Toward establishing low-lying $\Lambda$ and $\Sigma$ hyperon resonances with the $\bar{K}+d\to \pi +Y+N$ reaction

Abstract

A model for the $\bar{K}d\to \pi YN$ reactions with $Y=\Lambda ,\Sigma$ is developed, aiming at establishing the low-lying $\Lambda$ and $\Sigma$ 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 $\bar{K}N\to \pi Y$ subprocesses in the $\bar{K}d\to \pi YN$ 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 $\bar{K}N$ 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 $d\sigma /(d{M}_{\pi \Sigma }d{\Omega }_{p_n})$ for the $K^{-}d\to \pi \Sigma n$ reaction below the $\bar{K}N$ threshold can be used to test the predictions of the resonance poles associated with $\Lambda (1405)$. We also find that the momentum dependence of the threefold differential cross sections for the $K^{-}d\to {\pi }^{-}\Lambda p$ reaction can be used to examine the existence of a low-lying $J^P=1/2^{+}$ $\Sigma$ 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.

21 pages, 15 figures. Version to appear in PRC

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Cited by in corpus (3)

• QCD and the Strange Baryon Spectrum
• Pole position of $\Lambda (1405)$ measured in $d(K^{-},n)\pi \Sigma$ reactions
• Low-lying $\Lambda$ and $\Sigma$ resonances studied with the forward $K^{\ast }$ productions off the proton induced by a high-momentum $\pi$ beam