$J/\psi$-$p$ Scattering Length from the Total and Differential Photoproduction Cross Sections

The $J/\psi$-$p$ scattering length, $\alpha_{J/\psi p}$, can be extracted from the $J/\psi$ photoproduction cross section near threshold using the Vector Meson Dominance (VMD) model to relate the reaction $\gamma p \to J/\psi p$ to $J/\psi p \to J/\psi p$. Such estimates based on experimental data result in values for $|\alpha_{J/\psi p}|$, which are much lower than most of the theoretical predictions. In this work, we study the relations between the different results, depending on the use of the total or the differential cross sections, and the method of extrapolating the data to threshold in the case of a low-statistics data sample, such as the near threshold $J/\psi$ photoproduction dataset. We estimate a range for $|\alpha_{J/\psi p}|$ of $0.003$ to $0.025$~fm as extracted from experimental data within the VMD model and discuss possible reasons for such lower values compared to the theoretical results.