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We measured missing mass spectrum of the $^{12}{\rm C}(\gamma,p)$ reactionfor the first time in coincidence with potential decay products from $\eta'$bound nuclei. We tagged an ($\eta+p$) pair associated with the $\eta'N\to\etaN$ process in a nucleus. After applying kinematical selections to reducebackgrounds, no signal events were observed in the bound-state region. An upperlimit of the signal cross section in the opening angle $\cos\theta^{\etap}_{lab}<-0.9$ was obtained to be 2.2 nb/sr at the 90$\%$ confidence level. Itis compared with theoretical cross sections, whose normalization ambiguity issuppressed by measuring a quasifree $\eta'$ production rate. Our resultsindicate a small branching fraction of the $\eta'N\to\eta N$ process and/or ashallow $\eta'$-nucleus potential.

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