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

TL;DR

This work analyzes the Cabibbo-favored decay $\Lambda_c^+ \to n \bar{K}^0 \pi^+$ within the chiral unitary framework, treating $N(1535)$ and $\Lambda(1670)$ as dynamically generated from coupled-channel meson–baryon interactions. By constructing the total amplitude $\mathcal{T}=\mathcal{T}^{N(1535)}+\mathcal{T}^{\Lambda(1670)}\,e^{i\phi}$, the study predicts a narrow $N(1535)$-induced peak in the $\pi^+ n$ invariant mass near $1.50$ GeV and a pronounced dip in the $\bar{K}^0 n$ invariant mass near $1.67$ GeV, reflecting the $\Lambda(1670)$ line shape seen in $\bar{K}N$ scattering. The results justify the interpretation of $\Lambda(1670)$ as a dynamically generated state and show how interference between resonant and non-resonant contributions, modulated by a relative phase $\phi$ and a color factor $C$, can reconcile isospin puzzles observed in different decay modes. The paper emphasizes the importance of precise amplitude analyses of $\Lambda_c^+ \to n K_S^0 \pi^+$ (and related channels) to constrain model parameters and illuminate the nature of these two enigmatic resonances, with implications for future experiments at BESIII, Belle II, LHCb, and Super Tau-Charm Factory.

Abstract

The Cabibbo-favored decay $Λ_c^+ \to n \bar{K}^0π^+$ 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 $Λ_c^+ \to p K^-π^+$ suggest the $pK^-$ ($I=0$) component dominates, while the BESIII hints at significant contributions from both isospin $0$ and $1$ in the $n\bar{K}^0$ system of $Λ_c^+ \to n K_S^0 π^+$. Furthermore, the measured branching fraction of $Λ_c^+ \to n K_S^0 π^+$ 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 $Λ_c^+ \to n \bar{K}^0π^+$ within the coupled-channel chiral unitary approach, where the $N(1535)$ and $Λ(1670)$ can be dynamically generated. Our calculations show a narrow peak from $N(1535)$ in the $π^+ n$ invariant mass spectrum and a distinct dip from $Λ(1670)$ in the $\bar{K}^0 n$ spectrum. The dip structure is qualitatively consistent with the $Λ(1670)$ 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 $Λ_c^+ \to n \bar{K}^0π^+$ as a crucial process to disentangle the nature of $N(1535)$ and $Λ(1670)$. Future precise measurements of this decay channel by the BESIII, Belle II, LHCb, and the proposed Super Tau-Charm Factory are strongly encouraged.

Figures (10)

• Figure 1: Quark level diagram for the process $\Lambda_c^+ \to \bar{K}^0MB$ via the $W^+$ internal emission.
• Figure 2: Quark level diagram for the process $\Lambda_c^+ \to \pi^+ M^{\prime}B^{\prime}$ via the $W^+$ external emission.
• Figure 3: The diagrams for the Tree-level (a) and the $MB$ rescattering (b) of the $\Lambda_c^+ \to n \bar{K}^0\pi^+$ decay.
• Figure 4: The diagrams for the Tree-level (a) and the $M^{\prime}B^{\prime}$ rescattering (b) of the $\Lambda_c^+ \to n \bar{K}^0\pi^+$ decay.
• Figure 5: Modulus squared of the transition amplitudes $t_{MB} \to \pi^+n$ in S-wave.