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

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.

arXiv comment27 pages

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Cited by in corpus (11)

• $CP$-odd gluonic operators in QCD spin physics
• The $g_T(x)$ contribution to single spin asymmetries in SIDIS
• Twist-3 Gluon Fragmentation Contribution to Polarized Hyperon Production in Unpolarized Proton-Proton Collision
• Transverse Polarization of Hyperons Produced in Semi-Inclusive Deep Inelastic Scattering
• Transverse Nucleon Single-Spin Asymmetry for Single-Inclusive Hadron and Jet Production at NLO Accuracy
• On the odderon mechanism for transverse single spin asymmetry in the Wandzura-Wilczek approximation
• The twist-3 gluon contribution to Sivers asymmetry in $J/\psi$ production in semi-inclusive deep inelastic scattering
• Reformulation of the twist-3 gluon Sivers effect toward the application to the heavy quarkonium production
• Novel relations for twist-3 tensor-polarized fragmentation functions in spin-1 hadrons
• Twist-2 relations for the twist-3 tensor-polarized distribution function $f_{LT}$ of a spin-1 hadron by the operator-product-expansion method
• Twist-3 Gluon Fragmentation Contribution to Hyperon Polarization in Semi-Inclusive Deep Inelastic Scattering