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

Abstract

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 $p{K}^{-}$ ($I=0$) 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.

10 pages, 10 figures

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