Exact Relations for Twist-3 Gluon Distribution and Fragmentation Functions from Operator Identities

TL;DR

This paper derives exact operator-based relations among twist-3 gluon distribution and fragmentation functions, simplifying their analysis and ensuring gauge invariance in high-energy QCD processes.

Contribution

It establishes operator identities linking intrinsic, kinematical, and dynamical twist-3 functions, enabling their expression in terms of twist-2 and dynamical functions.

Findings

Derived exact relations for all twist-3 gluonic functions.

Expressed intrinsic and kinematical functions via twist-2 and dynamical functions.

Ensured gauge invariance and frame independence of twist-3 cross sections.

Abstract

We perform a systematic study on the twist-3 gluon distribution and fragmentation functions which appear in the collinear twist-3 factorization for hard inclusive processes. Three types of twist-3 distribution and fragmentation functions, i.e., intrinsic, kinematical and dynamical ones, which are necessary to describe all kinds of twist-3 cross sections, are related to each other by the operator identities based on the QCD equation of motion and the Lorentz invariance properties of the correlation functions. We derive the exact relations for all twist-3 gluonic distribution and fragmentation functions for a spin-1/2 hadron. Those relations allow one to express intrinsic and kinematical twist-3 gluon functions in terms of the twist-2 and dynamical twist-3 functions, which provides a basis for the renormalization of intrinsic and kinematical twist-3 functions. In addition, those model independent relations are crucial to guarantee gauge invariance and frame independence properties of the twist-3 cross sections.