Resonance-like structure near the $\eta d$ threshold in the $\gamma{d}${$\to$}$\pi^0\eta{d}$ reaction

To investigate the interaction between the nucleon $N$ and nucleon resonance $N(1535)1/2^-$, the $\eta d$ threshold structure, connected to the isoscalar $S$-wave $N$-$N(1535)1/2^-$ system, has been experimentally studied in the $\gamma{d}${$\to$}$\pi^0\eta{d}$ reaction at incident photon energies ranging from the reaction threshold to 1.15 GeV. A strong enhancement is observed near the $\eta d$ threshold over the three-body phase-space contribution in the $\eta d$ invariant-mass distribution. An analysis incorporating the known isovector resonance $\mathcal{D}_{12}$ with a spin-parity of $2^+$ in the $\pi^0d$ channel has revealed the existence of a narrow isoscalar resonance-like structure $\mathcal{D}_{\eta d}$ with $1^-$ in the $\eta d$ system. The Breit-Wigner mass of $\mathcal{D}_{\eta d}$ is found to be $2.425^{-0.006}_{+0.003}$ GeV, located just close to the $\eta d$ threshold, and the width is $0.034_{-0.003}^{+0.004}$ GeV. The $\mathcal{D}_{\eta d}$ would be a predicted isoscalar $1^-$ $\eta NN$ bound state from the $\eta NN$ and $\pi NN$ coupled-channel calculation, or $\eta d$ virtual state owing to strong $\eta d$ attraction.