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

There has been much speculation as to the origin of the Delta I = 1/2 rule (ReA(0)= ReA(2) similar or equal to 22:5). We find that the two dominant contributions to the Delta I = 3/2, K -> pi pi correlation functions have opposite signs, leading to a significant cancelation. This partial cancelation occurs in our computation of ReA(2) with physical quark masses and kinematics (where we reproduce the experimental value of A(2)) and also for heavier pions at threshold. For ReA(0), although we do not have results at physical kinematics, we do have results for pions at zero momentum with m pi similar or equal to 420 MeV [ReA(0)/ReA(2) = 9:1(2:1)] and m pi similar or equal to 330 MeV [ReA(0)/ReA(2) = 12:0(1:7)] . The contributions which partially cancel in ReA(2) are also the largest ones in ReA(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 ReA(2) through the cancelation of the two dominant contributions, and the corresponding enhancement of ReA(0). QCD and electroweak penguin operators make only very small contributions at such scales. DOI: 10.1103/PhysRevLett.110.152001