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.

Twist-3 gluon fragmentation contribution to transversely polarized hyperon production in semi-inclusive deep-inelastic scattering

“…Here we summarize the twist-3 gluon FFs which contribute to 𝑒(ℓ)+𝑝( 𝑝) → 𝑒(ℓ ′ )+Λ ↑ (𝑃 ℎ )+𝑋. They are classified into intrinsic, kinematical and dynamical ones [9]. The intrinsic ones are defined from the 2-gluon correlators as…”

“…According to the formalism developed in [6], intrinsic, kinematical, and the dynamical twist-3 FFs as well as the derivative of kinematical FFs appear in the cross section. By using the QCD equation-of-motion relations and the Lorentz invariance relations [9], one can eliminate the intrinsic FF, Δ Ĝ3 T (𝑧), and the derivative of the kinematical FFs, 𝜕 Ĝ (1) 𝑇 (𝑧)/𝜕 (1/𝑧) and 𝜕Δ Ĥ (1) 𝑇 (𝑧)/𝜕 (1/𝑧), in favor of the other twist-3 FFs. Therefore the final form of the cross section can be written in terms of the twist-3 gluon FFs, Ĝ (1) 𝑇 , Δ Ĥ (1) 𝑇 , ℑ N1,2 , ℑ Ô1,2 , ℑ D𝐹𝑇 and ℑ G𝐹𝑇 as in (7).…”

Vision for QCD to the 2030s and Beyond

“…( 2) are only the first term in a series expansion in momentum transfer. So-called "higher twist" terms involve more fields, and depend on matrix elements such as [10,11] P | Q(x)ΓG(y)Q(0)|P , with Q a quark and G a gluon field. For some observables, especially involving spin, this is the leading effect, offering information on short-distance correlations between partons of different flavor.…”

Transverse Polarization of Hyperons Produced in Semi-Inclusive Deep Inelastic Scattering

“…Those functions are, in general, not independent from each other but obey some constraint relations based on the operator identities. The complete set of those relations have been also derived [21,22], which are crucial to obtain the frame-independent expressions for the twist-3 cross sections [21][22][23]. There have been also some attempts to extend the twist-3 calculation to the next-to-leading order level [24][25][26].…”