Revisiting the deuteron mass radius via near-threshold $\rho^0$, $\omega$ and $\phi$ meson photoproduction

We present a comprehensive analysis of the near-threshold photoproduction of the $\rho^0$, $\omega$, and $\phi$ mesons on a deuterium target, leveraging published datasets from the DESY and SLAC facilities. In our extraction of the deuteron mass radius, we employ a dipole-form scalar gravitational form factor to effectively model the $|t|$-dependence of the differential cross sections associated with vector meson photoproductions. Utilizing the vector-meson dominance model alongside a low-energy Quantum Chromodynamics (QCD) theorem assumption, we derive the deuteron mass radius from the near-threshold photoproduction data of the $\rho^0$, $\omega$, and $\phi$ mesons. The mass radii obtained from various datasets demonstrate consistency within the statistical uncertainties, yielding an average value of $2.07 \pm 0.15$ fm. This precision surpasses previous estimates solely based on the $\phi$ meson photoproduction data. Our findings provide novel constraints for theoretical nuclear structure models and significantly enhance our understanding of the mass distribution within the deuteron.