Calculation of $K \to \pi\pi$ decay amplitudes with improved Wilson fermion in 2+1 flavor lattice QCD

TL;DR

This paper reports on lattice QCD calculations of $K o\pi\pi$ decay amplitudes using improved Wilson fermions, providing new results for both $\Delta I=1/2$ and 3/2$ channels with variance reduction techniques.

Contribution

First lattice QCD calculation of $K o\pi\pi$ decay amplitudes with Wilson-type fermions, demonstrating effective variance reduction and providing results for both isospin channels.

Findings

Obtained ${ m Re}A_0$ and ${ m Im}A_0$ with Wilson fermions.

Variance reduction techniques are highly effective.

Results show weak dependence on the matching scale.

Abstract

We present results for the $K\to\pi\pi$ decay amplitudes for both the $\Delta I=1/2$ and $3/2$ channels. This calculation is carried out on 480 gauge configurations in $N_f=2+1$ QCD generated over 12,000 trajectories with the Iwasaki gauge action and non-perturbatively $O(a)$-improved Wilson fermion action at $a=0.091\,{\rm fm}$, $m_\pi=280\,{\rm MeV}$ and $m_K=580\,{\rm MeV}$ on a $32^3\times 64$ ($La=2.9\,{\rm fm}$) lattice. For the quark loops in the Penguin and disconnected contributions in the $I=0$ channel, the combined hopping parameter expansion and truncated solver techniques work very well for variance reduction. We obtain, for the first time with a Wilson-type fermion action, that ${\rm Re}A_0 = 60(36) \times10^{ -8}\,{\rm GeV}$ and ${\rm Im}A_0 =-67(56) \times10^{-12}\,{\rm GeV}$ for a matching scale $q^* =1/a$. The dependence on the matching scale is weak.