$η$ photoproduction off the deuteron and low-energy $η$-nucleon interaction

We study $η$ photoproduction off the deuteron ($γd\toηpn$) at a special kinematics: $\sim 0.94$ GeV of the photon beam energy and $\sim 0^\circ$ of the scattering angle of the proton. This kinematics is ideal to extract the low-energy $η$-nucleon scattering parameters such as $a_{ηN}$ (scattering length) and $r_{ηN}$ (effective range) because the $η$-nucleon elastic scattering is significantly enhanced. We show that if a ratio $R$, the $γd\toηpn$ cross section divided by the $γp\toηp$ cross section convoluted with the proton momentum distribution in the deuteron, is measured with 5% error, ${\rm Re}[a_{ηN}]$ (${\rm Re}[r_{ηN}]$) can be determined at the precision of $\sim\pm$0.1 fm ($\sim\pm$0.5 fm), significantly narrowing down the currently estimated range of the parameters. The measurement is ongoing at the Research Center for Electron Photon Science (ELPH), Tohoku University.

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