Low-energy η-nucleon interaction studied with η photoproduction off the deuteron

We develop a reaction model for eta photoproduction off the deuteron (gamma -> eta pn) and study the reaction at a special kinematics, where the photon beam energy is similar to 0.94 GeV and the scattered proton is detected at similar to 0 degrees, 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 are suppressed. We show that a ratio R, the gamma d -> eta pn cross section divided by the gamma d -> 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 Re[a(eta)N] (Re[r(eta)N]) at the precision of similar to +/- 0.1 fm (similar to +/- 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 -> eta pn reaction model equipped with elementary amplitudes that are well constrained by pi N and gamma N reaction data through a sophisticated coupled-channel analysis. This result strongly motivates the Research Center for Electron Photon Science (ELPH) at Tohoku University to measure R.