Low-energy $\eta$-nucleon interaction studied with $\eta$ photoproduction off the deuteron

Abstract

We develop a reaction model for $\eta$ photoproduction off the deuteron ($\gamma d\to \eta pn$), and study the reaction at a special kinematics, where the photon beam energy is $\sim 0.94$ GeV and the scattered proton is detected at $\sim 0^{\circ }$, for the purpose of determining the $\eta$-nucleon scattering length ($a_{\eta N}$) and effective range ($r_{\eta N}$). In this kinematics, the $\eta$-nucleon elastic rescattering is significantly enhanced while other background mechanisms being suppressed. We show that 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, has a very good resolving power of $a_{\eta N}$ and $r_{\eta N}$. We conclude that the $R$ data with 5% error, binned in 1 MeV width of the $\eta$-neutron invariant mass, can determine $\mathrm{Re}[a_{\eta N}]$ ($\mathrm{Re}[r_{\eta N}]$) at the precision of $\sim \pm$0.1 fm ($\sim \pm$0.5 fm), significantly narrowing down the previously estimated ranges of the parameters. To arrive at the conclusion, it is essential to use the $\gamma d\to \eta pn$ reaction model equipped with elementary amplitudes that are well constrained by $\pi N$ and $\gamma N$ reaction data through a sophisticated coupled-channels analysis. This result strongly motivates the Research Center for Electron Photon Science (ELPH) at Tohoku University to measure $R$.

6 pages, 6 figures, published version, 1 figure added, several references added, discussion on the previous works elaborated

References in corpus (3)

• Study of the gp-->etap reaction with the Crystal Ball detector at the Mainz Microtron(MAMI-C)
• Isospin decomposition of $\gamma N\to N^{\ast }$ transitions within a dynamical coupled-channels model
• The role of pion exchange in $\eta$ meson photo production on the deuteron

Cited by in corpus (6)

• Electroweak pion-production on nuclei within the extended factorization scheme
• Impact of final state interactions on neutrino-nucleon pion production cross sections extracted from neutrino-deuteron reaction data
• Extraction of $\gamma n\to \pi N$ observables from deuteron-target data
• Photo- and Electro-excitation of Bound Neutrons and Protons
• Dynamical coupled-channels approach to electroweak meson productions on nucleon and deuteron
• $\eta$ photoproduction off the deuteron and low-energy $\eta$-nucleon interaction