# Lorentz invariance relations and Wandzura-Wilczek approximation

## TL;DR

This paper reviews Lorentz invariance relations among parton distribution functions, discusses their potential violations, and shows that some relations approximately hold within a generalized Wandzura-Wilczek approximation, implying small violations.

## Contribution

It provides a complete list of Lorentz invariance relations and analyzes their violations in a model-independent manner, highlighting the approximation's effectiveness.

## Key findings

- Several Lorentz invariance relations are approximately valid within the Wandzura-Wilczek approximation.
- The violation of these relations can be small, supporting their use in phenomenological analyses.
- The paper discusses the implications for sum rules like the Burkhardt-Cottingham sum rule.

## Abstract

A complete list of the so-called Lorentz invariance relations between parton distribution functions is given and some of their consequences are discussed, such as the Burkhardt-Cottingham sum rule. The violation of these relations is considered in a model independent way. It is shown that several Lorentz invariance relations are not violated in a generalized Wandzura-Wilczek approximation, indicating that numerically their violation may be small.