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

Possibilities of observing a signal of an ${\eta }^{\mathrm{\prime }}n$ bound state are investigated by considering photoproductions of the $\eta$ and ${\eta }^{\mathrm{\prime }}$ mesons on a deuteron target with forward proton emission. For this purpose, we take the ${\eta }^{\mathrm{\prime }}n$ interaction from the linear sigma model with a coupling to $\eta n$, in which an $s$-wave ${\eta }^{\mathrm{\prime }}n$ 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 $\gamma d\to \eta np$ and $\eta ^{\prime} n p$reactionswithforwardprotonemissioninsingleand$\eta ^{(\prime )}$-exchange double scattering processes. As a result, we find that the signal of the ${\eta }^{\mathrm{\prime }}n$ bound state can be seen below the ${\eta }^{\mathrm{\prime }}n$ threshold in the $\eta n$ invariant mass spectrum of the $\gamma d \to \eta n p$reactionandiscomparablewiththecontributionfromthequasifree$\eta ^{\prime}$productionabovethe$\eta ^{\prime} n$ threshold. We also discuss the behavior of the signal of the ${\eta }^{\mathrm{\prime }}n$ bound state in several experimental conditions and model parameters.