Calculation of K→ππK \to \pi\pi decay amplitudes with an improved Wilson fermion action in a nonzero momentum frame in lattice QCD

We present our result for the $K\to\pi\pi$ decay amplitudes for both the $\Delta I=1/2$ and $3/2$ processes with the improved Wilson fermion action. In order to realize the physical kinematics, where the pions in the final state have finite momenta, we consider the decay process $K({\bf p}) \to \pi({\bf p}) + \pi({\bf 0})$ in the nonzero momentum frame with momentum ${\bf p}=(0,0,2\pi/L)$ on the lattice. Our calculations are carried out with $N_f=2+1$ gauge configurations generated with the Iwasaki gauge action and nonperturbatively $O(a)$-improved Wilson fermion action at $a=0.091\,{\rm fm}$ ($1/a=2.176\,{\rm GeV}$), $m_\pi=260\,{\rm MeV}$, and $m_K=570\,{\rm MeV}$ on a $48^3\times 64$ ($La=4.4\,{\rm fm}$) lattice. For these parameters the energy of the $K$ meson is set at that of two-pion in the final state. We obtain ${\rm Re}A_2 = 2.431(19) \times10^{ -8}\,{\rm GeV}$, ${\rm Re}A_0 = 51(28) \times10^{ -8}\,{\rm GeV}$, and $\epsilon'/\epsilon = 1.9(5.7) \times10^{-3}$ for a matching scale $q^* =1/a$ where the errors are statistical. The dependence on the matching scale $q^*$ of these values is weak. The systematic error arising from the renormalization factors is expected to be around $1.3\%$ for ${\rm Re}A_2$ and $11 \%$ for ${\rm Re}A_0$. Prospects toward calculations with the physical quark mass are discussed.Comment: LaTeX2e, 19 pages, 5 eps figures, uses revtex4 and graphicx. arXiv admin note: substantial text overlap with arXiv:1505.05289. Published in PR

B_K with the Wilson Quark Action: A Non-Perturbative Resolution of Operator Mixing using Chiral Ward Identities

We propose a non-perturbative method to determine the mixing coefficients of $\Delta s=2$ four-quark operators for the Wilson quark action using chiral Ward identities. The method is applied to calculate B_K in quenched QCD.Comment: 3 pages including 3 figures, Talk presented at LATTICE96(phenomenology) by Y. Kuramash

Light hadron spectrum with two flavors of O(a)O(a) improved dynamical quarks : final results from JLQCD

We present the final results of the JLQCD calculation of the light hadron spectrum and quark masses with two flavors of dynamical quarks using the plaquette gauge action and fully $O(a)$-improved Wilson quark action at $\beta=5.2$. We observe that sea quark effects lead to a closer agreement of the strange meson and baryon masses with experiment and a reduction of quark masses by about 25.Comment: 3 pages, 5 figures, Lattice2002 (spectrum