We report the first lattice QCD calculation of the complex kaon decay amplitude $A_0$ with physical kinematics, using a $32^3times 64$ lattice volume and a single lattice spacing $a$, with $1/a= 1.3784(68)$ GeV. We find Re$(A_0) = 4.66(1.00)(1.26) ti
mes 10^{-7}$ GeV and Im$(A_0) = -1.90(1.23)(1.08) times 10^{-11}$ GeV, where the first error is statistical and the second systematic. The first value is in approximate agreement with the experimental result: Re$(A_0) = 3.3201(18) times 10^{-7}$ GeV while the second can be used to compute the direct CP violating ratio Re$(varepsilon/varepsilon)=1.38(5.15)(4.59)times 10^{-4}$, which is $2.1sigma$ below the experimental value $16.6(2.3)times 10^{-4}$. The real part of $A_0$ is CP conserving and serves as a test of our method while the result for Re$(varepsilon/varepsilon)$ provides a new test of the standard-model theory of CP violation, one which can be made more accurate with increasing computer capability.
We present results for several light hadronic quantities ($f_pi$, $f_K$, $B_K$, $m_{ud}$, $m_s$, $t_0^{1/2}$, $w_0$) obtained from simulations of 2+1 flavor domain wall lattice QCD with large physical volumes and nearly-physical pion masses at two la
ttice spacings. We perform a short, O(3)%, extrapolation in pion mass to the physical values by combining our new data in a simultaneous chiral/continuum `global fit with a number of other ensembles with heavier pion masses. We use the physical values of $m_pi$, $m_K$ and $m_Omega$ to determine the two quark masses and the scale - all other quantities are outputs from our simulations. We obtain results with sub-percent statistical errors and negligible chiral and finite-volume systematics for these light hadronic quantities, including: $f_pi$ = 130.2(9) MeV; $f_K$ = 155.5(8) MeV; the average up/down quark mass and strange quark mass in the $bar {rm MS}$ scheme at 3 GeV, 2.997(49) and 81.64(1.17) MeV respectively; and the neutral kaon mixing parameter, $B_K$, in the RGI scheme, 0.750(15) and the $bar{rm MS}$ scheme at 3 GeV, 0.530(11).
From simultaneous fits to the data from the 2+1 flavor DWF ensembles generated by the RBC and UKQCD collaborations at two different lattice spacings, we present preliminary continuum results for light hadrons. We focus on light pseudoscalar decay con
stants and quark masses. Several approaches to the calculation of the lattice spacing are discussed and the errors associated with the chiral extrapolation are explained. We make use of reweighting in the dynamical strange quark mass such that our ensembles have a self-consistently determined strange quark mass.
In this paper we investigate the benefits of using Z(2)xZ(2) single timeslice stochastic sources for the calculation of light quark physics on the lattice. Meson 2-point correlators measured using sources stochastic in only spin and those stochastic
in both spin and colour indices are compared to point source correlators on the unit gauge and on a 16^3 x 32 Domain Wall QCD ensemble. It is found that the use of stochastic sources gives a considerable improvement in statistics for the same computational cost. The neutral kaon mixing matrix element B_K is also calculated on this ensemble with stochastic sources, but we conclude that the stochastic method offers no significant advantage over the traditional gauge-fixed wall source approach which already offers an exact volume average. We also discuss the application to semileptonic form factors in conjunction with partially twisted boundary conditions.
