Emerging understanding of the \Delta I = 1/2 Rule from Lattice QCD

TL;DR

This paper uses lattice QCD calculations to explore the  I=1/2 rule, revealing that cancellations and enhancements in decay amplitudes explain the rule's origin, with results matching experimental data.

Contribution

It provides a novel lattice QCD analysis showing how cancellations and enhancements in decay amplitudes account for the  I=1/2 rule, incorporating physical quark masses and kinematics.

Findings

Re A_2 is reproduced with physical quark masses and kinematics.

Partial cancellation of dominant contributions explains Re A_2.

Enhancement of Re A_0 arises from same-sign contributions that cancel in Re A_2.

Abstract

There has been much speculation as to the origin of the \Delta I = 1/2 rule (Re A_0/Re A_2 \simeq 22.5). We find that the two dominant contributions to the \Delta I=3/2, K \to \pi \pi{} correlation functions have opposite signs leading to a significant cancellation. This partial cancellation occurs in our computation of Re A_2 with physical quark masses and kinematics (where we reproduce the experimental value of A_2) and also for heavier pions at threshold. For Re A_0, although we do not have results at physical kinematics, we do have results for pions at zero-momentum with m_\pi{} \simeq 420 MeV (Re A_0/Re A_2=9.1(2.1)) and m_\pi{} \simeq 330 MeV (Re A_0/Re A_2=12.0(1.7)). The contributions which partially cancel in Re A_2 are also the largest ones in Re A_0, but now they have the same sign and so enhance this amplitude. The emerging explanation of the \Delta I=1/2 rule is a combination of the perturbative running to scales of O(2 GeV), a relative suppression of Re A_2 through the cancellation of the two dominant contributions and the corresponding enhancement of Re A_0. QCD and EWP penguin operators make only very small contributions at such scales.