rho-Meson Nucleon Scattering Length from CLAS Threshold Photoproduction Measurements

Extending our study of the vector meson-nucleon scattering lengths (summary is given in Ref.~\cite{Strakovsky:2021vyk}), we are focusing on the $\rho$-meson case using recent CLAS threshold data for the reaction $\gamma p \to \rho p$ within the meson-baryon reaction model~\cite{CLAS:2018drk}. The total $\sigma_t(\gamma p\to \rho p)$ and $\sigma_t(\gamma p\to \omega p)$ cross sections are close below the momentum of the vector meson in CM $q = 0.2~\mathrm{GeV/c}$. Then the $\rho p$ photoproduction cross section grows rapidly. Our result for $\rho N$ scattering length is a factor of 4 smaller than the size of the hadron and the phenomenological determination of the $\omega$ nucleon scattering length using threshold photoproduction cross sections. The observed difference between $\rho N$ and $\omega N$ scattering lengths is of interest for further understanding within the hadron structure theory.