[en] After a brief overview of quantum chromodynamics (QCD), the fundamental theory of the strong interactions, we describe the QCDOC computer, its architecture, construction, software and performance. Three 12K-node, 4 Teraflops (sustained) QCDOC computers have been constructed, two at the Brookhaven National Lab and one at the University of Edinburgh. The present status of these machines and their first physics results and objectives are discussed and the catalytic role of the SciDAC program in enabling the effective use of this new architecture by the US lattice QCD community outlined

[en] Here, we present a first-principles lattice QCD+QED calculation at physical pion mass of the leading-order hadronic vacuum polarization contribution to the muon anomalous magnetic moment. The total contribution of up, down, strange, and charm quarks including QED and strong isospin breaking effects is found to be a ^{HVP LO}_μ = 715.4(16.3)(9.2) × 10 ^–10, where the first error is statistical and the second is systematic.

[en] As part of the UKQCD and RBC collaborations'N_f=2+1 domain-wall fermion phenomenology programme, we calculate the first two moments of the light-cone distribution amplitudes of the pseudoscalar mesons π and K and the (longitudinally polarized) vector mesons ρ, K^*, and φ. We obtain the desired quantities with good precision and are able to discern the expected quark-mass dependence of SU(3)-flavor breaking effects. An important ingredient of the calculation is the nonperturbative renormalization of lattice operators using a regularization-independent momentum scheme.

[en] We present the latest results from the UKQCD/RBC collaborations for the K_l3 form factor from simulations with 2 + 1 flavours of dynamical domain wall quarks. Simulations are performed on lattices with two different volumes and four values of the light quark mass, allowing for an extrapolation to the chiral limit. The analysis includes a thorough investigation into the sources of systematic error in our fits. After interpolating to zero momentum transfer, we obtain f₊(0) = 0.964(5) (or δf = -0.013(5)) which, when combined with the latest experimental results for K_l3 decays, leads to |V_us| = 0.2249(14)

[en] We present the first results for the K_l3 form factor from simulations with 2+1 flavors of dynamical domain wall quarks. Combining our result, namely, f₊(0)=0.964(5) with the latest experimental results for K_l3 decays leads to |V_us|=0.2249(14), reducing the uncertaintity in this important parameter. For the O(p⁶) term in the chiral expansion we obtain Δf=-0.013(5)

[en] We demonstrate a method for calculating the neutral B-meson decay constants and mixing matrix elements in unquenched lattice QCD with domain-wall light quarks and static b-quarks. Our computation is performed on the '2+1' flavor gauge configurations generated by the RBC and UKQCD Collaborations with a lattice spacing of a≅0.11 fm (a^-1=1.729 GeV) and a lattice spatial volume of approximately (1.8 fm)³. We simulate at three different light sea quark masses with pion masses down to approximately 430 MeV, and extrapolate to the physical quark masses using a phenomenologically-motivated fit function based on next-to-leading order heavy-light meson SU(2) chiral perturbation theory. For the b-quarks, we use an improved formulation of the Eichten-Hill action with static link-smearing to increase the signal-to-noise ratio. We also improve the heavy-light axial current used to compute the B-meson decay constant to O(α_spa) using one-loop lattice perturbation theory. We present initial results for the SU(3)-breaking ratios f_Bs/f_Bd and ξ=f_Bs√(B_Bs)/f_Bd√(B_Bd), thereby demonstrating the viability of the method. For the ratio of decay constants, we find f_Bs/f_Bd=1.15(12) and for the ratio of mixing matrix elements, we find ξ=1.13(12), where in both cases the errors reflect the combined statistical and systematic uncertainties, including an estimate of the size of neglected O(1/m_b) effects.

