Emerging understanding of the \Delta I = 1/2 rule from lattice QCD
P. A. Boyle, N. H. Christ, N. Garron, E. J. Goode, T. Janowski, C. Lehner, Q. Liu, A. T. Lytle, C. T. Sachrajda, A. Soni, and D. Zhang
Accepted
There has been much speculation as to the origin of the DI = 1/2 rule (ReA0/ReA2 @ 22.5). We find that the two dominant contributions to the DI=3/2, Kpp correlation functions have opposite signs leading to a significant cancellation. This partial cancellation occurs in our computation of ReA2 with physical quark masses and kinematics (where we reproduce the experimental value of A2) and also for heavier pions at threshold. For ReA0, although we do not have results at physical kinematics, we do have results for pions at zero-momentum with mp @ 420 MeV (ReA0/ReA2=9.1(2.1)) and mp @ 330 MeV (ReA0/ReA2=12.0(1.7)). The contributions which partially cancel in ReA2 are also the largest ones in ReA0, but now they have the same sign and so enhance this amplitude. The emerging explanation of the DI=1/2 rule is a combination of the perturbative running to scales of O(2 GeV), a relative suppression of ReA2 through the cancellation of the two dominant contributions and the corresponding enhancement of ReA0. QCD and EWP penguin operators make only very small contributions at such scales.