$d_{N \Omega}$ production in $\Omega d$ scattering process

In the present work, we propose to investigate the production of $d_{N \Omega}$ in the $\Omega^{-} d \rightarrow p d_{N \Omega}^-$ process by utilizing an effective Lagrangian approach, where $d_{N \Omega}$ is identified as $N\Omega$ bound state with the binding energy $E_{b}=2.46$ MeV. Experimentally, the J-PARC hadron facility proposed to investigate the $K^{-}p \rightarrow \Omega^{-} \bar{K}^{(*)0} K^{+}$ process, which is expected to yield an $\Omega$ beam with the momentum of approximately 3 GeV. Additionally, theoretical studies of the $\psi(2S) \rightarrow \Omega^{-} \bar{\Omega}^{+}$ process at BESIII provided an $\Omega$ beam with the momentum of 774 MeV. Considering these two potential $\Omega$ beam sources, our estimations show that for the $\Omega^{-} d \rightarrow p d_{N \Omega}^-$ process, the cross sections are $\Big(329.7^{+26.9}_{-49.6}\Big)$ $\mu$b, $\Big(174.0^{+26.5}_{-38.2}\Big)$ $\mu$b, $\Big(16.9^{+7.4}_{-7.7}\Big)$ $\mu$b, and $\Big(2.0^{+1.8}_{-1.4}\Big)$ $\mu$b at $P_{\Omega} =$ 0.7, 0.9, 2.0, and 4.0 GeV, respectively, where the central values are estimated with $\Lambda_{r}=1.0$ GeV, and the errors come from the variation of $\Lambda_{r}$ from 0.8 to 1.2 GeV. We also estimate the differential cross sections, which reach the maximum at the forward angle limit. In addition, since the $d_{N \Omega}$ dibaryon predominantly decays into $\Xi \Lambda$. Therefore, we further investigate the $\Omega^{-} d \rightarrow p \Xi^- \Lambda$ process and estimate the relevant cross sections. It is expected that the present estimations can be tested by further experimental measurements at J-PARC and STCF in the future.