Representation of the virtual Compton amplitude for polarized scattering in the generalized Bjorken region

TL;DR

This paper calculates the virtual Compton amplitude for polarized scattering using light-ray operators and the nonlocal light-cone expansion, simplifying the relation between structure functions in the forward scattering limit.

Contribution

It introduces a method to express vector light-ray operator expectation values via scalar operators, simplifying the analysis of the Compton amplitude.

Findings

Derived integral relations between twist-2 structure functions in forward scattering.

Simplified the calculation of the Compton amplitude for polarized scattering.

Connected vector and scalar light-ray operator expectation values.

Abstract

The Compton amplitude is calculated in terms of expectation values of light-ray quark operators. As a technical tool we apply the nonlocal light-cone expansion. Thereby we express the expectation value of the vector light-ray operator with the help of the expectation value of the corresponding scalar operator of twist 2. This allows important simplifications. In the limit of forward scattering the integral relations between the twist-2 contributions of the structure functions are implied directly.