Probing the isospin structure and low-lying resonances in $\Lambda_c^+ \to n\bar{K}^0 \pi^+$ decays

The Cabibbo-favored decay $\Lambda_c^+ \to n \bar{K}^0\pi^+$ offers a unique window to explore unresolved puzzles in the low-energy baryon spectroscopy and the isospin dynamics of the $\bar{K}N$ system. Recent experimental results present a, for now, contradiction: LHCb and Belle analyses of $\Lambda_c^+ \to p K^-\pi^+$ suggest the $pK^-$ ($I=0$) component dominates, while the Beijing Spectrometer III (BESIII) hints at significant contributions from both isospin $0$ and $1$ in the $n\bar{K}^0$ system of $\Lambda_c^+ \to n K_S^0 \pi^+$. Furthermore, the measured branching fraction of $\Lambda_c^+ \to n K_S^0 \pi^+$ exceeds SU(3) symmetry predictions by a factor of 3-4, signaling strong contributions from low-lying resonances. In this work, we provide a theoretical analysis of $\Lambda_c^+ \to n \bar{K}^0\pi^+$ within the coupled-channel chiral unitary approach, where the $N(1535)$ and $\Lambda(1670)$ can be dynamically generated. Our calculations show a narrow peak from $N(1535)$ in the $\pi^+ n$ invariant mass spectrum and a distinct dip from $\Lambda(1670)$ in the $\bar{K}^0 n$ spectrum. The dip structure is qualitatively consistent with the $\Lambda(1670)$ manifestation in $\bar{K}N \to \bar{K}N$ scattering, supporting its molecular interpretation. This study not only connects the experimental observations but also highlights $\Lambda_c^+ \to n \bar{K}^0\pi^+$ as a crucial process to disentangle the nature of $N(1535)$ and $\Lambda(1670)$. Future precise measurements of this decay channel by the BESIII, Belle II, LHCb, and the proposed Super Tau-Charm Factory are strongly encouraged.