Twist Three Distribution e(x) : Sum Rules and Equation of Motion Relations

TL;DR

This paper studies the twist three distribution function e(x) in light-front perturbation theory, deriving sum rules and relations, and comparing results with other models to deepen understanding of quark-gluon dynamics.

Contribution

It provides a detailed derivation of e(x) including mass, transverse momentum, and quark-gluon interaction terms within light-front Hamiltonian framework, verifying key sum rules.

Findings

Sum rules and equations of motion are satisfied at one loop.

Identifies intrinsic transverse momentum and genuine twist three contributions.

Results are consistent with other model calculations.

Abstract

We investigate the twist three distribution function $e(x)$ in light-front Hamiltonian perturbation theory. In light-front gauge, by eliminating the constrained field, we find a mass term, an intrinsic transverse momentum dependent term and a 'genuine twist three' quark-gluon interaction term in the operator. The equation of motion relation, moment relation and the sum rules are satisfied for a quark at one loop. We compare the results with other model calculations.