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 $etaNtoeta N$ 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 $costheta^{eta p}_{lab}<-0.9$ 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 quasifree $eta$ production rate. Our results indicate a small branching fraction of the $etaNtoeta N$ process and/or a shallow $eta$-nucleus potential.