The Kaon B-parameter and K-π and K-ππ transition amplitudes on the lattice

Abstract

We present the results of a computation of the K 0− K 0 and ΔI = 3 2 K−π and K−ππ amplitudes in lattice QCD. The numerical simulation has been done using the standard one-plaquette action and Wilson fermions, in the quenched approximation. Combining the tesults obtained at β = 6 on a 10 2 × 20 × 40 lattice with 30 configurations with those at β = 6.2 on a 16 3 × 48 lattice with 15 configurations, we have obtained for the kaon B- parameterB K 0 − K 0 = 0.65 ± 0.15 at μ = 3 GeV. We have also evaluated the ΔI = 3 2 K−π and K− π weak hamiltonian matrix elements. The relevant renormalized operator O 4 has been found to satisfy soft-pion theorems and chiral lagrangian relations at the 30% level, and this makes us confident about our results. We find (〈K +| H W| π + π 0〉/ m K) = (7 ± 2) × 10 −8 to be compared with the experimental value of 3.7 × 10 −8.