Hyperon production in $\Lambda_c^+\to K^-p\pi^+$ and $\Lambda_c^+\to K^0_Sp\pi^0 $

We investigate $S=-1$ hyperon production from the $\Lambda_c^+\to K^-p\pi^+$ and $\Lambda_c^+\to K^0_Sp\pi^0$ decays within the effective Lagrangian approach. We consider the $\Sigma/\Lambda$ ground states, $\Lambda(1520)$, $\Lambda(1670)(J^p=1/2^-)$, $\Lambda(1890)(J^p=3/2^+)$; $\Lambda/\Sigma$-pole contributions from the combined resonances between 1800 MeV and 2100 MeV; and $N/\Delta$-pole and $K^\ast$-pole contributions, which include the proton, $\Delta(1232)$, and $K(892)$. We calculate the Dalitz plot density $(d^2\Gamma/dM_{K^-p}dM_{K^-\pi^+}$) for the $\Lambda_c^+\to K^-p\pi^+$ decay. The calculated result is in good agreement with experimental data from the Belle Collaboration. Using the parameters from the fit, we present the Dalitz plot density for the $\Lambda_c^+\to K^0_Sp\pi^0$ decay. In our calculation, a sharp peak-like structure near 1665 MeV is predicted in the $\Lambda_c^+\to K^-p\pi^+$ decay because of the interference effects between the $\Lambda(1670)$ resonance and $\eta$-$\Lambda$ loop channels. We also demonstrate that we can access direct information regarding the weak couplings of $\Lambda(1670)$ and $\Sigma(1670)$ from the $\Lambda_c^+\to K^0_Sp\pi^0$ decay. Finally, a possible interpretation for the 1665 MeV structure beyond our prediction is briefly discussed.