[Paper Review] Parametrization of Quark and Gluon Generalized Parton Distributions in a Dynamical Framework

Brandon Kriesten, Philip Velie+3 more|arXiv (Cornell University)|Jan 5, 2021

Particle physics theoretical and experimental studiesPhysics and Astronomy52 references38 citations

TL;DR

This paper presents a flexible, dynamical parametrization of chiral-even generalized parton distributions (GPDs) for quarks, antiquarks, and gluons in the proton, using a spectator model framework with Regge-inspired behavior at low X. It achieves global consistency with electromagnetic, axial, pseudoscalar, and lattice QCD form factors, enabling perturbative QCD evolution and providing a first unified tool for global QCD analyses of deeply virtual exclusive processes.

ABSTRACT

We present a parametrization of the chiral even generalized parton distributions, $H$, $E$, $\widetilde{H}$, $\widetilde{E}$, for the quark, antiquark and gluon, in the perturbative QCD-parton framework. Parametric analytic forms are given as a function of two equivalent sets of variables $x,\xi,t$ (symmetric frame) and $X,\zeta,t$ (asymmetric frame), at an initial scale, $Q_o^2$. In the $X>\zeta$ region a convenient and flexible form is obtained as the product of a Regge term $\propto X^{-\alpha + \alpha' t}$, describing the low $X$ behavior, times a spectator model-based functional form depending on various mass parameters; the behavior at $X<\zeta$, is determined using the generalized parton distributions symmetry and polynomiality properties. The parameters are constrained using data on the flavor separated nucleon electromagnetic elastic form factors, the axial and pseudoscalar nucleon form factors, and the parton distribution functions from both the deep inelastic unpolarized and polarized nucleon structure functions. For the gluon distributions we use, in particular, constraints provided by recent lattice QCD moments calculations. The parametrization's kinematical range of validity is: $0.0001 \leq X \leq 0.85$, $0.01 \leq \zeta \leq 0.85$, $0 \leq -t \leq 1$ GeV$^2$, $2 \leq Q^2 \leq 100$ GeV$^2$. With the simultaneous description of the quark, anti-quark and gluon sectors, this parametrization represents a first tool enabling a global QCD analysis of deeply virtual exclusive experiments.

Motivation & Objective

• To develop a unified, flexible parametrization of chiral-even GPDs (H, E, eH, eE) for quarks, antiquarks, and gluons in the proton.
• To ensure consistency with electromagnetic, axial, pseudoscalar, and lattice QCD form factors across a wide kinematic range.
• To enable perturbative QCD evolution of GPDs from an initial scale Q²₀ ≈ 0.1–0.58 GeV² to higher scales relevant for experimental data.
• To provide a first global framework for analyzing deeply virtual exclusive processes, including DVCS and meson production.
• To extend the applicability of GPD models to include gluon and sea quark components with controlled dynamics from initial scale evolution.

Proposed method

• Constructs GPDs using a spectator model framework with variable spectator masses, modeling proton-parton-spectator vertices via form factors.
• Applies Regge-inspired behavior (X⁻α+α't) for low-X region (X > ζ), combined with spectator model forms for mass-dependent structure.
• Imposes polynomiality and symmetry constraints (e.g., GPD symmetry under X ↔ 1−X) to define behavior in the X < ζ region.
• Uses two kinematic frames: symmetric (x, ξ, t) and asymmetric (X, ζ, t), with X and ζ related by X = (1+ξ)x and ζ = ξ.
• Performs perturbative QCD evolution at leading order (LO), with a NLO extension outlined for future work.
• Constrains parameters recursively: first fitting forward limits (H, E) to PDFs and form factors, then fitting t-dependence to electromagnetic and axial form factors.

Experimental results

Research questions

• RQ1 How can a unified parametrization of quark, antiquark, and gluon GPDs be constructed that respects QCD symmetries and evolution?
• RQ2 What functional form best captures the low-X behavior of GPDs while maintaining consistency with polynomiality and symmetry constraints?
• RQ3 How can constraints from electromagnetic, axial, pseudoscalar, and lattice QCD form factors be simultaneously incorporated into a single GPD parametrization?
• RQ4 To what extent can the initial scale dynamics (Q²₀ ≈ 0.1–0.58 GeV²) be used to generate sea quark and gluon components via perturbative evolution?
• RQ5 Can this parametrization serve as a foundation for global QCD analyses of deeply virtual exclusive reactions across multiple channels?

Key findings

• The parametrization covers a kinematic range of 0.0001 ≤ X ≤ 0.85, 0.01 ≤ ζ ≤ 0.85, and 0 ≤ −t ≤ 1 GeV², with evolution up to Q² = 100 GeV².
• The model successfully reproduces the forward limit of GPDs (H, E) at Q²₀ ≈ 0.1 GeV², matching known PDFs for valence quarks.
• The inclusion of lattice QCD moments for gluon distributions provides strong constraints on the gluon GPD parameters.
• The parametrization achieves consistency with nucleon electromagnetic, axial, and pseudoscalar form factors across the kinematic range.
• The use of Regge behavior (X⁻α+α't) in the X > ζ region provides a flexible and physically motivated description of the low-X structure.
• The model is the first to simultaneously describe all chiral-even GPD components (H, E, eH, eE) for quarks, antiquarks, and gluons in a single, consistent framework with perturbative evolution.