# 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.

## Key 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.