Helicity-dependent Twist-two and Twist-three Generalized Parton Distributions in Light-front QCD

Abstract

We investigate the helicity dependent twist-two and twist-three generalized parton distributions in light-front Hamiltonian QCD for a massive dressed quark target. Working in the kinematical region $\xi <x<1$, we obtain the splitting functions for the evolutions of twist-two quark and gluon distributions in a straightforward way. For the twist-three distribution, we find that all contributions are proportional to the quark mass and thus the twist-three distribution is directly related to the chiral symmetry breaking dynamics in light-front QCD. We also show that the off-forward Wandzura-Wilczek relation is violated in perturbative QCD for a massive dressed quark.We calculate the quark mass correction to the WW relation in the off-forward case and show that it is related to $h_1(x)$ in the forward limit. We extract the 'genuine twist three' part of the matrix element in the forward case and verify the Burkhardt Cottingham and Efremov-Leader-Teryaev sum rules.

Comments: References and appendix added, minor points clarified, accepted for publication in PRD