On-shell Delta I = 3/2 kaon weak matrix elements with non-zero total momentum

TL;DR

This study computes on-shell Delta I = 3/2 kaon decay matrix elements using lattice QCD with domain wall fermions, evaluating in different frames and extrapolating to physical pion mass to compare with experimental results.

Contribution

It introduces a method to extract physical decay amplitudes from lattice calculations in multiple frames, extending the Lellouch-Lüscher formula for non-zero total momentum.

Findings

Re(A_2) = 1.66(23)(+48-3)(+53-0) x 10^{-8} GeV

Im(A_2) = -1.181(26)(+141-14)(+44-0) x 10^{-12} GeV

Results are consistent with experimental data.

Abstract

We present our results for the on-shell Delta I = 3/2 kaon decay matrix elements using domain wall fermions and the DBW2 gauge action at one coarse lattice spacing corresponding to 1/a = 1.31 GeV in the quenched approximation. The on-shell matrix elements are evaluated in two different frames: the center-of-mass frame and non-zero total-momentum frame. We employ the formula proposed by Lellouch and L\"uscher in the center-of-mass frame, and its extension for non-zero total momentum frame to extract the infinite volume, on-shell, center-of-mass frame decay amplitudes. We determine the decay amplitude at the physical pion mass and momentum from the chiral extrapolation and an interpolation of the relative momentum using the results calculated in the two frames. We have obtained Re(A_2) = 1.66(23)(^{+48}_{-03})(^{+53}_{-0}) x 10^{-8} GeV and Im(A_2) = -1.181(26)(^{+141}_{-014})(^{+44}_{-0}) x 10^{-12} GeV at the physical point, using the data at the relatively large pion mass, m_pi > 0.35 GeV. The first error is statistic, and the second and third are systematic. The second error is estimated with several fits of the chiral extrapolation including (quenched) chiral perturbation formula at next to leading order using only lighter pion masses. The third one is estimated with an analysis using the lattice dispersion relation. The result of Re(A_2) is reasonably consistent with experiment.