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

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