Low energy reaction $K^-p\rightarrowΛη$ and the negative parity $Λ$ resonances

Abstract

The reaction $K^-p\rightarrowΛη$ at low energies is studied with a chiral quark model approach. Good descriptions of the existing experimental data are obtained. It is found that $Λ(1670)$ dominates the reaction around threshold. Furthermore, $u$- and $t$-channel backgrounds play crucial roles in this reaction as well. The contributions from the $D$-wave state $Λ(1690)$ are negligibly small for its tiny coupling to $ηΛ$. To understand the strong coupling properties of the low-lying negative parity $Λ$ resonances extracted from the $\bar{K}N$ scattering, we further study their strong decays. It is found that these resonances are most likely mixed states between different configurations. Considering these low-lying negative parity $Λ$ resonances as mixed three-quark states, we can reasonably understand both their strong decay properties from Particle Data Group and their strong coupling properties extracted from the $\bar{K}N$ scattering. As a byproduct, we also predict the strong decay properties of the missing $D$-wave state $|Λ\frac{3}{2}^-\ >_3$ with a mass of $\sim1.8$ GeV. We suggest our experimental colleagues search it in the $Σ(1385)π$ and $Σπ$ channels.