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Exact Relations for Twist-3 Gluon Distribution and Fragmentation Functions from Operator Identities
High Energy Physics - Phenomenology · Submitted 24 Dec 2019
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We derive the exact relations for all twist-3 gluonic distribution and fragmentation functions for a spin-1/2 hadron.
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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | 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. | contribution 0.95 | 0.94 | 0.05 | asserted 0.98 |
| s1 | 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. | result 0.46 | 0.23 | 0.35 | asserted 1.00 |
| s2 | We derive the exact relations for all twist-3 gluonic distribution and fragmentation functions for a spin-1/2 hadron. | result 0.59 | 0.97 | 0.65 | asserted 1.00 |
| s3 | 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. | interpretation 0.79 | 0.76 | 0.33 | asserted 0.97 |
| s4 | In addition, those model independent relations are crucial to guarantee gauge invariance and frame independence properties of the twist-3 cross sections. | interpretation 0.99 | 0.47 | 0.16 | asserted 0.99 |
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The paper
Original 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.
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References
How the literature uses it
8 arXiv papers cite this in 19 sentences
Papers citing it · 16 sentences without a confident label
Cites it as background 3 papers
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The $d$-type tri-gluon correlator is commonly defined [ref] for a transversely polarized proton with spin $$ as (our notation follows ref.
Gluon Sivers function from forward exclusive $\chi_{c1}$ photoproduction on unpolarized protons · Exclusive $γp →χ_c1 p$ cross section · 0.80
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The dynamical collinear twist-3 gluon distributions are defined as the light-cone correlation functions of three field strength tensors ($f$-type distribution) [ref] [equation] The function $N(x_1,x_2)$ satisfies the symmetry relations $N(x_1,x_2)=N(x_2,x_1)$ and $N(-x_1,-x_2)=-N(x_1,x_2)$, and is supported over the kinematic region $|x_1,2|<1$ and $|x_1-x_2|<1$.
Twist-3 transverse momentum dependent gluon distributions in a spectator model · Dynamical twist-3 TMDs · 0.82
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Its properties have been studied in [ref] . $G_4(x)$ is the twist-four counterpart of these distributions whose properties are virtually unknown.
$CP$-odd gluonic operators in QCD spin physics · First moment · 0.90
What it cites · 21 sentences without a confident label
Builds on 1 paper
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In this paper, we extend the study to gluonic twist-3 DFs and FFs for a spin-1/2 hadron [ref] and derive all of those exact relations.
Polarized hyperon production in single-inclusive electron-positron annihilation at next-to-leading order · Introduction · 0.83
Uses the method or tool of 3 papers
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The method was originally developed in [ref] , and have been frequently used for the twist-3 distributions [ref] , the twist-3 fragmentation functions [ref] , and the distribution amplitudes for hard exclusive processes [ref] , etc.
Twist-three relations of gluonic correlators for the transversely polarized nucleon · Constraint relations from nonlocal operator product expansion · 0.81
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The method was originally developed in [ref] , and have been frequently used for the twist-3 distributions [ref] , the twist-3 fragmentation functions [ref] , and the distribution amplitudes for hard exclusive processes [ref] , etc.
Operator Constraints for Twist-3 Functions and Lorentz Invariance Properties of Twist-3 Observables · Constraint relations from nonlocal operator product expansion · 0.81
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The method was originally developed in [ref] , and have been frequently used for the twist-3 distributions [ref] , the twist-3 fragmentation functions [ref] , and the distribution amplitudes for hard exclusive processes [ref] , etc.
Single Transverse Spin Asymmetry for Large-p_T Pion Production in Semi-Inclusive Deep Inelastic Scattering · Constraint relations from nonlocal operator product expansion · 0.81
Compares with 1 paper
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The result in ([ref]) and ([ref]) agrees with that in [ref] .
Twist-three relations of gluonic correlators for the transversely polarized nucleon · Solution for intrinsic and kinematical DFs in terms of twist-2 and dynamical twist-3 DFs · 0.96
Cites as background 39 papers
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Collinear twist-3 DFs and FFs can be in general classified into three types: intrinsic, kinematical and dynamical ones [ref] .
Operator Constraints for Twist-3 Functions and Lorentz Invariance Properties of Twist-3 Observables · Introduction · 0.89
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Such theoretical studies include those for $g_2$-structure function of the nucleon measured in deep-inelastic scattering [ref] , single spin asymmetries (SSA) for a hadron or (virtual) photon production in proton-proton (nucleus) collisions with one proton transversely polarized, $p^↑p→h X$ ($h=π, D, γ, γ^*$ etc) [ref] , $p^↑A→hX$ [ref] , and semi-inclusive deep-inelastic scattering (SIDIS), $ep^↑→ehX$ [ref] , SSA in transversely polarized hyperon production in the unpolarized proton-proton collision, $pp→Λ^↑X$ [ref] and in $e^+e^-$-collision, $e^+e^-→Λ^↑X$ [ref] , and the longitudinal-transverse double spin asymmetry $A_LT$ in the proton-proton collision, $p⃗p^↑→{h,γ^*} X$ [ref] , etc.
Twist-3 Formalism for Single Transverse Spin Asymmetry Reexamined: Semi-Inclusive Deep Inelastic Scattering · Introduction · 0.95
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Such theoretical studies include those for $g_2$-structure function of the nucleon measured in deep-inelastic scattering [ref] , single spin asymmetries (SSA) for a hadron or (virtual) photon production in proton-proton (nucleus) collisions with one proton transversely polarized, $p^↑p→h X$ ($h=π, D, γ, γ^*$ etc) [ref] , $p^↑A→hX$ [ref] , and semi-inclusive deep-inelastic scattering (SIDIS), $ep^↑→ehX$ [ref] , SSA in transversely polarized hyperon production in the unpolarized proton-proton collision, $pp→Λ^↑X$ [ref] and in $e^+e^-$-collision, $e^+e^-→Λ^↑X$ [ref] , and the longitudinal-transverse double spin asymmetry $A_LT$ in the proton-proton collision, $p⃗p^↑→{h,γ^*} X$ [ref] , etc.
Single spin asymmetry in forward $pA$ collisions: Phenomenology at RHIC · Introduction · 0.95
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