Search for $\eta'$ bound nuclei in the $^{12}{\rm C}(\gamma,p)$ reaction with simultaneous detection of decay products

We measured missing mass spectrum of the $^{12}{\rm C}(\gamma,p)$ reaction for the first time in coincidence with potential decay products from $\eta'$ bound nuclei. We tagged an ($\eta$+p) pair associated with the $\eta'N\to\eta N$ process in a nucleus. After applying kinematical selections to reduce backgrounds, no signal events were observed in the bound-state region. An upper limit of the signal cross section in the opening angle $\cos\theta^{\eta p}_{lab}<-0.9$ was obtained to be 2.2 nb/sr at the 90$\%$ confidence level. It is compared with theoretical cross sections, whose normalization ambiguity is suppressed by measuring a quasi-free $\eta'$ production rate. Our results indicate a small branching fraction of the $\eta'N\to\eta N$ process and/or a shallow $\eta'$-nucleus potential.