We report the first global extraction of generalized parton distributions, GUMP 1.0, by combining deeply virtual Compton scattering and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>ρ</mi></mrow></math>-meson production data from Jefferson Lab and the Hadron-Electron Ring Accelerator with global fits of parton distribution functions, charge form factors, and lattice quantum chromodynamics simulations. Using a conformal moment space parametrization, we achieve a unified description across low- and high-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> regions at next to leading order accuracy in perturbative corrections. The results provide state-of-the-art generalized parton distributions consistent with almost all known facts, enabling three-dimensional nucleon imaging in impact parameter space and, at the same time, establishing a benchmark for future theoretical and experimental studies of the nucleon structure.

United States

Yuxun Guo

Fatma P. Aslan

Xiangdong Ji

M. Gabriel Santiago

First Global Extraction of Generalized Parton Distributions from Experiment and Lattice Data with Next-to-Leading-Order Accuracy

We phenomenologically constrain the small-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> and small-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ξ</mi></math> gluon generalized parton distributions (GPDs) with the deeply virtual <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> production (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>DV</mi><mi>J</mi><mo>/</mo><mi>ψ</mi><mi mathvariant="normal">P</mi></mrow></math>) in the framework of GPDs through universal moment parameterization (GUMP). We use a hybrid cross-section formula combining collinear factorization to the next-to-leading order (NLO) accuracy of the strong coupling <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mi>s</mi></msub></math>, with corrections from nonrelativistic QCD to account for the power corrections due to the heavy <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> mass. We reach reasonable fit to the measured differential cross sections of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>DV</mi><mi>J</mi><mo>/</mo><mi>ψ</mi><mi mathvariant="normal">P</mi></mrow></math> by H1 at the Hadron-Electron Ring Accelerator as well as forward gluon parton distribution functions (PDFs) from JAM22 global analysis. We find that both NLO and nonrelativistic corrections are significant for heavy vector meson productions. Of course, the gluon GPD we obtain still contains considerable freedom in need of inputs from other constraints, particularly in the distribution-amplitude-like region.

Jinghong Yang

China

Hao-Cheng Zhang

Small-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> gluon GPD constrained from deeply virtual <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> production and gluon PDF through universal-moment parametrization

With Bayesian inference, we investigate the impact of recent near-threshold <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> production measurements by the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi><mn>007</mn></mrow></math> experiment and GlueX Collaboration on the extraction of proton gravitational form factors. We apply the generalized parton distribution framework at the next to leading order and demonstrate a stable expansion for the near-threshold kinematics. We find that the experimental constraints are in good agreement with the state-of-the-art lattice simulations, where negative <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>C</mi><mi>q</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>C</mi></mrow><mrow><mi>g</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></math> are strongly preferred. This highlights a great potential to extract them from future high-precision experiments.

Feng Yuan

Wenbin Zhao

Bayesian Inferring Nucleon Gravitational Form Factors via Near-Threshold <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> Photoproduction

We study the forward-backward azimuthal angular correlations of hadrons in association with multiparticle production in the central rapidity region in proton-proton collisions at the LHC. We apply the nucleon energy-energy correlator framework, where the spinning gluon distribution introduces a nontrivial <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>cos</mi><mo stretchy="false">(</mo><mn>2</mn><mi>ϕ</mi><mo stretchy="false">)</mo></math> asymmetries. We will demonstrate that the fundamental helicity structure of quantym chromodynamics (QCD) amplitudes predicts a unique power counting rule: <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>cos</mi><mo stretchy="false">(</mo><mn>2</mn><mi>ϕ</mi><mo stretchy="false">)</mo></math> asymmetry starts at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msubsup><mi>α</mi><mi>s</mi><mn>2</mn></msubsup><mo stretchy="false">)</mo></math> order for dijet, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msub><mi>α</mi><mi>s</mi></msub><mo stretchy="false">)</mo></math> for three jet and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></math> for four (and more) jet productions. Our results will help us to understand the longstanding puzzle of nearside ridge behavior observed in high multiplicity events of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mi>p</mi></math> collisions at the LHC.

Xiaohui Liu

Germany

Long range energy-energy correlator at the LHC

We study the exclusive near threshold photoproduction of heavy quarkonium in the framework of the generalized parton distribution (GPD) factorization, taking the <math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> production as an example. Because of the threshold kinematics, the Compton-like amplitudes are related to gluon GPDs at large skewness <math><mi>ξ</mi></math>, distinct from the common kinematics in asymptotic high energy where the skewness is typically small. We discuss the nature of large-<math><mi>ξ</mi></math> expansion of these amplitudes in terms of the moments of gluon GPDs in the large-<math><mi>ξ</mi></math> limit. Based on that, we propose several ways to extract the first few moments of the gluon GPDs from these amplitudes, with the leading ones corresponding to the gluonic gravitational or energy-momentum tensor form factors (GFFs). We apply these methods to analyze the recent near threshold <math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> production measurements by the <math><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> 007 experiment and GlueX Collaboration and find that the <math><mi>ξ</mi></math> scaling of the measured differential cross sections is consistent with the asymptotic behavior. However, the current data are not accurate enough yet for a complete determination of the gluonic GFFs, and therefore we consider some prospects for better extractions in the future.

