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.
Highlights
During the past few decades twist-3 effects in inclusive processes have been receiving great attention, in that they show up as a leading contribution to interesting spin asymmetries and reveal an important role of multiparton correlations in the scattering processes which shed new lights on the hadron structure
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 have derived all the constraint relations for twist-3 gluonic fragmentation functions (FFs), which follow from the QCD e.o.m. and the operator product expansion
Summary
During the past few decades twist-3 effects in (semi-) inclusive processes have been receiving great attention, in that they show up as a leading contribution to interesting spin asymmetries and reveal an important role of multiparton correlations in the scattering processes which shed new lights on the hadron structure. There are several purely gluonic twist-3 FFs for a transversely polarized spin-1=2 hadron, so the present study is important for the study of their contribution to the polarized hyperon production in the unpolarized proton-proton collision (pp → Λ↑X) [37,38] and SIDIS (ep → eΛ↑X), etc Those exact relations for the gluonic DFs and FFs need to be taken into account in the derivation of the cross section and will be crucial to guarantee gauge invariance and the frame independence of the twist-3 cross sections as in the case of quark DFs and FFs. The remainder of this paper is organized as follows: In Sec. II, we derive the relations among the twist-3 gluon DFs. After summarizing the complete set of purely gluonic distributions up to twist-3, we derive all the constraint relations among those functions.
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