Near-Threshold J/$ψ\to μ^+μ^-$ Photoproduction and the Gluonic Gravitational Form Factors of the Proton

TL;DR

The paper tackles the problem of characterizing the proton's mechanical structure by probing gluonic gravitational form factors (GFFs) through near-threshold J/$\psi$ photoproduction. It combines the $J/\psi \to e^+e^-$ and $J/\psi \to \mu^+\mu^-$ decay channels in a holographic QCD framework to extract the gluonic GFF $\mathcal{C}_g(t)$ (with $\mathcal{A}_g(t)$ constrained as a dipole) from differential cross sections in photon energy $E_\gamma$ and momentum transfer $|t|$. The analysis finds no evidence for open-charm contributions near threshold and shows that the extracted $\mathcal{C}_g(t)$ is compatible with lattice QCD, enabling a gluonic pressure distribution in the Breit frame that supports a picture where gluons dominate at larger radii with an inward confining pressure. This work enhances our understanding of the proton's mechanical properties and sets the stage for higher-precision studies at facilities like SoLID-J/$\psi$ and the Electron-Ion Collider. The approach provides a path to quantify gluon contributions to mass and pressure in the proton from near-threshold photoproduction data.

Abstract

We report on the measurement of the two-dimensional differential cross section for near-threshold J/$ψ\to μ^+μ^-$ photoproduction from the J/$ψ$-007 experiment in Hall C at Jefferson Lab. Our results agree with the previously published J/$ψ\to e^+e^-$ results. We extract the integrated photoproduction cross section and find no evidence for open-charm contributions. A combined analysis of both decay channels following a Holographic QCD approach yields improved experimental constraints on the gluonic gravitational form factor $\mathcal{C}_g(t)$. Our results agree with recent lattice QCD calculations and we obtain $\mathcal{C}_g(t)$ with a comparable statistical precision to lattice QCD. Our results support a spatial picture where gluons dominate at larger radii with a confining inward pressure. This work provides new input for exploring the mechanical properties of gluons inside the proton.

Figures (4)

• Figure 1: Di-MIP invariant mass spectrum for kinematic setting 2. The figure shows the di-MIP signal sample (blue markers and histogram), di-pion background sample scaled to the signal sidebands (orange histogram), background fit (black curve), and background-subtracted di-muon signal (green histogram). The dashed lines indicate the integration window.
• Figure 2: Differential cross section for J/$\psi$$\to \mu^+\mu^-$ as a function of $|t|$ in slices of $E_\gamma$ (red circles) compared to the previous J/$\psi$$\to e^+e^-$ results from Ref. Duran:2022xag (blue squares). The orange band shows the 2D holographic QCD Mamo:2021krl*Mamo:2022eui fit to the combined J/$\psi$--007 data, with its associated uncertainty.
• Figure 3: Integrated cross section for the combined J/$\psi$--007 data as a function of $E_\gamma$, (purple squares), compared to GlueX GlueX:2023pev (open crosses) and Cornell Camerini:1975cy (open square).
• Figure 4: Gluonic pressure distribution in the Breit frame in GeV/fm, extracted from our combined data using a holographic QCD approach Mamo:2021krl*Mamo:2022eui (red), compared with gluon (green) and quark (blue) results from lattice QCD Pefkou:2021fni, based on a dipole-tripole GFF fit.