Search for the low-lying excited baryon $Σ^*(1/2^-)$ through process $Λ^+_c \to ΛK^0 π^+$

TL;DR

This paper investigates the singly Cabibbo-suppressed decay $\Lambda_c^+ \to \Lambda K^0 \pi^+$ to search for the low-lying $\Sigma^*(1/2^-)$ resonance, predicted to arise dynamically from $S$-wave meson-baryon interactions near the $\bar{K}N$ threshold. The authors construct a theoretical framework combining weak external emission, hadronization, and final-state interactions within a chiral unitary approach, explicitly including $\Sigma^*(1/2^-)$, $N(1535)$, and $K^*(892)$ intermediate contributions. They formulate amplitudes for both the $\Sigma^*(1/2^-)$ and $N(1535)$ channels via Bethe–Salpeter equations and implement a $K^*(892)$ mechanism, then compute invariant-mass distributions and Dalitz plots with two phase parameters and a normalization fixed by BESIII data. Fitting to BESIII $\pi^+K^0$ distributions yields a good description ($\chi^2/\text{d.o.f.}=0.92$) and predicts a cusp at $M(\pi^+\Lambda)\approx1.43$ GeV associated with $\Sigma^*(1/2^-)$, providing a concrete experimental signature. The results motivate precise measurements at BESIII, Belle II, and STCF to test the existence of $\Sigma^*(1/2^-)$ and deepen our understanding of the light-baryon spectrum within QCD.

Abstract

Motivated by recent BESIII measurements of the singly Cabibbo-suppressed processes $Λ^+_c \to ΛK^+ π^0$ and $Λ^+_c \to ΛK_S^0 π^+$, we investigate the process $Λ^+_c \to ΛK^0 π^+$ by taking into account the contribution from the low-lying excited baryon $Σ^*(1/2^-)$, dynamically generated via the $S$-wave pseudoscalar meson-octet baryon interaction, as well as from the intermediate resonances $K^*(892)$ and $N(1535)$. Our model successfully reproduces the BESIII $π^+K^0$ invariant mass distribution, and predicts a distinct cusp structure around 1.43~GeV in the $π^+Λ$ invariant mass distribution, which is associated with the predicted $Σ^*(1/2^-)$. Future high-precise measurements of this process at BESIII, Belle~II, and the proposed Super Tau-Charm Facility experiments will be crucial for testing the existence of $Σ^*(1/2^-)$ and advancing our understanding of the light baryon spectrum.

Figures (6)

• Figure 1: Feynman diagram at the quark level for the weakly process $\Lambda_{c}^{+}\rightarrow \pi^{+}d(\bar{u}u+\bar{d}d+\bar{s}s)ud$.
• Figure 2: Mechanisms for the process $\Lambda^+_c \to \Lambda K^0 \pi^+$ decay. (a) tree diagram, (b) the $\pi^+\Lambda$ final interaction, and (c) the $K^0\Lambda$ final interaction.
• Figure 3: Mechanisms for the $\Lambda^+_c \to \Lambda K^0 \pi^+$ decay via the intermediate $K^*(892)$.
• Figure 4: The $K^0 \Lambda$(a), $\pi^+ \Lambda$(b) and $\pi^+ K^0$(c) invariant mass distribution of the $\Lambda^+_c \to \Lambda K^0 \pi^+$ decay with the phase angles $\phi=\phi'=0$.
• Figure 5: $K^0 \Lambda$(a), $\pi^+ \Lambda$(b) and $\pi^+ K^0$(c) invariant mass distributions of the process $\Lambda^+_c \to \Lambda K^0 \pi^+$. The experimental data labeled by "EXP" are obtained from Ref BESIII:2024xny.