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 lattice 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).Comment: 131 pages, 30 figures. Updated to match published versio

We have simulated QCD using 2 þ 1 flavors of domain wall quarks and the Iwasaki gauge action on a ð2:74 fmÞ 3 volume with an inverse lattice scale of a À1 ¼ 1:729ð28Þ GeV. The up and down (light) quarks are degenerate in our calculations and we have used four values for the ratio of light quark masses to the strange (heavy) quark mass in our simulations: 0.217, 0.350, 0.617, and 0.884. We have measured pseudoscalar meson masses and decay constants, the kaon bag parameter B K , and vector meson couplings. We have used SU(2) chiral perturbation theory, which assumes only the up and down quark masses are small, and SU(3) chiral perturbation theory to extrapolate to the physical values for the light quark masses. While next-to-leading order formulas from both approaches fit our data for light quarks, we find the higher-order corrections for SU(3) very large, making such fits unreliable. We also find that SU(3) does not fit our data when the quark masses are near the physical strange quark mass. Thus, we rely on SU(2) chiral perturbation theory for accurate results. We use the masses of the baryon, and the and K mesons to set the lattice scale and determine the quark masses. We then find f ¼ 124:1ð3:6Þ stat  ð6:9Þ syst MeV, f K ¼ 149:6ð3:6Þ stat ð6:3Þ syst MeV, and f K =f ¼ 1:205ð0:018Þ stat ð0:062Þ syst . Using nonperturbative renormalization to relate lattice regularized quark masses to regularization independent momentum scheme masses, and perturbation theory to relate these to MS, we find m MS ud ð2 GeVÞ ¼ 3:72ð0:16Þ stat ð0:33Þ ren ð0:18Þ syst MeV, m MS s ð2 GeVÞ ¼ 107:3ð4:4Þ stat ð9:7Þ ren ð4:9Þ syst MeV, and mud : ms ¼ 1:28:8ð0:4Þ stat ð1:6Þ syst . For the kaon bag parameter, we find B MS K ð2 GeVÞ ¼ 0:524ð0:010Þ stat ð0:013Þ ren  ð0:025Þ syst . Finally, for the ratios of the couplings of the vector mesons to the vector and tensor currents (f V and f T V , respectively) in the MS scheme at 2 GeV we obtain f T =f ¼ 0:687ð27Þ; f T K à =f K à ¼ 0:712ð12Þ, and f T =f ¼ 0:750ð8Þ.

We present physical results obtained from simulations using 2+1 flavors of domain wall quarks and the Iwasaki gauge action at two values of the lattice spacing a, (a −1 = 1.73 (3) GeV and a −1 = 2.28 (3) GeV). On the coarser lattice, with 24 3 × 64 × 16 points (where the 16 corresponds to L s , the extent of the 5 th dimension inherent in the domain wall fermion (DWF) formulation

We present results of our numerical calculation of the mass spectrum for isospin one-half and spin one-half nonstrange baryons, i.e., the ground and excited states of the nucleon, in quenched lattice QCD. We use a new lattice discretization scheme for fermions, domain wall fermions, which possess almost exact chiral symmetry at nonzero lattice spacing. We make a systematic investigation of the negative-parity N* spectrum by using two distinct interpolating operators at ␤ϭ6/g 2 ϭ6.0 on a 16 3 ϫ32ϫ16 lattice. The mass estimates extracted from the two operators are consistent with each other. The observed large mass splitting between this state, N*(1535), and the positive-parity ground state, the nucleon N(939), is well reproduced by our calculations. We have also calculated the mass of the first positive-parity excited state and find that it is heavier than the negative-parity excited state for the quark masses studied.