Calculation of $K\to \ddot{I}€\ddot{I}€$ decay amplitudes from $K\to \ddot{I}€$ matrix elements in quenched domain-wall QCD

Abstract

We present a calculation of the $K\to \ddot{I}€\ddot{I}€$ decay amplitudes from the $K\to \ddot{I}€$ matrix elements using leading order relations derived in chiral perturbation theory. Numerical simulations are carried out in quenched QCD with the domain-wall fermion action and the renormalization group improved gluon action. Our results show that the I=2 amplitude is reasonably consistent with experiment whereas the I=0 amplitude is sizably smaller. Consequently the $\hat{I}”I=1/2$ enhancement is only half of the experimental value, and $\hat{I}{\mu }^{\prime }/\hat{I}\mu$ is negative.

Lattice2001(hadronic matrix elements), 3pages, 6 eps figures