Extracting the Mass Radius of $^4$He from $\phi$-Meson Photoproduction Data

We extract the mass radius of $^4$He, a light nucleus, from near-threshold $\phi$-meson photoproduction data of the LEPS Collaboration. We evaluate the gravitational form factor using several function forms, including the monopole, dipole, Gauss, and hard-sphere forms. Our analysis reveals that the Gauss and hard-sphere form factors more accurately describe the differential cross sections in the small-$|t|$ range near the production threshold. The extracted mass radii based on the Gauss and hard-sphere form factors are $1.70\pm0.14$ fm and $1.37\pm0.08$ fm, respectively, with the combined average being smaller than the charge radius of $^4$He. More precise and wider $|t|$-coverage measurements of the coherent photoproductions of vector mesons off the nuclear target are necessary to distinguish between different models for describing the gravitational form factor and provide further insights into the mass radius of the nucleus.