Theoretical study of photoproduction of $\eta ^{\prime} N$ bound state on deuteron target with forward proton emission

Abstract

Possibilities of observing a signal of an $\eta ^{\prime} n$ bound state are investigated by considering photoproductions of the $\eta$ and $\eta ^{\prime}$ mesons on a deuteron target with forward proton emission. For this purpose, we take the $\eta ^{\prime} n$ interaction from the linear sigma model with a coupling to $\eta n$, in which an $s$-wave $\eta ^{\prime} n$ bound state can be dynamically generated, and we fix the $\gamma p \to \eta p$ and $\eta ^{\prime} p$ scattering amplitudes so as to reproduce the experimental cross sections with forward proton emission. By using these $\gamma p \to \eta ^{( \prime )} p$ and $\eta ^{( \prime )} n \to \eta ^{( \prime )} n$ amplitudes, we calculate cross sections of the $\gamma d \to \eta n p$ and $\eta ^{\prime} n p$ reactions with forward proton emission in single and $\eta ^{(\prime )}$-exchange double scattering processes. As a result, we find that the signal of the $\eta ^{\prime} n$ bound state can be seen below the $\eta ^{\prime} n$ threshold in the $\eta n$ invariant mass spectrum of the $\gamma d \to \eta n p$ reaction and is comparable with the contribution from the quasifree $\eta ^{\prime}$ production above the $\eta ^{\prime} n$ threshold. We also discuss the behavior of the signal of the $\eta ^{\prime} n$ bound state in several experimental conditions and model parameters.