$\eta$ photoproduction off the deuteron and low-energy $\eta$-nucleon interaction

Abstract

We study $\eta$ photoproduction off the deuteron ($\gamma d\to \eta pn$) 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 $\eta$-nucleon scattering parameters such as $a_{\eta N}$ (scattering length) and $r_{\eta N}$ (effective range) because the $\eta$-nucleon elastic scattering is significantly enhanced. We show that if a ratio $R$, the $\gamma d\to \eta pn$ cross section divided by the $\gamma p\to \eta p$ cross section convoluted with the proton momentum distribution in the deuteron, is measured with 5% error, $\mathrm{Re}[a_{\eta N}]$ ($\mathrm{Re}[r_{\eta N}]$) 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.

Comments: 4 pages, 5 figures, Contribution to the Proceedings for 8th International Conference on Quarks and Nuclear Physics (QNP2018), November 13-17, 2018, Tsukuba, Japan