$J/ψ$-Meson Nucleon Scattering Length from Threshold Photoproduction on Light Nuclei

TL;DR

This paper assesses the feasibility of extracting the J/ψ–N scattering length on bound protons from near-threshold incoherent photoproduction on light nuclei using a plane-wave impulse approximation and Vector Meson Dominance. It surveys theoretical predictions from QCD sum rules, EFT, and lattice QCD, highlighting a broad spread that motivates experimental input. By generating quasi-data for the SRC/CT E12-25-002 experiment on liquid He-4, it projects a precision of about 3.08 mfm with an uncertainty around 0.45 mfm, competitive with the free-proton measurement, enabling a direct test of medium modifications to gluon structure in nuclei. The work thus provides a concrete feasibility study linking realistic fluxes, spectral-function modeling, and existing GlueX constraints to constrain the J/ψ–N interaction in nuclear matter.

Abstract

The quality of recent SRC/CT Collaboration $J/ψ$ photoproduction data off a $^4$He target from Hall~D at Jefferson Laboratory, combined with the feasibility of measuring the reaction close to the free-nucleon energy threshold, opens the door to using incoherent $J/ψ$ photoproduction to access a variety of interesting physics aspects. An example is an estimate of the $J/ψ~p$ scattering length $|α_{J/ψ~p}|$ on the bound proton obtained using the Vector Meson Dominance model. This value can be compared with that of the free proton from the GlueX Collaboration. One may then project what would be expected from the SRC/CT Collaboration Experiment E12--25--002, which was recently approved by the JLab PAC. Using a plane-wave theoretical model to generate quasi-data, we find the experiment could achieve a result of $|α_{J/ψ~p}| = 3.08\pm 0.45~\mathrm{mfm}$, an uncertainty competitive with that of the free-proton measurement. A comparison between the two would allow an evaluation of the effects of medium modification in the case of light nuclei.

Figures (2)

• Figure 1: Projected yields for ($\gamma^4\mathrm{He}\to J/\psi pX$) as a function of beam photon energy $\varepsilon_\gamma$. Our estimate, shown as brown bars, is comparable to the estimate provided in the proposal for E12--25--002 Pybus:2025rba, which is represented by black points. The horizontal bars indicate the binning of Ref. Pybus:2025rba.
• Figure 2: The total $\gamma p \to J/\psi p$ cross section $\sigma_t$ as a function of the $J/\psi$ CM momentum includes measurements of the GlueX Collaboration with small statistics (blue filled circles, $469\pm 22~\mathrm{events}$) GlueX:2019mkqStrakovsky:2019bev and with high statistics (magenta filled triangles, $2270\pm 58~\mathrm{ events}$) GlueX:2023pev. Quasi-data for the total $\gamma ^4\mathrm{He} \to J/\psi~X$ cross section obtained from GCP, are shown as brown diamonds. Experimental results from the SRC/CT Collaboration are indicated by filled circles with black rings Pybus:2024ifi. The black dash-dotted curves represent polynomial fits to the the proton data (Eq. (\ref{['eq:eq2']})) and to the light nucleus ($^4$He) data (Eq. (\ref{['eq:eq3']})).