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The ΔI = 1/2 rule is a universal pattern in weak interactions: decays involving an isospin change are dominated by transitions with ΔI = 1/2, far outweighing those with ΔI = 3/2. This regularity is surprising because weak interactions break many symmetries conserved in strong interactions, such as parity (P) and charge-parity (CP). Amid such extensive symmetry violation, the persistence of this rule is unexpected, making it a key puzzle in particle physics.
The famous example of ΔI = 1/2 rule is kaon decays, where it manifests as the isospin I = 0 final state being about 450 times more likely than the I = 2 state in K→ππ decays, reflecting the extreme enhancement of the ΔI = 1/2 transition over the ΔI = 3/2 transition. Specifically, the ratio of the real parts of the decay amplitudes, Re(A₀)/Re(A₂), is measured to be approximately 22.4, a value far larger than naive expectations (Eur. Phys. J. C (2017) 77:10).
Lattice QCD calculations have offered key insights into the ΔI=1/2 rule. They reveal that the two dominant contributions to the ΔI=3/2 K→ππ correlation functions have opposite signs, leading to significant cancellation in ReA₂, with this effect present in calculations using physical quark masses and kinematics and for heavier pions at threshold. These contributions, which partially cancel in ReA₂, are the largest in ReA₀ and carry the same sign, thereby enhancing this amplitude (Phys. Rev. Lett. 110, 152001). These calculations, performed with physical quark masses and kinematics, have successfully reproduced the experimental value of A₂ and provided a non-perturbative foundation for understanding the rule’s origin, though the precise dynamical mechanisms behind the large enhancement remain an active area of investigation (Phys. Rev. D 102, 054509).
Hyperons, as the hadronic counterparts of kaons, offer a complementary system to study the ΔI = 1/2 rule. Studying the ΔI = 1/2 rule in hyperons can provide supplementary information for understanding kaons and the relevant dynamical mechanisms in weak interactions. Early experimental results had large uncertainties, but theoretical studies, particularly within heavy-baryon chiral perturbation theory (HBChPT), suggested that the ΔI = 1/2 rule might also hold in hyperon decays, such as Λ→pπ⁻ and Λ→nπ⁰. These theories expect that observables like the ratio of asymmetry parameters (α_Λ₀/α_Λ₋) should approximate 1 if only ΔI = 1/2 transitions dominate. However, recent experiments, such as BESIII, reported deviations of around 10% in such ratios, suggesting at non-negligible ΔI = 3/2 contributions and challenging the strict validity of the rule in hyperon systems (arXiv:2508.03950). These results indicate that some important contributions may have neglected in previous theotical framework, such as some counterterms or parts of loop diagrams, which play a significant role in baryonic weak decays.
To address this discrepancy, we made efforts to re-examining the ΔI = 1/2 rule in hyperon decays using extended frameworks.We applied EOMS chiral perturbation theory to analyze the latest experimental data, with a more complete set of Feynman diagrams calculated.This research contributes to a deeper understanding of the ΔI = 1/2 rule and serves to examine the validity of chiral perturbation theory.
| Research field of your presentation | Theoretical high-energy nuclear physics |
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