Resonance-like structure near the $ηd$ threshold in the $γ{d}${$\to$}$π^0η{d}$ reaction
To investigate the interaction between the nucleon $N$ and nucleon resonance $N(1535)1/2^-$, the $ηd$ threshold structure connected to the isoscalar $S$-wave $N$-$N(1535)1/2^-$ system has been experimentally studied in the $γ{d}${$\to$}$π^0η{d}$ reaction at incident photon energies ranging from the reaction threshold to 1.15 GeV. A strong enhancement is observed near the $ηd$ threshold over the three-body phase-space contribution in the $ηd$ invariant-mass distribution. An analysis incorporating the known isovector resonance $\mathcal{D}_{12}$ with a spin-parity of $2^+$ in the $π^0d$ channel reveals the existence of a narrow isoscalar resonance-like structure with $1^-$ in the $ηd$ system. Using a Flatté parametrization, the mass is found to be $2.427_{-0.006}^{+0.013}$ GeV, close to the $ηd$ threshold, and the width is $\left(0.029_{-0.029}^{+0.006}{\rm\ GeV}\right)+\left(0.00_{-0.00}^{+0.41}\right) p_ηc$, where $p_η$ denotes the $η$ momentum in the rest frame of the $ηd$ system. The observed structure would be attributed to a predicted isoscalar $1^-$ $ηNN$ bound state from $ηNN$ and $πNN$ coupled-channel calculation, or an $ηd$ virtual state owing to strong $ηd$ attraction.