Emerging understanding of the \Delta I = 1/2 Rule from Lattice QCD
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.
Keywords
Cite
@article{arxiv.1212.1474,
title = {Emerging understanding of the \Delta I = 1/2 Rule from Lattice QCD},
author = {P. A. Boyle and N. H. Christ and N. Garron and E. J. Goode and T. Janowski and C. Lehner and Q. Liu and A. T. Lytle and C. T. Sachrajda and A. Soni and D. Zhang},
journal= {arXiv preprint arXiv:1212.1474},
year = {2019}
}
Comments
5 pages, 4 figures. v2 minor revisions to coincide w/ published version