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 $N\left(1535\right)1/2^{-}$, the $\eta d$ threshold structure connected to the isoscalar $S$-wave $N\text{−}N\left(1535\right)1/2^{-}$ 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 ${\pi }^{0}d$ channel reveals the existence of a narrow isoscalar resonance-like structure with $1^{-}$ in the $\eta d$ system. Using a Flatté parametrization, the mass is found to be $2.{427}_{-0.006}^{+0.013}$ GeV, close to the $\eta d$ threshold, and the width is $(0.{029}_{-0.029}^{+0.006}\mathrm{GeV})+(0.{00}_{-0.00}^{+0.41})p_{\eta }c$, 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.

Figure 1

Total cross section $\sigma$ as a function of the incident photon energy $E_{\gamma }$. The circles (blue) show $\sigma$ obtained in this work, and the triangles (magenta) show that obtained at the Mainz MAMI facility [52]. The horizontal error of each data point corresponds to the $E_{\gamma }$ coverage, and the vertical error corresponds to the statistical error of $\sigma$. The solid (red) and dashed (black) curves show theoretical calculations with $\eta d$ and other FSIs in Refs. [53, 54], respectively. The squares (cyan) show $\sigma$ obtained for the events with $M_{\eta d}<2.47$ GeV, and the dotted curve (green) shows the corresponding phase space contribution. The lower hatched histograms show the systematic errors of $\sigma$ with right-up straight lines for all the events (blue) and with left-up lines for $M_{\eta d}<2.47$ GeV (cyan).

Figure 2

Differential cross sections $d\sigma /d{M}_{\eta d}$ (left) and $d\sigma /d{M}_{\pi d}$ (right) at $E_{\gamma }=1.01$–1.15 GeV (top) and 0.95–1.01 GeV (bottom).

Figure 3

Acceptance-corrected angular distributions for ${\pi }^0$ with respect to the photon beam direction in the $\gamma d$-c.m. frame (left) and for $\eta$ with respect to the opposite direction to ${\pi }^0$ in the $\eta d$ rest frame (right) at $E_{\gamma }=1.01$–1.15 GeV (top) and 0.95–1.01 GeV (bottom). Events with $M_{\eta d}\le 2.47$ GeV are selected.