Proton’s gluon GPDs at large skewness and gravitational form factors from near threshold heavy quarkonium photoproduction

There has been growing interest in the near-threshold production of heavy quarkonium which can access the gluonic structure in the nucleon. Previously [ , Phys. Rev. D 103, 096010 (2021)], we studied this process with QCD and showed that it can be factorized with the gluon generalized parton distributions in the heavy quark limit. We further argued that the hadronic matrix element is dominated by its leading moments corresponding to the gluonic gravitational form factors (GFFs) in this limit. Since then, there have been many new developments on this subject. More experimental measurements have been made and published, and the lattice simulation of gluonic GFFs has been improved as well. In this work, we make an important revision to a previous result and perform an updated analysis with the new inputs. We also study the importance of the large momentum transfer to extract these gluonic structures reliably in this framework.

Poland

Yizhuang Liu

Updated analysis of near-threshold heavy quarkonium production for probe of proton’s gluonic gravitational form factors

We present the first global analysis of generalized parton distributions (GPDs) combing lattice quantum chromodynamics (QCD) calculations and experiment measurements including global parton distribution functions (PDFs), form factors (FFs) and deeply virtual Compton scattering (DVCS) measurements. Following the previous work where we parameterize GPDs in terms of their moments, we extend the framework to allow for the global analysis at non-zero skewness. Together with the constraints at zero skewness, we fit GPDs to global DVCS measurements from both the recent JLab and the earlier Hadron-Electron Ring Accelerator (HERA) experiments with two active quark flavors and leading order QCD evolution. With certain choices of empirical constraints, both sea and valence quark distributions are extracted with the combined inputs, and we present the quark distributions in the proton correspondingly. We also discuss how to extend the framework to accommodate more off-forward constraints beyond the small ξ expansion, especially the lattice calculated GPDs.

M. Santiago

Canada

Kyle Shiells

Generalized parton distributions through universal moment parameterization: non-zero skewness case

We present a global analysis program for the generalized parton distributions (GPDs) based on conformal moment expansion. We apply the strategy of universal moment parameterization to fit both the collinear parton distribution functions (PDFs) from phenomenology and generalized form factors from lattice calculations, and show that the parameterization is flexible enough to accommodate these constraints. In addition, we can also fit direct lattice calculations of GPDs from large-momentum effective theory. In this work we focus on the analysis of t-dependent PDFs which correspond to GPDs in the ξ → 0 limit. The strategy also applies to the ξ ≠ 0 region with extra parameters, and therefore can be fitted to experimental observables in the future. With a demonstrative example of fitted GPDs, we exhibit the quark transverse angular momentum densities of the proton as well as the impact parameter space distributions of quarks in both unpolarized and transversely polarized protons.

Generalized parton distributions through universal moment parameterization: zero skewness case

We investigate the exercise of locally extracting the real and imaginary parts of the four twist-2 Compton form factors (CFFs) <math> <mfenced> <mi>H</mi> <mi>E</mi> <mover> <mi>H</mi> <mo>~</mo> </mover> <mover> <mi>E</mi> <mo>~</mo> </mover> </mfenced> </math> $$ \left\{\mathcal{H},\mathcal{E},\overset{\sim }{\mathcal{H}},\overset{\sim }{\mathcal{E}}\right\} $$ which arise in the deeply virtual Compton scattering (DVCS) process e + p → e + p + γ. Neglecting dynamical higher-twist contributions, we find that there are a sufficient number of DVCS observables and degrees of freedom to extract all 8 leading quantities model-independently, exploiting the azimuthal dependence of the absolute cross sections across all possible beam and target polarizations at a common kinematical point in {Q, t, x B , y}. As an example, for typical JLab lab-frame kinematics, we simplify the reduced DVCS observables to their dominant terms, providing a sufficient number of equations for local determination of the twist-2 CFFs. We demonstrate the feasibility using harmonic fitting to both cross sections and beam spin asymmetries with both real and pseudo-data.

On extraction of twist-two Compton form factors from DVCS observables through harmonic analysis

We study the deeply virtual Compton scattering process with both twist-two and twist-three Compton form factors and present our cross-sections formulas with all polarization configurations. While the twist-three contributions are generally assumed to be negligible in the literature due to the kinematical suppression, we compare them with the twist-two ones at typical JLab 6 GeV and 12 GeV kinematics as well as EIC kinematics and show their kinematical suppression explicitly, justifying the leading-twist approximation made in the literature. In addition, we also estimate the twist-three Compton form factors using Wandzura-Wilczek relations and inputs of twist-two generalized parton distributions based on a reggeized spectator model. With those estimated Compton form factors, we analyze the kinematical behavior of twist-two and twist-three cross-sections in a wide range of kinematics, and discuss the optimal regions for separating the leading-twist effects from the higher-twist ones.