A unified approach for the hadronic weak decays of $Λ$ and $Σ^{\pm}\to Nπ$

TL;DR

This work develops a unified description of the hadronic weak decays $\Lambda,\,\Sigma^{\pm} \to N\pi$ within a non-relativistic constituent quark model, incorporating direct pion emission, color-suppressed W emission, and pole terms. It demonstrates that FSIs via coupled-channel rescattering crucially affect $\Lambda\to n\pi^0$, providing the leading one-loop correction that reconciles theory with data, while pole terms and SU(3) breaking are essential across channels. A dynamic selection rule suppresses the radial excitation $N(1710)$ in particular PC amplitudes, and the $\Lambda(1405)$ resonance plays a key role in certain PV/PC pole contributions, offering constraints on low-lying $J^P=1/2^{\pm}$ baryons. The study uses three fitting schemes to isolate the mechanisms and shows FSIs can resolve the longstanding $\Lambda\to n\pi^0$ anomaly, highlighting the importance of non-perturbative QCD effects in light baryon weak decays and informing resonance spectroscopy and CP-violation probes in hyperon systems.

Abstract

We provide a unified approach for the two-body hadronic weak decays of hyperons with $S=-1$, i.e. $Λ$ and $Σ^\pm$, in the framework of the non-relativistic constitute quark model (NRCQM). A combined analysis shows that the branching ratios and asymmetry parameters of the decay channels $Λ\to pπ^-$ and $Σ^\pm\to Nπ$ can be well described in the same framework with the direct pion emission, color suppressed internal $W$ emission, and pole terms included. However, the channel $Λ\to nπ^0$ indicates significant deviations from the experimental data based on these mentioned transition mechanism. We demonstrate that the final state interactions (FSIs) via the coupled-channel rescatterings play a crucial role in $Λ\to nπ^0$. Namely, the dominant decay channel of $Λ\to pπ^-$ can contribute to $Λ\to nπ^0$ via the $pπ^-\to nπ^0$ rescatterings. This is a leading correction effect for $Λ\to nπ^0$ at the one-loop level. We find that such FSIs only become the leading effects in $Λ\to nπ^0$, but contribute as subleading contributions in other channels. We also demonstrate that the pole terms are indispensable in these hyperon decays. In particular, for $Σ^-\to nπ^-$ and $Σ^+\to nπ^+$, it shows that $Λ(1405)$ as the intermediate state in the pole term amplitude is necessary for reproducing the experimental data. We also find that a dynamic selection rule forbids the radial excitation state $N(1710)$ of the quark model multiplet $|70, ^28,2,0^+,1/2^+\rangle$ from contribution. To some extent, the hyperon hadronic weak decays serve as a special probe for the underlying transition mechanisms and can provide some constraints on the intermediate $J^P=1/2^\pm$ baryon resonances.

Figures (6)

• Figure 1: Illustrations for the two-body hadronic weak decay of $\Lambda$ into $p\pi$ and $n\pi$ at the quark level. (a) Direct pion emission (DPE) processes, (b)-(d) Color suppressed (CS) pion emission processes.
• Figure 2: Illustrations for the two-body hadronic weak decay of $\Sigma^-\to n\pi^-$ and $\Sigma^+\to p\pi^0$ at the quark level. (a) Direct pion emission (DPE) processes, (b)-(d) Color suppressed (CS) pion emission processes.
• Figure 3: Illustrations of the type-A and type-B pole terms for the initial baryon $\Lambda$ to hadronic final states $p\pi^-$ and $n\pi^0$. The intermediate states are $N$ and $\Sigma$ with quantum numbers of $\frac{1}{2}^{\pm}$ and which could be off-shell (the intermediate state cannot be $\Lambda$ due to isospin violation). Black squares and red dots represent weak and strong vertices respectively.
• Figure 4: Illustrations of the type-A and type-B pole terms for the initial baryon $\Sigma^\pm$ to hadronic final states $n\pi^\pm$ and $p\pi^0$. The intermediate states are $N$ and $\Sigma/\Lambda$ with quantum numbers of $\frac{1}{2}^{\pm}$ and which could be off-shell. Only type-B pole terms contribute to the decay $\Sigma^-\to n\pi^-$. Black squares and red dots represent weak and strong vertices respectively.
• Figure 5: Schematic diagram of the FSIs from $p\pi^-$ rescattering to $n\pi^0$. Black squares and red dots represent weak and strong vertices respectively.