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

We measured missing mass spectrum of the $^{12}{\rm C}(γ,p)$ reaction for the first time in coincidence with potential decay products from $η&#39;$ bound nuclei. We tagged an ($η+p$) pair associated with the $η&#39;N\toηN$ 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 $\cosθ^{ηp}_{lab}<-0.9$ 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 quasifree $η&#39;$ production rate. Our results indicate a small branching fraction of the $η&#39;N\toηN$ process and/or a shallow $η&#39;$-nucleus potential.