Near-threshold heavy quarkonium photoproduction in a light-front spectator model

TL;DR

This paper develops a light-front gluon–spectator model to compute the proton's gluon gravitational form factors (GFFs) from gluonic EMT matrix elements, validating the results against lattice QCD and GPD analyses. It then embeds these GFFs into a generalized parton distribution framework to predict near-threshold photoproduction cross sections for heavy quarkonia, notably $J/\psi$ and $Upsilon$, via a leading-moment expansion that links the amplitude to $A_g(t)$, $B_g(t)$, and related GFFs. The model reproduces the measured differential and total cross sections for $J/\psi$ photoproduction from GlueX and $J/\psi$-007 across near-threshold energies, while illustrating the need for NLO corrections at large $|t|$ and providing robust predictions for $\Upsilon$ production. Overall, the work offers a coherent framework connecting the proton's gluonic structure to experimentally accessible observables, informing future measurements at JLab and EICs and highlighting the role of gluon dynamics in nucleon mechanics.

Abstract

The near-threshold photo- and electroproduction of heavy vector quarkonia off the proton provides direct access to its gluonic structure. In particular, the cross section for $J/Ψ$ photoproduction near threshold is governed by the proton's gluon gravitational form factors (GFFs). In this work, we employ the generalized parton distribution framework together with gluon GFFs calculated in a light-front gluon-spectator model inspired by soft-wall AdS/QCD to predict both the differential and total cross sections for near-threshold $J/Ψ$ and $Υ$ photoproductions. Our results for $J/Ψ$ photoproduction show good agreement with recent experimental data from the $J/Ψ$-007 and GlueX Collaborations at Jefferson Lab, as well as with earlier measurements from SLAC and Cornell.

Figures (6)

• Figure 1: The kinematically allowed regions, $-t_{\rm min} < -t < -t_{\rm max}$ (shown within the magenta curve), together with the corresponding skewness $\xi$ are displayed on the $(W,\,-t)$ plane using $M_{J/\psi} = 3.10~\text{GeV}$ for the $J/\psi$ and $M_{\Upsilon} = 9.46~\text{GeV}$ for $\Upsilon$ mesons, respectively.
• Figure 2: The gluon GFFs in the proton, $A_{g}(Q^2)$ (upper), $D_{g}(Q^2)$ (middle) and $J_g(Q^2)$ (lower), where $-t=Q^2$. Our results (solid blue line with blue band corresponding to the uncertainty in model parameters) are compared with the recent lattice QCD simulations Hackett:2023rif.
• Figure 3: The gluonic contribution to the proton angular momentum distribution, $\mathcal{J}_{g}(x)$ at $\mu_{0}=2$ GeV. Our result (solid blue line with blue band) is compared with the global analysis based on the GUMP1.0 GPDs (dashed red lin with red band) Guo:2025muf.
• Figure 4: Differential cross section $d\sigma/dt$ for $J/\psi$ photoproduction as a function of $-t$ at (upper panel) $\langle E_\gamma \rangle \approx 8.93\ \mathrm{GeV}$, (middle panel) $\langle E_\gamma \rangle \approx 9.85\ \mathrm{GeV}$, and (lower) $\langle E_\gamma \rangle \approx 10.82\ \mathrm{GeV}$. The blue lines with blue bands represent predictions from the gluon--spectator model, with widths indicating theoretical uncertainties from model parameters. Our results are compared with the data from the GlueX (solid circles) GlueX:2023pev and $J/\Psi$--007 (solid squares and triangles) Duran:2022xag experiments at JLab. The $J/\Psi$–007 data set with photon energy closest to that of the GlueX measurement is shown in the same plot for comparison.
• Figure 5: Total cross section $\sigma(\gamma p \to J/\psi p)$ as a function of photon energy $E_\gamma$. The blue line with blue band represent our prediction from the gluon--spectator model, with widths indicating theoretical uncertainties from model parameters. Experimental data are from GlueX 2019 (black circles) GlueX:2019mkq, GlueX 2023 (green squares) GlueX:2023pev, SLAC 1975 (orange triangles) Gittelman:1975ix, and Cornell 1975 (red diamond) Camerini:1975cy. Theoretical results from Guo et al. (I and II) Guo:2021ibgGuo:2023qgu are shown for comparison.