[Paper Review] Global analysis of generalized parton distributions -- collider kinematics --

Tobias Lautenschlager, A.H. Mueller+1 more|arXiv (Cornell University)|Dec 19, 2013

Particle physics theoretical and experimental studies29 references3 citations

TL;DR

This paper presents a global next-to-leading order (NLO) analysis of generalized parton distributions (GPDs) using H1 and ZEUS data on exclusive electroproduction of photons, ρ⁰, and φ mesons at HERA. Employing Bayesian inference with flexible parametrization and perturbative QCD, it provides a quantitative partonic interpretation of sea quarks and gluons, revealing a mild t-dependence of the GPDs in the small-xB region and confirming compatibility with prior DVCS-based GPD models.

ABSTRACT

We utilize H1 and ZEUS data for exclusive electroproduction of photons, $ρ^0$- and $ϕ$-mesons to access generalized parton distributions at small momentum fraction. To do so, we employ state-of-the art techniques, based on next-to-leading order perturbation theory, flexible model parametrization, and Bayesian inference. We provide a partonic interpretation of our analysis, where emphasize is given to the transverse distribution of sea quarks and gluons.

Motivation & Objective

• To perform a global, next-to-leading order (NLO) analysis of generalized parton distributions (GPDs) using hard exclusive electroproduction data from H1 and ZEUS.
• To access the transverse partonic structure of the nucleon, particularly the distribution of sea quarks and gluons, in the small-xB region.
• To test the validity of the perturbative framework in the small-xB regime, where the onset of perturbative QCD is debated.
• To assess the sensitivity of GPDs to the t-dependence of the effective soft-overlap wave functions and the impact of model assumptions.

Proposed method

• Utilizes H1 and ZEUS data on exclusive electroproduction of photons, ρ⁰, and φ mesons in the small-xB region.
• Applies next-to-leading order (NLO) perturbative QCD for the hard scattering amplitudes and evolution kernels.
• Employs a flexible model parametrization of GPDs and distribution amplitudes (DAs) at the input scale Q₀ = 2 GeV.
• Uses Bayesian inference to extract GPD parameters, enabling full posterior probability distributions and error propagation.
• Implements Mellin-Barnes integrals to compute Compton form factors (CFFs) and transition form factors (TFFs) from GPD and DA moments.
• Analyzes the t-dependence of the effective soft-overlap wave functions and their impact on transverse partonic densities in impact parameter space.

Experimental results

Research questions

• RQ1 Can a global NLO GPD analysis be successfully performed using DVCS and DVMP data in the small-xB region, despite the complexity of the kinematics and the need for high-order angular resolution?
• RQ2 To what extent do the t-dependences of the effective soft-overlap wave functions differ for different meson channels, and what does this imply for the transverse structure of partons?
• RQ3 How sensitive are the extracted GPDs to assumptions about flavor symmetry, distribution amplitudes, and the neglect of the GPD E function?
• RQ4 What is the role of the flavor-singlet GPD component in governing the longitudinal polarization electroproduction of vector mesons at small xB?
• RQ5 Can Bayesian inference provide a robust, probabilistic interpretation of GPD parameters and their uncertainties, especially in the context of high-precision future data?

Key findings

• The NLO global GPD analysis provides a satisfactory description of H1 and ZEUS data on exclusive electroproduction of photons, ρ⁰, and φ mesons in the small-xB region.
• The transverse partonic density profiles for sea quarks and gluons at x = 10⁻³ and Q² = 4 GeV² show a mild t-dependence, indicating limited sensitivity to the t-structure of the soft-overlap wave functions.
• The analysis confirms compatibility with previous DVCS-based GPD models, particularly regarding the skewness effect and the transverse distribution of sea quarks and gluons.
• Bayesian inference successfully propagates experimental errors and allows for a probabilistic interpretation of parameter sensitivities, showing that the t-dependence differences among effective soft-overlap wave functions are likely small.
• The results suggest that future global GPD analyses should include fixed-target data and update models, especially for DVCS, to improve consistency across kinematic regimes.
• The study indicates that a consistent NLO framework is sufficient for quantitative GPD studies, and that higher-twist or non-collinear extensions are not currently necessary for the present data.