Role of $\Sigma^*(1/2^-)$ baryons in $\Lambda_c\to \Lambda\pi^+\pi^+\pi^-$ decay

Based on Belle data, the structure around 1435 MeV and the role of the $\Sigma(1380)$ resonance in the decay process $\Lambda_c \to \Lambda \pi^- \pi^+ \pi^+$ are investigated. The $\Lambda \pi^\pm$ invariant mass spectra are approximately reproduced by the contribution from the $\Sigma(1385)$, modeled as a Breit-Wigner resonance combined with background. However, an additional contribution is required to account for the pronounced enhancement near 1435 MeV. To describe this structure, two scenarios are considered for the $\Sigma(1435)$: one as a Breit-Wigner resonance with spin-parity $1/2^-$ described via effective Lagrangians, and the other as a rescattering effect arising from coupled-channel interactions. Specifically, the channels $\bar{K}^0p$, $\pi^0\Sigma^+$, $\pi^+\Sigma^0$, $\pi^+\Lambda$, and $\eta\Sigma^+$ are included for the positively charged mode, and $K^-n$, $\pi^0\Sigma^-$, $\pi^-\Sigma^0$, $\pi^-\Lambda$, and $\eta\Sigma^-$ for the negatively charged mode. The rescattering contributions are evaluated using the quasipotential Bethe-Salpeter equation approach. Simulated invariant mass spectra are generated and fitted to the experimental data. Both the Breit-Wigner and rescattering mechanisms provide reasonable descriptions of the enhancement near 1435 MeV. The rescattering approach naturally generates a cusp-like structure near threshold, which closely resembles the feature observed in the data. Furthermore, the inclusion of the $\Sigma(1380)$ resonance with spin-parity $1/2^-$ significantly improves the fit in the low-energy region and further enhances the description near 1435 MeV through interference effects. These results underscore the essential roles of the two $\Sigma^*(1/2^-)$ states in accurately describing the invariant mass distributions in the decay $\Lambda_c \to \Lambda \pi^+ \pi^+ \pi^-$.