Unveiling the elusive Sigma(1380) resonance through coupled-channel dynamics in Λ_c^+toηπ^+Λ reaction

We investigate the $\Lambda_c^+ \to \eta \pi^+ \Lambda$ decay measured by the Belle and BESIII Collaborations, focusing on the possible role of the $\Sigma(1380)$ state with spin-parity $J^P=1/2^-$. In our theoretical framework, the $\Lambda(1670)$ and $a_0(980)$ are dynamically generated from meson-baryon and meson-meson final-state interactions, respectively, and the corresponding line shapes of these two states used here are applicable to all relevant hadronic reactions. Furthermore, the contributions from the intermediate $\Sigma(1385)$ resonance and the possible $\Sigma(1380)$ state are included explicitly. By comparing the invariant mass and angular distributions obtained with and without the $\Sigma(1380)$ state, we demonstrate that this state plays an important role in improving the description of the experimental data. We also identify the kinematic regions most sensitive to the possible $\Sigma(1380)$ contribution. Future high-precision measurements of this process will be instrumental for testing the existence of the $\Sigma$ state with $J^P=1/2^-$.