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The anti-triplet charmed baryon decays with the light scalar mesons arerarely measured, whereas the recent observation of the Cabibbo-favored$\Lambda_c^+\to \Lambda\eta\pi^+$ decay hints a possible $\Lambda_c^+\to\Lambdaa_0(980)^+,a_0(980)^+\to \eta\pi^+$ process. We hence study the$\Lambda_c^+\to\Lambda a_0(980)^+$ decay. Particularly, it is found that thefinal state interaction can give a significant contribution, where$\Sigma^{+}(1385)$ and $\eta$ in $\Lambda_c^+\to \Sigma^{+}(1385)\eta$ byexchanging a charged pion are transformed as $\Lambda$ and $a_0(980)^+$,respectively. Accordingly, we predict ${\cal B}(\Lambda_c^+\to\Lambdaa_0(980)^+)=(1.7^{+2.8}_{-1.0}\pm 0.3)\times 10^{-3}$, accessible to theBESIII, BELLEII and LHCb experiments.

Cabibbo-favored $\Lambda^+_c\to\Lambda a_{0}(980)^+$ decay in the final state interaction