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 $N(1535)1\mathrm{/}{2}^{-}$, the $\eta d$ threshold structure connected to the isoscalar $S$-wave $N$-$N(1535)1\mathrm{/}{2}^{-}$ 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 ${\pi }^{0}d$ channel reveals the existence of a narrow isoscalar resonance-like structure with $1^{-}$ in the $\eta d$ system. Using a Flatt'e parametrization, the mass is found to be $2.427_{-0.006}^{+0.013}$ GeV, close to the $\eta d$ threshold, and the width is $\left(0.029_{-0.029}^{+0.006}{\rm
GeV}\right)+\left(0.00_{-0.00}^{+0.41}\right) p_\eta c$,where$p_\eta$ denotes the $\eta$ momentum in the rest frame of the $\eta d$ system. The observed structure would be attributed to a predicted isoscalar $1^{-}$ $\eta NN$ bound state from $\eta NN$ and $\pi NN$ coupled-channel calculation, or an $\eta d$ virtual state owing to strong $\eta d$ attraction.