K →ππ Δ I=3/2 decay amplitude in the continuum limit

We present new results for the amplitude A2 for a kaon to decay into two pions with isospin I=2: ReA2=1.50(4)stat(14)syst×10-8GeV; ImA2=-6.99(20)stat(84)syst×10-13GeV. These results were obtained from two ensembles generated at physical quark masses (in the isospin limit) with inverse lattice spacings a-1=1.728(4)GeV and 2.358(7) GeV. We are therefore able to perform a continuum extrapolation and hence largely to remove the dominant systematic uncertainty from our earlier results [1,2], that due to lattice artifacts. The only previous lattice computation of K→ππ decays at physical kinematics was performed using an ensemble at a single, rather coarse, value of the lattice spacing [a-1≃1.37(1)GeV]. We confirm the observation reported in [3] that there is a significant cancellation between the two dominant contributions to ReA2 which we suggest is an important ingredient in understanding the ΔI=1/2 rule, ReA0/ReA2≃22.5, where the subscript denotes the total isospin of the two-pion final state. Our result for A2 implies that the electroweak penguin contribution to ε′/ε is Re(ε′/ε)EWP=-(6.6±1.0)×10-4.