First extraction of proton mass radius and scattering length $\left|α_{ρ^0 p}\right|$ from $ρ^0$ photoproduction

Xiao-Yun Wang, Fancong Zeng, Quanjin Wang, Li Zhang

Published 2022-06-18Version 1

As the lightest physical states excited from the vacuum by the scalar gluon, $\rho^0$ photoproduction is considered to be a suitable way to extract proton mass radius and scattering lengths of $\rho^0$ and proton interaction. In this work, under the assumption of the scalar form factor of dipole form, the value of proton mass radius is calculated as $0.86\pm 0.08 \text{ fm }$ by fitting the differential cross section of $\gamma p \rightarrow \rho^0 p$ reaction at near-threshold energy $W=1.78 \text{ GeV}$. Moreover, the $\rho^0$-proton scattering lengths $\alpha_{\rho^0 p}=0.24 \pm 0.02 \text{ fm}$ is obtained for the first time within the vector meson dominance model. Correspondingly, the binding energy of $\rho^0$ in nuclear matter is calculated to be $23.6$ MeV. These results may provide useful theoretical information for an in-depth understanding of proton structure and its interaction with vector mesons.