Comparative analysis of $omega p$, $phi p$, and $J/psi p$ scattering lengths from A2, CLAS, and GlueX threshold measurements

The high accuracy $phi $-meson photoproduction data from the CLAS experiment in Hall~B of Jefferson Laboratory allow us to determine the near-threshold total cross section of the $gamma ptophi p$ reaction and use it for evaluating the $phi p$ scattering length $alpha_{phi p}$. These data result in an absolute value of $|alpha_{phi p}| = (0.063pm 0.010)$~fm, which is smaller than the typical hadron size. A comparative analysis of $alpha_{phi p}$ with the previously determined scattering lengths for $omega p$ and $J/psi p$ from the A2 and GlueX experiments is performed.