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

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 $a=0.091\mathrm{fm}$, $m_{\pi }=280\mathrm{MeV}$ and $m_K=580\mathrm{MeV}$ on a $32^3\times 64$ ($La=2.9\mathrm{fm}$) 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 $\mathrm{Re}{A}_0=60(36)\times 10^{-8}\mathrm{GeV}$ and $\mathrm{Im}{A}_0=-67(56)\times 10^{-12}\mathrm{GeV}$ for a matching scale $q^{\ast }=1/a$. The dependence on the matching scale is weak.

Comments: 7 pages, 3 figures, Contribution to the 32nd International Symposium on Lattice Field Theory (Lattice 2014), 23-28 June 2014, Columbia University, New York, NY, USA