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Recently, the Belle Collaboration has measured the $\Lambda_c^+ \to \eta\Lambda \pi^+$ decay and reported the $\eta\Lambda$ and $\Lambda\pi^+ $invariant mass distributions, which show the clear signals of the resonances$\Lambda(1670)$ and $\Sigma(1385)$, respectively. Based on our previous works[Eur. Phys. J. C 76 (2016) 496 and Phys. Rev. D 95 (2017) 074024], were-analyze this process by considering the $S$-wave $\eta\Lambda$ and$\eta\pi^+$ final state interactions within the chiral unitary approach, whichdynamically generate the $\Lambda(1670)$ and $a_0(980)$, respectively. Ourresults are in good agreement with the Belle measurements, which supports themolecular nature of the $\Lambda(1670)$ and $a_0(980)$. In addition, the $\eta\pi^+$ invariant mass distributions are also computed and a cusp structure of$a_0(980)$ is cleary shown around the $K\bar{K}$ mass threshold.

Roles of $a_0(980)$, $\Lambda(1670)$, and $\Sigma(1385)$ in the $\Lambda_c^+ \to \eta \Lambda \pi^+$ decay