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

TL;DR

This paper predicts an $ ext{eta'}d$ bound state with specific binding energy and width, and suggests it can be observed experimentally through a distinct peak in the $ ext{gamma}d o ext{eta}d$ reaction cross section around 1.2 GeV.

Contribution

It introduces a theoretical prediction of an $ ext{eta'}d$ bound state and analyzes its formation and experimental signatures in photon-deuteron reactions.

Findings

Predicted an $ ext{eta'}d$ bound state with 25 MeV binding energy and 19 MeV width.

Calculated a clear peak in the cross section at 1.2 GeV indicating the bound state's formation.

The signal is prominent in backward $ ext{eta}$ emission and observable even in forward emission depending on phase.

Abstract

We theoretically investigate a possibility of an $\eta ^{\prime} d$ bound state and its formation in the $\gamma d \to \eta d$ reaction. First, in the fixed 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 $\eta N$ channel from the linear $\sigma$ model. Then, in order to investigate the feasibility from an experimental point of view, we calculate the cross section of the $\gamma d \to \eta d$ reaction at the photon energy in the laboratory frame around 1.2 GeV. As a result, we find a clear peak structure with the strength $\sim$ 0.2 nb/sr, corresponding to a signal of the $\eta ^{\prime} d$ bound state in case of backward $\eta$ emission. This structure will be prominent because a background contribution coming from single-step $\eta$ emission off a bound nucleon is highly suppressed. In addition, the signal can be seen even in case of forward $\eta$ emission as a bump or dip, depending on the relative phase between the bound-state formation and the single-step background.