in the scaling region. The nonforward structure functions in this limit are functions of the scaling variable, the momentum transfer, and the finite mass difference of the currents. The restrictions placed on these functions due to causality are derived by using the Jost-Lehmann-Dyson representation. It is shown that the scaling structure functions are independent of the mass difference of the currents. A light-cone representation is derived which exhibits the singular part of the current commutator in terms of the structure functions. The operator-product expansion for the current commutator near the light cone is introduced and the nature of operators contributing to the scaling region is discussed. These operators, which are the highest-spin components of the equal-time commutators of the current with itself, are expressed in terms of moments of the structure functions with respect to the scaling variable. Various inequalities for the form factors of these operators are derived from unitarity. An analytic function of angular momentum is constructed which interpolates the highest-dimension operators in the light-cone expansion. It is argued that due to the locality of these operators the interpolating operator contains the singularities in angular momentum that are present in the strong interactions. This implies that the structure functions have Regge behavior in the scaling limit.