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.

United States

Yuxun Guo

Xiangdong Ji

Feng Yuan

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

Jinghong Yang

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.

Brandon Kriesten

Twist-three cross-sections in deeply virtual Compton scattering

We study the deeply virtual Compton scattering cross-section in twist-two generalized parton distribution (GPD) approximation, and show that different choices of light-cone vectors and gauges for the final photon polarization will lead to different higher-order kinematical corrections to the cross-section formula. The choice of light-cone vectors affects kinematic corrections at the twist-three level, accounting for the differences between the cross-section formulas in the literature. On the other hand, kinematical corrections from higher-twist GPDs should eliminate the light-cone dependence at twist three. Those light-cone dependencies are studied systematically at JLab 12 GeV and future EIC kinematics. They serve as the intrinsic systematic uncertainties in extracting the Compton form factors through the cross-section formula. More importantly, they are also necessary for understanding cross-section measurements with higher-twist precision and to reconstruct higher-order Compton form factors.

Higher-order kinematical effects in deeply virtual Compton scattering

We derive a new twist-3 partonic sum rule for the transverse spin of the proton, which involves the well-know quark spin structure function <math><msub><mrow><mi>g</mi></mrow><mrow><mi>T</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><msub><mrow><mi>g</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>+</mo><msub><mrow><mi>g</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo></math>, the less-studied but known transverse gluon polarization density <math><mi>Δ</mi><msub><mrow><mi>G</mi></mrow><mrow><mi>T</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo></math>, and quark and gluon canonical orbital angular momentum densities associated with transverse polarization. This is the counter part of the sum rule for the longitudinal spin of the proton derived by Jaffe and Manohar previously. We relate the partonic canonical orbital angular momentum densities to a new class of twist-3 generalized parton distribution functions which are potentially measurable in deep-virtual exclusive processes. We also discuss in detail an important technicality related to the transverse polarization in the infinite momentum frame, i.e., separation of intrinsic contributions from the extrinsic ones. We apply our finding to the transverse-space distributions of partons, angular momentum, and magnetic moment, respectively, in a transversely polarized proton.

Novel twist-three transverse-spin sum rule for the proton and related generalized parton distributions

The near-threshold photo or electroproduction of heavy vector quarkonium off the proton is studied in quantum chromodynamics. Similar to the high-energy limit, the production amplitude can be factorized in terms of gluonic generalized parton distributions and the quarkonium distribution amplitude. At the threshold, the threshold kinematics has a large skewness parameter <math><mi>ξ</mi></math>, leading to the dominance of the spin-2 contribution over higher-spin twist-2 operators. Thus, threshold production data are useful to extract the gluonic gravitational form factors, allowing studying the gluonic contributions to the quantum anomalous energy, mass radius, spin, and mechanical pressure in the proton. We use the recent GlueX data on the <math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> photoproduction to illustrate the potential physics impact from the high-precision data from the future Jefferson Laboratory 12 GeV and Electron-Ion Collider physics program.

Germany

QCD analysis of near-threshold photon-proton production of heavy quarkonium

Recently, Guo and Sun derived an identity for factorial Grothendieck polynomials which is a generalization of the one for Schur polynomials by Fehér, Némethi and Rimányi. We analyze the identity from the point of view of quantum integrability, based on the correspondence between the wavefunctions of a five-vertex model and the Grothendieck polynomials. We give another proof using the quantum inverse scattering method. We also apply the same idea and technique to derive an identity for factorial Grothendieck polynomials for rectangular Young diagrams. Combining with the Guo-Sun identity, we get a duality formula. We also discuss a q-deformation of the Guo-Sun identity.