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.

Over the last twenty years, the open source community has provided more and more software on which the world's High Performance Computing (HPC) systems depend for performance and productivity. The community has invested millions of dollars and years of effort to build key components. But although the investments in these separate software elements have been tremendously valuable, a great deal of productivity has also been lost because of the lack of planning, coordination, and key integration of technologies necessary to make them work together smoothly and efficiently, both within individual PetaScale systems and between different systems. It seems clear that this completely uncoordinated development model will not provide the software needed to support the unprecedented parallelism required for peta/exascale computation on millions of cores, or the flexibility required to exploit new hardware models and features, such as transactional memory, speculative execution, and GPUs. This report describes the work of the community to prepare for the challenges of exascale computing, ultimately combing their efforts in a coordinated International Exascale Software Project.

The results of an exploratory lattice study of heavy baryon spectroscopy are presented. We have computed the full spectrum of the eight baryons containing a single heavy quark, on a 24 3 × 48 lattice at β = 6.2, using an O(a)-improved fermion action.We discuss the lattice baryon operators and give a method for isolating the contributions of the spin doublets (Σ, Σ * ), (Ξ ′ , Ξ * ) and (Ω, Ω * ) to the correlation function of the relevant operator. We compare our results with the available experimental data and find good agreement in both the charm and the beauty sectors, despite the long extrapolation in the heavy quark mass needed in the latter case. We also predict the masses of several undiscovered baryons. We compute the Λ − pseudoscalar meson and Σ − Λ mass splittings. Our results, which have errors in the range 10 − 30%, are in good agreement with the experimental numbers. For the Σ * − Σ mass splitting, we

2We determine the neutral kaon mixing matrix element B K in the continuum limit with 2+1 flavors of domain wall fermions, using the Iwasaki gauge action at two different lattice spacings. These lattice fermions have near exact chiral symmetry and therefore avoid artificial lattice operator mixing.We introduce a significant improvement to the conventional NPR method in which the bare matrix elements are renormalized non-perturbatively in the RI-MOM scheme and are then converted into the MS scheme using continuum perturbation theory. In addition to RI-MOM, we introduce and implement four non-exceptional intermediate momentum schemes that suppress infrared non-perturbative uncertainties in the renormalization procedure. We compute the conversion factors relating the matrix elements in this family of RI-SMOM schemes and MS at one-loop order.Comparison of the results obtained using these different intermediate schemes allows for a more reliable estimate of the unknown higher-order contributions and hence for a correspondingly more robust estimate of the systematic error. We also apply a recently proposed approach in which twisted boundary conditions are used to control the Symanzik expansion for off-shell vertex functions leading to a better control of the renormalization in the continuum limit.We control chiral extrapolation errors by considering both the NLO SU(2) chiral effective theory, and an analytic mass expansion. We obtain B MS K (3 GeV) = 0.529(5) stat (15) χ (2) FV (11) NPR . This corresponds toB RGI K = 0.749(7) stat (21) χ (3) FV (15) NPR . Adding all sources of error in quadrature we obtainB RGI K = 0.749(27) combined , with an overall combined error of 3.6%.3

Michael; RBC Collaboration; UKQCD Collaboration Kl3 semileptonic form factor from (2+1)-flavor lattice QCD

The spectrum of orbitally excited D s mesons is computed in the continuum limit of quenched lattice QCD. The results are consistent with the interpretation that the narrow resonance in the D s π 0 channel discovered by the BABAR Collaboration is a J P = 0 + cs meson. Furthermore, within statistical errors, the 1 + − 1 − and the 0 + − 0 − mass splittings are equal, in agreement with the chiral multiplet structure predicted by heavy hadron chiral effective theory. On our coarsest lattice we present results from the first study of orbitally excited D s mesons with two flavors of dynamical quarks, with mass slightly larger than the strange quark mass. These results are consistent with the quenched data.

We present results of a lattice analysis of the B parameter B B , the decay constant f B , and several mass splittings using the static approximation. Results were obtained for 60 quenched gauge configurations computed at ␤ϭ6.2 on a lattice size of 24 3 ϫ48. Light quark propagators were calculated using the O(a)-improved Sheikholeslami-Wohlert action. We findcorresponding to B B static ϭ1.02 Ϫ6 Ϫ2 ϩ5 ϩ3 , f B static ϭ266 Ϫ20 Ϫ27 ϩ18 ϩ28 MeV, and f B s 2 B B s / f B 2 B B ϭ1.34 Ϫ8 Ϫ3 ϩ9 ϩ5 , where a variational fitting technique was used to extract f B static . For the mass splittings we obtain M B s ϪM B d ϭ87 Ϫ12 Ϫ12 ϩ15 ϩ6 MeV, M ⌳ b ϪM B d ϭ420 Ϫ90 Ϫ30 ϩ100 ϩ30 MeV, and M B* 2 ϪM B 2 ϭ0.281 Ϫ16 Ϫ37 ϩ15 ϩ40 GeV 2 . We compare different smearing techniques in-tended to improve the signal/noise ratio. From a detailed assessment of systematic effects, we conclude that the main systematic uncertainties are associated with the renormalization constants relating a lattice matrix element to its continuum counterpart. The dependence of our findings on lattice artifacts is to be investigated in the future. ͓S0556-2821͑96͒04715-7͔