Bottomonium spectrum at order v^6 from domain-wall lattice QCD: precise results for hyperfine splittings

The bottomonium spectrum is computed in dynamical 2+1 flavor lattice QCD, using NRQCD for the b quarks. The main calculations in this work are based on gauge field ensembles generated by the RBC and UKQCD collaborations with the Iwasaki action for the gluons and a domain-wall action for the sea quarks. Lattice spacing values of approximately 0.08 fm and 0.11 fm are used, and simultaneous chiral extrapolations to the physical pion mass are performed. As a test for gluon discretization errors, the calculations are repeated on two ensembles generated by the MILC collaboration with the Luscher-Weisz gauge action. Gluon discretization errors are also studied in a lattice potential model using perturbation theory for four different gauge actions. The nonperturbative lattice QCD results for the radial and orbital bottomonium energy splittings obtained from the RBC/UKQCD ensembles are found to be in excellent agreement with experiment. To get accurate results for spin splittings, the spin-dependent order-v^6 terms are included in the NRQCD action, and suitable ratios are calculated such that most of the unknown radiative corrections cancel. The cancellation of radiative corrections is verified explicitly by repeating the calculations with different values of the couplings in the NRQCD action. Using the lattice ratios of the S-wave hyperfine and the 1P tensor splitting, and the experimental result for the 1P tensor splitting, the 1S hyperfine splitting is found to be 60.3+-5.5(stat)+-5.0(syst)+-2.1(exp) MeV, and the 2S hyperfine splitting is predicted to be 23.5+-4.1(stat)+-2.1(syst)+-0.8(exp) MeV.Comment: 36 pages, 14 figures. v2: added Appendix D containing detailed analysis of gluon discretization errors using a lattice potential model and comparison to results from MILC ensembles. Estimates of systematic errors in hyperfine splittings now include gluon discretization errors and b-bbar annihilation contribution. Accepted for publication in PR

Localized eigenmodes of the covariant lattice Laplacian

We study numerically the eigenmode spectrum of the covariant lattice Laplacian, in the fundamental SU(2) color group representation. It is found that eigenmodes at the lower and upper ends of the spectrum are localized, and that the localization volume scales. In contrast, the eigenmodes of the lattice Faddeev-Popov operator are all extended rather than localized (as required for confinement) despite the similarity of the kinetic and Faddeev-Popov operators.Comment: Talk presented by J. Greensite at Lattice2005 (Topology and Confinement), Dublin, July 25-30, 2005; 6 pages, 4 figures, uses PoS.cls; to appear in Proceedings of Scienc

Nucleon electromagnetic form factors from lattice QCD using a nearly physical pion mass

We present lattice QCD calculations of nucleon electromagnetic form factors using pion masses $m_\pi$ = 149, 202, and 254 MeV and an action with clover-improved Wilson quarks coupled to smeared gauge fields, as used by the Budapest-Marseille-Wuppertal collaboration. Particular attention is given to removal of the effects of excited state contamination by calculation at three source-sink separations and use of the summation and generalized pencil-of-function methods. The combination of calculation at the nearly physical mass $m_\pi$ = 149 MeV in a large spatial volume ($m_\pi L_s$ = 4.2) and removal of excited state effects yields agreement with experiment for the electric and magnetic form factors $G_E(Q^2)$ and $G_M(Q^2)$ up to $Q^2$ = 0.5 GeV$^2$.Comment: v2: published version; 30 pages, 25 figures, 6 table

Initial nucleon structure results with chiral quarks at the physical point

We report initial nucleon structure results computed on lattices with 2+1 dynamical M\"obius domain wall fermions at the physical point generated by the RBC and UKQCD collaborations. At this stage, we evaluate only connected quark contributions. In particular, we discuss the nucleon vector and axial-vector form factors, nucleon axial charge and the isovector quark momentum fraction. From currently available statistics, we estimate the stochastic accuracy of the determination of $g_A$ and $_{u-d}$ to be around 10%, and we expect to reduce that to 5% within the next year. To reduce the computational cost of our calculations, we extensively use acceleration techniques such as low-eigenmode deflation and all-mode-averaging (AMA). We present a method for choosing optimal AMA parameters.Comment: 7 pages, 11 figures; talk presented at the 32nd International Symposium on Lattice Field Theory, 23-28 June, 2014, Columbia University, New York, US

Quark Contributions to Nucleon Momentum and Spin from Domain Wall fermion calculations

We report contributions to the nucleon spin and momentum from light quarks calculated using dynamical domain wall fermions with pion masses down to 300 MeV and fine lattice spacing a=0.084 fm. Albeit without disconnected diagrams, we observe that spin and orbital angular momenta of both u and d quarks are opposite, almost canceling in the case of the d quark, which agrees with previous calculations using a mixed quark action. We also present the full momentum dependence of n=2 generalized form factors showing little variation with the pion mass.Comment: 7 pages, 5 figures, NT-LBNL-11-020, MIT-CTP-4323. Presented at the 29th International Symposium on Lattice Field Theory (Lattice 2011), Squaw Valley, California, 10-16 Jul 201

Peculiarities in the Spectrum of the Adjoint Scalar Kinetic Operator in Yang-Mills Theory

We study the spectrum of low-lying eigenmodes of the kinetic operator for scalar particles, in the color adjoint representation of Yang-Mills theory. The kinetic operator is the covariant Laplacian, plus a constant which serves to renormalize mass. In the pure gauge theory, our data indicates that the interval between the lowest eigenvalue and the mobility edge tends to infinity in the continuum limit. On these grounds, it is suggested that the perturbative expression for the scalar propagator may be misleading even at distance scales that are small compared to the confinement scale. We also measure the density of low-lying eigenmodes, and find a possible connection to multi-critical matrix models of order m=1.Comment: 9 pages, 14 figure

High Energy Physics from High Performance Computing

We discuss Quantum Chromodynamics calculations using the lattice regulator. The theory of the strong force is a cornerstone of the Standard Model of particle physics. We present USQCD collaboration results obtained on Argonne National Lab's Intrepid supercomputer that deepen our understanding of these fundamental theories of Nature and provide critical support to frontier particle physics experiments and phenomenology.Comment: Proceedings of invited plenary talk given at SciDAC 2009, San Diego, June 14-18, 2009, on behalf of the USQCD collaboratio