Toward establishing low-lying Λ and Σ hyperon resonances with the K ¯ + d → π + Y + N reaction
In this paper, a model for the $\bar{K}d→πYN$ reactions with $Y=Λ,Σ$ is developed, aiming at establishing the low-lying Λ and Σ hyperon resonances through analyzing the forthcoming data from the J-PARC E31 experiment. The off-shell amplitudes generated from the dynamical coupled-channels (DCC) model, which was developed in Kamano et al., are used as input to the calculations of the elementary $\bar{K}N→ \bar{K}N$ and $\bar{K}N→πY$ subprocesses in the $\bar{K}d→πYN$ reactions. It is shown that the cross sections for the J-PARC E31 experiment with a rather high incoming-$\bar{K}$ momentum, $|\vec{p}_\bar{K}|=1$ GeV, can be predicted reliably only when the input $\bar{K}N→ \bar{K}N$ amplitudes are generated from a $\bar{K}N$ model, such as the DCC model used in this investigation, which describes the data of the $\bar{K}N$ reactions at energies far beyond the $\bar{K}N$ threshold. We find that the data of the threefold differential cross section $dσ/(dM_{πΣ}dΩ_{p_n})$ for the $K^-d → πΣn$ reaction below the $\bar{K}N$ threshold can be used to test the predictions of the resonance poles associated with $Λ(1405)$. We also find that the momentum dependence of the threefold differential cross sections for the $K^-d → π^-Λp$ reaction can be used to examine the existence of a low-lying $J^P = 1/2^+Σ$ resonance with a pole mass $M_R=1457-i39$ MeV, which was found from analyzing the $K^-p$ reaction data within the employed DCC model.