$K \to \pi \pi$ Decays with Domain Wall Fermions: Towards Physical Results

TL;DR

This paper employs domain wall fermions to compute $K o \pi \pi$ decay matrix elements on the lattice, addressing residual chiral symmetry breaking and quenched approximation issues to approach physical results.

Contribution

It introduces a method combining lattice measurements and chiral perturbation theory with analysis of chiral symmetry breaking effects for $K o \pi \pi$ decays.

Findings

Residual chiral symmetry breaking affects matrix element measurements.

Ward-Takahashi identities help analyze divergence and symmetry breaking.

Quenched approximation introduces pathologies at small quark masses.

Abstract

We are using domain wall fermions to study $K \to \pi \pi$ matrix elements by measuring $K \to \pi$ and $K \to 0$ matrix elements on the lattice and employing chiral perturbation theory to relate these to the desired physical result. The residual chiral symmetry breaking of domain wall fermions with a finite extent in the fifth dimension impacts these measurements. Using the Ward-Takahashi identities, we investigate residual chiral symmetry breaking effects for divergent quantities and study pathologies of the quenched approximation for small quark mass. We then discuss the $\Delta S = 1$ operator $O_2$, where chiral symmetry is vital for the subtraction of unphysical effects.