arXiv:hep-lat/0110142·v1·High Energy Physics — Lattice

Calculation of $K \to π π$ decay amplitudes from $K \to π$ matrix elements in quenched domain-wall QCD

CP-PACS Collaboration: S.Aoki🇯🇵 · Y.Aoki🇯🇵 · R.Burkhalter🇯🇵 · S.Ejiri🇯🇵 · M.Fukugita🇯🇵 · S.Hashimoto🇯🇵 · N.Ishizuka🇯🇵 · Y.Iwasaki🇯🇵 · T.Izubuchi🇯🇵 · K.Kanaya🇯🇵 · T.Kaneko🇯🇵 · Y.Kuramashi🇯🇵

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Abstract

We present a calculation of the $K \to π π$ decay amplitudes from the $K \to π$ 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 $Δ I = 1/2$ enhancement is only half of the experimental value, and $ϵ^{'} / ϵ$ is negative.