Extraction of the proton mass radius from the vector meson photoproductions near thresholds

We present an analysis of the proton mass radius by studying the $t$-dependence of the differential cross sections of the vector meson photoproductions near the thresholds. At low energy, the photoproduction of a quarkonium off the proton is connected to the scalar gravitational form factor of the proton, which is sensitive to the proton mass distribution from the QCD trace anomaly. Under an assumption of the scalar form factor of dipole form, the proton mass radius is extracted via the near-threshold photoproduction data of J/$\psi$, $\phi$ and $\omega$ vector mesons. The average value of the proton mass radius is estimated to be $\sqrt{\left<R_{\rm m}^2\right>} = 0.67\pm0.03$ fm, with the dipole cutoff $m_{\rm s}=1.01\pm0.04$ GeV.