Calculation of K→ππK \to \pi\pi decay amplitudes with improved Wilson fermion action 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. Expanding on the earlier works by Bernard {\it et al.} and by Donini {\it et al.}, we show that mixings with four-fermion operators with wrong chirality are absent even for the Wilson fermion action for the parity odd process in both channels due to CPS symmetry. Therefore, after subtraction of an effect from the lower dimensional operator, a calculation of the decay amplitudes is possible without complications from operators with wrong chirality, as for the case with chirally symmetric lattice actions. As a first step to verify the possibility of calculations with the Wilson fermion action, we consider the decay amplitudes at an unphysical quark mass $m_K \sim 2 m_\pi$. 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 $a=0.091\,{\rm fm}$, $m_\pi=280\,{\rm MeV}$, 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 method 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 $q^*$ for these values is weak.Comment: LaTeX2e, 31 pages, 12 eps figures, uses revtex4 and graphicx, published in PR

Study of unstable particle through the spectral function in O(4) ϕ4\phi^4 theory

We test application of the maximum entropy method to decompose the states contributing to the unstable $\sigma$ correlation function through the spectral function in the four dimensional O(4) $\phi^4$ theory. Reliable results are obtained for the $\sigma$ mass and two-particle $\pi\pi$ state energy using only the $\sigma$ correlation function. We also find that the property of the $\sigma$ particle is different between the unstable ($m_{\sigma}/m_{\pi}>2$) and stable ($m_{\sigma}/m_{\pi}<2$) cases.Comment: Lattice2002(spectrum), 3 page

Pion decay constant in quenched QCD with Kogut-Susskind quarks

We present a non-perturbative calculation for the pion decay constant with quenched Kogut-Susskind quarks. Numerical simulations are carried out at $\beta = 6.0$ and 6.2 with various operators extending over all flavors. The renormalization correction is applied for each flavor by computing non-perturbative renormalization constants, and it is compared with a perturbative calculation. We also study the behavior of $f_\pi$ in the continuum limits for both non-perturbative and perturbative calculations. The results in the continuum limit is also discussed.Comment: LATTICE99(matrix elements) 3 pages, 4 eps figure

Sea Quark Effects on the Strong Coupling Constant

We present results showing that the strong coupling constant measured in two-flavor full QCD with dynamical Kogut-Susskind quarks at $\beta=5.7$ exhibit a 15\% increase due to sea quarks over that for quenched QCD at the scale $\mu\approx 7$GeV . (talk at lattice93)Comment: 3 pages, compressed, uuencoded PostScript file(name:lat93ch.ps.Z

Lattice QCD with domain wall quarks and applications to weak matrix elements

Using domain wall fermions, we estimate $B_K(\mu\approx 2 GeV)=0.628(47)$ in quenched QCD which is consistent with previous calculations. At \gbeta=6.0 and 5.85 we find the ratio $f_K/m_\rho$ in agreement with the experimental value, within errors. These results support expectations that $O(a)$ errors are exponentially suppressed in low energy ($E\ll a^{-1}$) observables, and indicate that domain wall fermions have good scaling behavior at relatively strong couplings. We also demonstrate that the axial current numerically satisfies the lattice analog of the usual continuum axial Ward identity.Comment: Contribution to Lattice '97. 3 pages, 2 epsf figure

Two-particle wave function in four dimensional Ising model

An exploratory study of two-particle wave function is carried out with a four dimensional simple model. The wave functions not only for two-particle ground and first excited states but also for an unstable state are calculated from three- and four-point functions using the diagonalization method suggested by L\"uscher and Wolff. The scattering phase shift is evaluated from these wave functions.Comment: Poster presented at Lattice2004(spectrum), Fermilab, June 21-26, 200