[en] We have simulated QCD using 2+1 flavors of domain wall quarks and the Iwasaki gauge action on a (2.74 fm)³ volume with an inverse lattice scale of a^-1=1.729(28) 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 Ω baryon, and the π and K mesons to set the lattice scale and determine the quark masses. We then find f_π=124.1(3.6)_stat(6.9)_syst MeV, f_K=149.6(3.6)_stat(6.3)_syst MeV, and f_K/f_π=1.205(0.018)_stat(0.062)_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_ud^MS(2 GeV)=3.72(0.16)_stat(0.33)_ren(0.18)_syst MeV, m_s^MS(2 GeV)=107.3(4.4)_stat(9.7)_ren(4.9)_syst MeV, and m-tilde_ud ratio m-tilde_s=1 ratio 28.8(0.4)_stat(1.6)_syst. For the kaon bag parameter, we find B_K^MS(2 GeV)=0.524(0.010)_stat(0.013)_ren(0.025)_syst. Finally, for the ratios of the couplings of the vector mesons to the vector and tensor currents (f_V and f_V^T, respectively) in the MS scheme at 2 GeV we obtain f_ρ^T/f_ρ=0.687(27); f_K*^T/f_K*=0.712(12), and f_φ^T/f_φ=0.750(8).

[en] We present a calculation of the renormalization coefficients of the quark bilinear operators and the K-K mixing parameter B_K. The coefficients relating the bare lattice operators to those in the RI/MOM scheme are computed nonperturbatively and then matched perturbatively to the MS scheme. The coefficients are calculated on the RBC/UKQCD 2+1 flavor dynamical lattice configurations. Specifically we use a 16³x32 lattice volume, the Iwasaki gauge action at β=2.13 and domain wall fermions with L_s=16.

[en] We report a direct lattice calculation of the K to ππ decay matrix elements for both the ΔI=1/2 and 3/2 amplitudes A₀ and A₂ on 2+1 flavor, domain wall fermion, 16³x32x16 lattices. This is a complete calculation in which all contractions for the required ten, four-quark operators are evaluated, including the disconnected graphs in which no quark line connects the initial kaon and final two-pion states. These lattice operators are nonperturbatively renormalized using the Rome-Southampton method and the quadratic divergences are studied and removed. This is an important but notoriously difficult calculation, requiring high statistics on a large volume. In this paper, we take a major step toward the computation of the physical K→ππ amplitudes by performing a complete calculation at unphysical kinematics with pions of mass 422 MeV at rest in the kaon rest frame. With this simplification, we are able to resolve Re(A₀) from zero for the first time, with a 25% statistical error and can develop and evaluate methods for computing the complete, complex amplitude A₀, a calculation central to understanding the Δ=1/2 rule and testing the standard model of CP violation in the kaon system.

[en] 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 24³x64x16 points (where the 16 corresponds to L_s, the extent of the 5th dimension inherent in the domain wall fermion formulation of QCD), the analysis of C. Allton et al. (RBC-UKQCD Collaboration), Phys. Rev. D 78 is extended to approximately twice the number of configurations. The ensembles on the finer 32³x64x16 lattice are new. We explain in detail how we use lattice data obtained at several values of the lattice spacing and for a range of quark masses in combined continuum-chiral fits in order to obtain results in the continuum limit and at physical quark masses. We implement this procedure for our data at two lattice spacings and with unitary pion masses in the approximate range 290-420 MeV (225-420 MeV for partially quenched pions). We use the masses of the π and K mesons and the Ω baryon to determine the physical quark masses and the values of the lattice spacing. While our data in the mass ranges above are consistent with the predictions of next-to-leading order SU(2) chiral perturbation theory, they are also consistent with a simple analytic ansatz leading to an inherent uncertainty in how best to perform the chiral extrapolation that we are reluctant to reduce with model-dependent assumptions about higher order corrections. In some cases, particularly for f_π, the pion leptonic decay constant, the uncertainty in the chiral extrapolation dominates the systematic error. Our main results include f_π=124(2)_stat(5)_syst MeV, f_K/f_π=1.204(7)(25) where f_K is the kaon decay constant, m_s^MS(2 GeV)=(96.2±2.7) MeV and m_ud^MS(2 GeV)=(3.59±0.21) MeV (m_s/m_ud=26.8±1.4) where m_s and m_ud are the mass of the strange quark and the average of the up and down quark masses, respectively, [Σ^MS(2 GeV)]^1/3=256(6) MeV, where Σ is the chiral condensate, the Sommer scale r₀=0.487(9) fm and r₁=0.333(9) fm.