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We propose to study the $a_0(980)$ and the $\Lambda(1670)$ resonances in the$\Lambda^+_c \to \pi^+ \eta \Lambda$ decay via the final state interactions ofthe $\pi^+ \eta$ and $\eta \Lambda$ pairs. The weak interaction part proceedsthrough the $c$ quark decay process: $c(ud) \to (s + u + \bar d)(ud)$, whilethe hadronization part takes place in two different mechanisms. In the firstmechanism, the $sud$ cluster picks up a $q\bar{q}$ pair from the vacuum to formthe $\eta\Lambda$ meson-baryon pair while the $u\bar{d}$ pair from the weakdecay hadronizes into a $\pi^+$. In the second, the $sud$ cluster turns into a$\Lambda$, while the $u\bar{d}$ pair from the $c$ decay picks up a $q\bar{q}$pair and hadronizes into a meson-meson pair ($\pi\eta$ or $K\bar{K}$). Becausethe final $\pi^+ \eta$ and $\eta \Lambda$ states are in pure isospin $I = 1$and $I=0$ combinations, the $\Lambda^+_c \to \pi^+ \eta \Lambda$ decay can bean ideal process to study the $a_0(980)$ and $\Lambda(1670)$ resonances.Describing the final state interaction in the chiral unitary approach, we findthat the $\pi^+ \eta$ and $\eta \Lambda$ invariant mass distributions, up to anarbitrary normalization, show clear cusp and peak structures, which can beassociated with the $a_0(980)$ and $\Lambda(1670)$ resonances, respectively.The proposed mechanism can provide valuable information on the nature of theseresonances and can in principle be test by facilities such as BEPCII.

The $a_0(980)$ and $\Lambda(1670)$ in the $\Lambda^+_c \to \pi^+ \eta \Lambda$ decay