Wandzura-Wilczek approximation for the twist-3 DVCS amplitude

TL;DR

This paper derives Wandzura-Wilczek relations for twist-3 skewed parton distributions in DVCS, analyzing their discontinuities and implications for factorization and polarization-dependent observables.

Contribution

It introduces WW-like relations for twist-3 distributions and examines their discontinuities, showing that divergences affect only transverse polarization at higher order.

Findings

Discontinuities occur at x=±ξ in twist-3 distributions under WW approximation.

Divergences impact transverse polarization observables at order 1/Q^2.

Longitudinal polarization twist-3 amplitude is divergence-free.

Abstract

We present a derivation of Wandzura-Wilczek (WW) like relations for skewed parton distributions. It is demonstrated for photon-pion scattering that the skewed twist-3 parton distributions contributing to the DVCS amplitude have discontinuities at the points $x=\pm\xi$ in the WW approximation. This may lead to a violation of factorisation for the twist-3 DVCS amplitude with transverse polarization of the virtual photon. We show, however, that the contribution of the divergencies to the scattering of a transversely polarized virtual photon affects DVCS observables only at order $1/Q^2$ and can be neglected at twist-3 accuracy. For the scattering of a longitudinally polarized photon the twist-3 amplitude is free of such divergencies.