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Evidence for a narrow $D_{03}$ state in $K^- p \rightarrow ηΛ$ near threshold

Recently, we reported a theoretical study on the $K^- p \to ηΛ$ reaction near threshold by using an effective Lagrangian approach. It was found that the description of angular distribution data measured by the Crystal Ball Collaboration needs a $D_{03}$ resonance with mass $M=1668.5\pm 0.5$ MeV and total decay width $Γ=1.5\pm 0.5$ MeV, which is not the conventional $Λ$(1690) or other $Λ$ state listed in the Particle Data Group book. In the present work, we study the $Λ$ polarization in the $K^- p \to ηΛ$ reaction within the same framework. The results show that the existence of this narrow $D_{03}$ state is also compatible with current $Λ$ polarization data and that the more accurate $Λ$ polarization data at $P_{K^-}=735$MeV can offer further evidence for the existence of this resonance. Furthermore, the role of the $Λ(1690)$ resonance in this reaction is also discussed.