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We theoretically investigate a possibility of an $\eta ^{\prime} d$ boundstate and its formation in the $\gamma d \to \eta d$ reaction. First, in thefixed center approximation to the Faddeev equations we obtain an $\eta^{\prime} d$ bound state with a binding energy of 25 MeV and width of 19 MeV,where we take the $\eta ^{\prime} N$ interaction with a coupling to the $\etaN$ channel from the linear $\sigma$ model. Then, in order to investigate thefeasibility from an experimental point of view, we calculate the cross sectionof the $\gamma d \to \eta d$ reaction at the photon energy in the laboratoryframe around 1.2 GeV. As a result, we find a clear peak structure with thestrength $\sim$ 0.2 nb/sr, corresponding to a signal of the $\eta ^{\prime} d$bound state in case of backward $\eta$ emission. This structure will beprominent because a background contribution coming from single-step $\eta$emission off a bound nucleon is highly suppressed. In addition, the signal canbe seen even in case of forward $\eta$ emission as a bump or dip, depending onthe relative phase between the bound-state formation and the single-stepbackground.

Possible $\eta' d$ bound state and its $s$-channel formation in the $\gamma d \to \eta d$ reaction