Proton and deuteron mass radii from near-threshold $phi$-meson photoproduction

We analyze the exclusive $phi$-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. From the precise CLAS data of wide $|t|$ range, we find that the proton and deuteron mass radii are $0.62 pm 0.09$ fm and $1.94 pm 0.45$ 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 the near-threshold $phi$ photoproduction on the hadronic systems.