Higher twist and transverse momentum dependent parton distributions: a light-front hamiltonian approach

TL;DR

This paper investigates higher-twist and transverse momentum dependent distributions using light-front Hamiltonian perturbation theory with a dressed quark target to test Lorentz invariance relations. It distinguishes two sets of Lorentz invariance relations (Set-A and Set-B) and shows that only Set-B holds when quark-gluon-quark correlators are included, highlighting the incompleteness of Set-A in gauge theories. The authors compute twist-3 distributions $g_T$ and $h_L$ and twist-2 distributions $g_1$, $h_1$, along with their $k_T$-dependent moments, at order ${\alpha_s}$, and demonstrate cancellation of potential singularities while confirming the necessity of quark-gluon-quark correlators. They find that the Burkhardt-Cottingham sum rule for $g_2$ is satisfied, but the corresponding sum rule for $h_2$ is violated at this perturbative level, a novel result with implications for the understanding of rotational invariance in QCD and for modeling higher-twist TMDs.

Abstract

In order to study twist-3 and transverse momentum dependent parton distributions, we use light-front time-ordered pQCD at order $α_s$ to calculate various distribution functions for a dressed quark target. This study enables us to investigate in detail the existing relations between twist-3 and transverse momentum dependent parton distributions. Our calculation shows explicitly that two versions of such relations, considered to be equivalent, occur in the literature which need to be distinguished. Moreover, we examine sum rules for higher twist distributions. While the Burkhardt-Cottingham sum rule for $g_2$ is fulfilled, the corresponding sum rule for $h_2$ is violated.