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 $ρ$-meson case using recent CLAS threshold data for the reaction $γp \to ρp$ within the meson-baryon reaction model~\cite{CLAS:2018drk}. The total $σ_t(γp\to ρp)$ and $σ_t(γp\to ωp)$ cross sections are close below the momentum of the vector meson in CM $q = 0.2~\mathrm{GeV/c}$. Then the $ρp$ photoproduction cross section grows rapidly. Our result for $ρN$ scattering length is a factor of 4 smaller than the size of the hadron and the phenomenological determination of the $ω$ nucleon scattering length using threshold photoproduction cross sections. The observed difference between $ρN$ and $ωN$ scattering lengths is of interest for further understanding within the hadron structure theory.