Calculation of $K\to \pi$ matrix elements in quenched domain-wall QCD

TL;DR

This paper investigates calculating $K o ext{pi}$ matrix elements in quenched domain-wall QCD to estimate non-leptonic $K$ decay amplitudes, comparing results from different gauge actions and relating them to $K o ext{pi} ext{pi}$ processes.

Contribution

It demonstrates the feasibility of computing $K o ext{pi}$ matrix elements in quenched domain-wall QCD and compares results from different gauge actions, providing preliminary insights into $K o ext{pi} ext{pi}$ decays.

Findings

Reasonable signals obtained for $K o ext{pi}$ matrix elements.

Comparison of results from standard and improved gauge actions.

Preliminary results on $K o ext{pi} ext{pi}$ matrix elements.

Abstract

We explore the possibility for an evaluation of non-leptonic $\Delta S=1$ $K$ decay amplitudes through the calculation of $K\to\pi$ matrix elements using domain-wall QCD. The relation between the physical $K\to\pi\pi$ matrix elements and $K\to\pi$ matrix elements deduced from chiral perturbation theory is recapitulated. Quenched numerical simulations are performed on an $16^3\times 32\times 16$ lattice at a lattice spacing $a^{-1}\approx 2$GeV for both the standard plaquette gauge action and a renormalization-group improved gauge action, and reasonable signals for $K\to\pi$ matrix elements are obtained. Preliminary results are reported on the $K\to\pi\pi$ matrix elements, and results from two actions are compared.