Light Hadron Weak Matrix Elements

The kaon bag parameter BK , which is required for constraining the CP violation parameter in the Cabibbo-Kobayashi-Maskawa matrix from experiment, has been successfully calculated with the Kogut-Susskind(KS) quark action, taking advantage of its UA(1) chiral symmetry[1]. A recent systematic calculation of BK with high statistics[2], however, reveals that the systematic uncertainties in the perturbative renormalization factors to connect lattice and continuum operators have sizable magnitude, which indicates the necessity of non-perturbative renormalization. For the calculation of BK with the Wilson quark action we have to deal with the operator mixing problem caused by the explicit chiral symmetry breaking in the action, which turned out to be not effectively treated by perturbation theory[3]. Several non-perturbative methods have been proposed to control the operator mixing. The CP conserving K → ππ decay amplitudes give an intriguing testing ground for lattice QCD calculations. It would be exciting to be able to show that QCD explains the ∆I = 1/2 rule: A0/A2 ≈ 22 where A0,2 = A(K → ππ[I = 0, 2]). Although studies of K → ππ decay amplitudes with lattice QCD were initiated a decade ago, little progress has been achieved since then. Recent work on the one-loop calculation of K → ππ decay amplitudes using chiral perturbation theory(ChPT)[4,5], however, provides some impor-