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Toward establishing low-lying $Λ$ and $Σ$ hyperon resonances with the $\bar K + d \to π+ Y + N$ reaction

A model for the $\bar K d \to πY N$ 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. [Phys. Rev. C 90, 065204 (2014)], are used as input to the calculations of the elementary $\bar K N \to \bar K N$ and $\bar K N \to πY$ subprocesses in the $\bar K d \to πY N$ 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 $\bar K N \to \bar K N$ amplitudes are generated from a $\bar KN$ 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 $K^- d \to πΣn$ 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 $K^- d \to π^- Λp$ 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.