$B_7$, $B_8$ and chiral Ward identities

TL;DR

This paper investigates the calculation of weak matrix elements related to $K^+ o ext{pi}^+$ decays using lattice QCD with HYP staggered fermions, focusing on chiral Ward identities, operator mixing issues, and a specific ratio measurement.

Contribution

It demonstrates the use of improved staggered fermions for weak matrix elements, addresses operator mixing with a subtraction method, and measures a key ratio in lattice QCD.

Findings

Chiral Ward identities are consistent with the improved staggered fermion approach.

A subtraction method effectively handles mixing with unphysical operators.

The gold-plated ratio R is successfully measured.

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.