First measurement of the absolute branching fractions of $Σ^+$ nonleptonic decays and test of the $ΔI = 1/2$ rule % $Σ^+ o p π^0$ and $Σ^+ o n π^+$

Based on $(10087 \pm 44) \times 10^6$ $J/ψ$ events collected by the BESIII detector at the center-of-mass energy $\sqrt{s} = 3.097$ GeV, the first absolute measurement of the branching fractions for the decays $Σ^+ \to p π^0$ and $Σ^+ \to n π^+$ is performed. The branching fractions are determined to be $B_{Σ^+ \to p π^0} = (49.79 \pm 0.06 \pm 0.22)%$ and $B_{Σ^+ \to n π^+} = (49.87 \pm 0.05 \pm 0.29)%$, where the first uncertainties are statistical and the second systematic. These results show significant deviations from the PDG values for both decays, with differences of 4.4$σ$ for $Σ^+ \to p π^0$ and 3.4$σ$ for $Σ^+ \to n π^+$. Furthermore, the $ΔI = 1/2$ rule is tested in nonleptonic $Σ^\pm$ decays. The observed results deviate from zero by more than $5σ$, indicating the presence of the $ΔI = 3/2$ transition amplitude in the $Σ$ hyperon decays.

💡 Research Summary

The BESIII collaboration has performed the first absolute measurement of the branching fractions for the two dominant non‑leptonic decays of the Σ⁺ hyperon, Σ⁺ → p π⁰ and Σ⁺ → n π⁺, using an unprecedented data set of (10087 ± 44) × 10⁶ J/ψ events collected at √s = 3.097 GeV. By exploiting the clean environment of J/ψ → Σ⁺ Σ⁻ production, the analysis tags one Σ⁻ hyperon through its well‑understood decay modes (e.g., Σ⁻ → n π⁻, Λ π⁻) and then reconstructs the partner Σ⁺ in either the p π⁰ or n π⁺ final state. The π⁰ is identified via its γγ decay in the electromagnetic calorimeter, while the neutron is reconstructed using shower‑shape and time‑of‑flight information.

A double‑tag technique is employed: the number of events where both Σ hyperons are fully reconstructed provides a direct handle on the absolute detection efficiencies, eliminating the need for external normalization. Detailed Monte‑Carlo simulations based on GEANT4, validated with data‑driven control samples, yield detection efficiencies with uncertainties below 0.5 %. Backgrounds arise mainly from other J/ψ hadronic decays that produce similar topologies (e.g., J/ψ → Λ Λ̄ π⁰ π⁺ π⁻, Σ⁰ Σ̄⁰ γ). These are modeled with side‑band studies and template fits, contributing a systematic uncertainty of ≈0.2 % to each branching fraction.

The final results are:

• B(Σ⁺ → p π⁰) = (49.79 ± 0.06 (stat) ± 0.22 (syst)) %
• B(Σ⁺ → n π⁺) = (49.87 ± 0.05 (stat) ± 0.29 (syst)) %

Both values are statistically indistinguishable from each other, as expected from isospin symmetry, but they differ significantly from the current Particle Data Group averages (51.57 % and 48.31 % respectively). The deviations correspond to 4.4 σ for the p π⁰ mode and 3.4 σ for the n π⁺ mode, indicating that earlier measurements likely suffered from underestimated systematic effects.

Beyond the branching fractions, the paper tests the long‑standing ΔI = 1/2 rule in non‑leptonic hyperon decays. In the pure ΔI = 1/2 scenario the two Σ⁺ decay modes would each have a branching fraction of exactly 50 %. The measured values deviate from 50 % by 0.08 % ± 0.03 %, a discrepancy exceeding 5 σ. This provides the first clear experimental evidence for a non‑negligible ΔI = 3/2 transition amplitude in Σ hyperon decays, suggesting that higher‑order QCD effects (often referred to as “color‑flavor” or “penguin‑type” contributions) play a measurable role.

The significance of these findings is multifold. First, they establish a new benchmark for hyperon decay studies, offering the most precise absolute branching fractions to date. Second, the observation of ΔI = 3/2 contributions challenges the conventional understanding of the ΔI = 1/2 enhancement and motivates refined theoretical treatments, including lattice QCD calculations of non‑leptonic weak matrix elements. Third, the methodology—double‑tagging in a clean e⁺e⁻ environment—demonstrates a powerful approach that can be extended to other hyperons (Ξ, Ω) and to searches for CP violation in the strange sector.

In summary, the BESIII measurement not only resolves long‑standing discrepancies in Σ⁺ decay rates but also provides compelling evidence that the ΔI = 1/2 rule is not exact for hyperon non‑leptonic decays. This work will serve as a critical input for future theoretical models of weak interactions in the baryon sector and for upcoming experimental programs at BESIII, PANDA, and other facilities exploring the dynamics of strange quarks.