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The reaction $K^-p\rightarrow\Lambda\eta$ at low energies is studied with achiral quark model approach. Good descriptions of the existing experimentaldata are obtained. It is found that $\Lambda(1670)$ dominates the reactionaround threshold. Furthermore, $u$- and $t$-channel backgrounds play crucialroles in this reaction as well. The contributions from the $D$-wave state$\Lambda(1690)$ are negligibly small for its tiny coupling to $\eta\Lambda$. Tounderstand the strong coupling properties of the low-lying negative parity$\Lambda$ resonances extracted from the $\bar{K}N$ scattering, we further studytheir strong decays. It is found that these resonances are most likely mixedstates between different configurations. Considering these low-lying negativeparity $\Lambda$ resonances as mixed three-quark states, we can reasonablyunderstand both their strong decay properties from Particle Data Group andtheir strong coupling properties extracted from the $\bar{K}N$ scattering. As abyproduct, we also predict the strong decay properties of the missing $D$-wavestate $|\Lambda\frac{3}{2}^-\ >_3$ with a mass of $\sim1.8$ GeV. We suggest ourexperimental colleagues search it in the $\Sigma(1385)\pi$ and $\Sigma\pi$channels.

Low energy reaction $K^-p\rightarrow\Lambda\eta$ and the negative parity $\Lambda$ resonances