We analyze the exclusive $\varphi$-meson photoproduction on both hydrogen and deuterium targets based on the published data of CLAS, SAPHIR and LEPS collaborations. A dipole-form scalar gravitational form factor is applied to describe the $|t|$-dependence of the differential cross section. Based on the average of all the near-threshold data from CLAS, SAPHIR and LEPS, we find that the proton and deuteron mass radii are $0.75\pm 0.02\mathrm{fm}$ and $1.95\pm 0.19\mathrm{fm}$ respectively. The coherent and near-threshold quarkonium photoproduction seems to be sensitive to the radius of the hadronic system. The vector-meson-dominance model together with a low-energy QCD theorem well describe the data of near-threshold $\varphi$ photoproduction on the hadronic systems.

• Received 18 August 2021
• Accepted 8 October 2021

DOI:https://doi.org/10.1103/PhysRevD.104.074033

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Published by the American Physical Society