DVCS amplitude at tree level: Transversality, twist-3, and factorization

TL;DR

This paper analyzes the virtual Compton scattering amplitude in QCD at tree level, ensuring electromagnetic gauge invariance through twist-3 operators, and discusses the finiteness of physical helicity amplitudes within a specific approximation.

Contribution

It introduces a method to maintain transversality in the DVCS amplitude using twist-3 operators and relates skewed distributions via reduction formulas, providing a new perspective on factorization.

Findings

The tensor amplitude for longitudinal polarization is finite.

Transverse polarization amplitude contains a divergence, but physical helicity amplitudes are finite.

The approach is equivalent to a Wandzura-Wilczek type approximation.

Abstract

We study the virtual Compton amplitude in the generalized Bjorken region (q^2 -> Infinity, t small) in QCD by means of a light-cone expansion of the product of e.m. currents in string operators in coordinate space. Electromagnetic gauge invariance (transversality) is maintained by including in addition to the twist-2 operators 'kinematical' twist-3 operators which appear as total derivatives of twist-2 operators. The non-forward matrix elements of the elementary twist-2 operators are parametrized in terms of two-variable spectral functions (double distributions), from which twist-2 and 3 skewed distributions are obtained through reduction formulas. Our approach is equivalent to a Wandzura-Wilczek type approximation for the twist-3 skewed distributions. The resulting Compton amplitude is manifestly transverse up to terms of order t/q^2. We find that in this approximation the tensor amplitude for longitudinal polarization of the virtual photon is finite, while the one for transverse polarization contains a divergence already at tree level. However, this divergence has zero projection on the polarization vector of the final photon, so that the physical helicity amplitudes are finite.