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

Authors :
Boyle, P. A.
Christ, N. H.
Garron, N.
Goode, E. J.
Janowski, T.
Lehner, C.
Liu, Q.
Lytle, A. T.
Sachrajda, C. T.
Soni, A.
Zhang, D.
Publication Year :
2012

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.<br />Comment: 5 pages, 4 figures. v2 minor revisions to coincide w/ published version

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.1212.1474
Document Type :
Working Paper
Full Text :
https://doi.org/10.1103/PhysRevLett.110.152001