$B_7$, $B_8$ and chiral Ward identities

Abstract

We present recent progress in understanding weak matrix elements on the lattice. We use HYP staggered fermions in quenched QCD to study numerically various properties of the $K^+\to\pi^+$ amplitudes of the electroweak penguin operators $Q_7$ and $Q_8$. We check chiral Ward identities to probe the validity of using improved staggered fermions in the calculation of weak matrix elements. We address the issue of mixing with unphysical lower dimension operators, which causes a divergent term in the case of the $\Delta I = 1/2$ amplitudes. We propose a particular subtraction method as the best choice. We also measure the gold-plated ratio $R$ originally suggested by Becirevic and Villadoro.