Revisiting the deuteron mass radius via near-threshold $ρ^0$, $ω$ and $ϕ$ meson photoproduction

We present a comprehensive analysis of near-threshold photoproduction of $ρ^0$, $ω$, and $ϕ$ mesons on a deuterium target, utilizing published datasets from DESY and SLAC for $ρ^0$ and $ω$ production, as well as data from the LEPS and CLAS Collaborations for $ϕ$ production. In extracting the deuteron mass radius, we adopt a dipole parametrization for the scalar gravitational form factor, which effectively captures the $|t|$-dependence of the differential cross sections associated with vector meson photoproduction. In addition, results from alternative commonly used form factor parametrizations are also considered and compared. Employing the vector meson dominance (VMD) framework and invoking low-energy Quantum Chromodynamics (QCD) theorems, we extract the deuteron mass radius from near-threshold photoproduction data of $ρ^0$, $ω$, and $ϕ$ mesons. The mass radii obtained from the various datasets are found to be consistent within statistical uncertainties, yielding an average value of $2.03 \pm 0.13$ fm under the dipole form assumption. We also provide a detailed discussion of the sensitivity of the extracted radius to different choices of gravitational form factor models. Our result represents a significant improvement in precision compared to earlier estimates based solely on $ϕ$ meson photoproduction, offering new constraints for theoretical models of nuclear structure and deepening our understanding of the mass distribution within the deuteron.