Calculation of $\Delta I=3/2$ kaon weak matrix elements including two-pion interaction effects in finite volume

Abstract

We calculate $\Delta I=3/2$ kaon decay matrix elements using domain wall fermions and the DBW2 gauge action at one coarse lattice spacing corresponding to $a^{-1}=1.3$ GeV. We employ the Lellouch and Lüscher formula and its extention for non-zero total momentum to extract the infinite volume, center-of-mass frame decay amplitudes. The decay amplitudes obtained from the methods correspond to those from the indirect method with full order chiral perturbation theory. We confirm that the result is consistent with the previous result calculated with H-parity (anti-periodic) boundary condition by investigating the relative momentum dependence. We evaluate the decay amplitude Re$A_2$ at the physical point by a chiral extrapolation with a polynomial function of $m_{\pi }^2$ and the relative momentum as well as the Delta I = 3/2 electroweak penguin contributions to ${ϵ}^{\prime }/ϵ$. We found that the result of Re$A_2$ reasonably agrees with the experiment.

Comments: 7 pages, 9 figures, talk presented at Lattice2006(Electroweak Decays and Mixing)