The twist-three distribution $e^q(x,k_\perp)$ in a light-front model

TL;DR

This paper models the twist-three TMD $e^q(x,k_ot)$ in a light-front framework, decomposing it into various components, and provides numerical predictions highlighting quark-gluon correlations in the proton.

Contribution

It introduces a light-front model for the twist-three TMD $e^q(x,k_ot)$, incorporating Fock states with three quarks and a gluon, and fits parameters to phenomenological data.

Findings

Numerical predictions for $e^q(x,k_ot)$ and $e^q(x)$ are provided.

The model emphasizes the role of quark-gluon correlations.

Parameters fitted to reproduce known parton distributions.

Abstract

We discuss the twist-three, unpolarized, chiral-odd, transverse momentum dependent parton distribution (TMD) $e^q(x,k_\perp)$ within a light-front model. We review a model-independent decomposition of this TMD, which follows from the QCD equations of motion and is given in terms of a leading-twist mass term, a pure interaction-dependent contribution, and singular terms. The leading-twist and pure twist-three terms are represented in terms of overlap of light-front wave functions (LFWFs), taking into account the Fock states with three valence quark ($3q$) and three-quark plus one gluon ($3q+g$). The $3q$ and $3q+g$ LFWFs with total orbital angular momentum zero are modeled using a parametrization derived from the conformal expansion of the proton distribution amplitudes, with parameters fitted to reproduce available phenomenological information on the unpolarized leading-twist quark and gluon collinear parton distributions. Numerical predictions for both the quark TMD $e^q(x,k_\perp)$ and the collinear parton distribution $e^q(x)$ are presented, discussing the role of the quark-gluon correlations in the proton.