[Paper Review] Genuine twist-3 contributions to the generalized parton distributions from instantons

D. V. Kiptily, Maxim V. Polyakov|ArXiv.org|Dec 26, 2002

Quantum Chromodynamics and Particle Interactions17 references4 citations

TL;DR

This paper investigates genuine twist-3 quark-gluon contributions to generalized parton distributions (GPDs) in the instanton vacuum model. Using sum rules derived from the instanton vacuum, it finds that these contributions are parametrically suppressed by the small packing fraction of instantons, indicating they are negligible compared to leading-twist and kinematical twist-3 effects in the QCD vacuum.

ABSTRACT

The genuine twist-3 quark-gluon contributions to the Generalized Parton Distributions (GPDs) are estimated in the model of the instanton vacuum. These twist-3 effects are found to be parametrically suppressed relative to the ``kinematical'' twist-3 ones due to the small packing fraction of the instanton vacuum. We derive exact sum rules for the twist-3 GPDs.

Motivation & Objective

• To estimate genuine twist-3 quark-gluon (qGq) contributions to generalized parton distributions (GPDs) in the instanton vacuum model.
• To determine the relative magnitude of these twist-3 effects compared to kinematical twist-3 and twist-2 contributions.
• To derive exact sum rules for twist-3 GPDs within the instanton vacuum framework.
• To assess the role of the instanton packing fraction in suppressing genuine twist-3 matrix elements.

Proposed method

• The study employs the instanton vacuum model to compute non-perturbative matrix elements of bilocal light-cone operators relevant to GPDs.
• It derives exact sum rules for twist-3 GPDs using the structure of the instanton vacuum and the associated quark-gluon correlation functions.
• The analysis focuses on the $x^2$-moments of vector and axial-vector GPDs, decomposed into twist-2 (WW) and genuine twist-3 components.
• The suppression factor is quantified via the packing fraction $\pi^2(\rho^2/R^2)^2\ln(\rho^2/R^2)$, which governs the relative size of genuine twist-3 contributions.
• The model uses light-cone quantization and infinite momentum frame formalism to define the GPDs and their moments.
• The results are expressed in terms of the coefficient $d^{(2)}$, which is related to the instanton size and density.

Experimental results

Research questions

• RQ1 How do genuine twist-3 quark-gluon contributions to GPDs compare in magnitude to twist-2 and kinematical twist-3 effects in the instanton vacuum?
• RQ2 What is the role of the instanton packing fraction in suppressing genuine twist-3 matrix elements?
• RQ3 Can exact sum rules be derived for twist-3 GPDs within the instanton vacuum model?
• RQ4 What is the quantitative suppression factor of genuine twist-3 GPDs relative to the WW (twist-2) contributions?
• RQ5 How do the $x^2$-moments of the twist-3 GPDs depend on the Bjorken variable $\xi$ and the instanton parameters?

Key findings

• The genuine twist-3 contributions to the GPDs are parametrically suppressed relative to the twist-2 (WW) contributions by a factor of $\pi^2(\rho^2/R^2)^2\ln(\rho^2/R^2) \ll 1$.
• The $x^2$-moments of the genuine twist-3 vector GPDs $G_i^{tw3}$ vanish for $i=1$ and are proportional to $d^{(2)}$ for $i=2,3,4$, with explicit expressions given in Eqs. (92)–(94).
• The $x^2$-moments of the genuine twist-3 axial-vector GPDs $\widetilde{G}_i^{tw3}$ are zero for $i=1$ and proportional to $d^{(2)}$ for $i=2,3,4$, as shown in Eqs. (96)–(98).
• The suppression is driven by the small packing fraction of the instanton vacuum, which strongly reduces the effective strength of quark-gluon correlations.
• The coefficient $d^{(2)}$ is determined by the instanton size and density and is responsible for the overall scale of the genuine twist-3 contributions.
• The results indicate that in the instanton vacuum, genuine twist-3 effects are negligible compared to leading-twist and kinematical twist-3 terms in the GPD framework.