On-shellΔI=3/2kaon weak matrix elements with nonzero total momentum

Abstract

We present our results for the on-shell $\ensuremath{\Delta}I=3/2$ kaon decay matrix elements using domain wall fermions and the DBW2 gauge action at one coarse lattice spacing corresponding to ${a}^{\ensuremath{-}1}=1.31\text{ }\text{ }\mathrm{GeV}$ in the quenched approximation. The on-shell matrix elements are evaluated in two different frames: the center-of-mass frame and nonzero total-momentum frame. We employ the formula proposed by Lellouch and L\"uscher in the center-of-mass frame, and its extension for a nonzero 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 $\mathrm{Re}{A}_{2}=1.66(23)(\genfrac{}{}{0}{}{+48}{\ensuremath{-}03})(\genfrac{}{}{0}{}{+53}{\ensuremath{-}0})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}\text{ }\text{ }\mathrm{GeV}$ and $\mathrm{Im}{A}_{2}=\ensuremath{-}1.181(26)(\genfrac{}{}{0}{}{+141}{\ensuremath{-}014})(\genfrac{}{}{0}{}{+44}{\ensuremath{-}0})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}\text{ }\text{ }\mathrm{GeV}$ at the physical point, using the data at the relatively large pion mass, ${m}_{\ensuremath{\pi}}>0.35\text{ }\text{ }\mathrm{GeV}$. 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 the (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 $\mathrm{Re}{A}_{2}$ is reasonably consistent with experiment.