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

The quality of recent SRC/CT Collaboration $J/\psi$ 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 $J/\psi$ photoproduction to access a variety of interesting physics aspects. An example is an estimate of the $J/\psi~p$ scattering length $|\alpha_{J/\psi~p}|$ 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 $|\alpha_{J/\psi~p}| = 3.08\pm 0.45~\mathrm{mfm}$, 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.