[en] The status of lattice calculations of some phenomenology of heavy quarks is presented. Emphasis is on progress made in calculating those quantities relevant to estimating parameters of the quark mixing matrix, namely leptonic decay constants, the bag parameter of neutral B mixing, and semileptonic form factors. New results from studies of quarkonia are highlighted

[en] We study the quenched chiral behavior of hadrons with the pseudoscalar mass as low as ∼ 280 MeV. We look for quenched chiral logs in the pion mass, determine the renormalized quark mass, and observe quenched artifacts in the a₀ and N* propagators. The calculation is done on a quenched lattice of size 20⁴ and a = 0.148(2) fm using overlap fermions and an improved gauge action

[en] We introduce the 'Sequential Empirical Bayes Method', an adaptive constrained-curve fitting procedure for extracting reliable priors. These are then used in standard augmented-chi-square fits on separate data. This better stabilizes fits to lattice QCD overlap-fermion data at very low quark mass where a priori values are not otherwise known. We illustrate the efficacy of the method with data from overlap fermions, on a quenched 16³ x 28 lattice with spatial size La = 3.2 fm and pion mass as low as ∼ 180 MeV

[en] We study the quenched chiral behavior of the pion with mass as low as ∼ 180 MeV. The calculation is done on a quenched lattice of size 16³ x 28 and a = 0.2 fm with 80 configurations using overlap fermions and an improved gauge action. Using an improved constrained curve fitting technique, we find that the ground state pseudoscalar mass versus bare quark mass behavior is well controlled with small statistical errors; this permits a reliable fit of the quenched chiral log effects, a determination of the chiral log parameter (δ = 0.26(3)), and an estimate of the renormalized mass of the light quark (m^MS-bar(μ = 2 GeV) = 3.7(3) MeV)

[en] We extend the study of lowest moments, < x> and < x²>, of the parton distribution function of the nucleon to include those of the sea quarks; this entails a disconnected insertion calculation in lattice QCD. This is carried out on a 16³ x 24 quenched lattice with Wilson fermion. The quark loops are calculated with Z₂ noise vectors and unbiased subtractions, and multiple nucleon sources are employed to reduce the statistical errors. We obtain 5σ signals for < x> for the u,d, and s$ quarks, but < x²> is consistent with zero within errors. We provide results for both the connected and disconnected insertions. The perturbatively renormalized < x> for the strange quark at μ = 2 GeV is < x>_s+#bar s# = 0.027 ± 0.006 which is consistent with the experimental result. The ratio of < x> for s$ vs. u/d in the disconnected insertion with quark loops is calculated to be 0.88 ± 0.07. This is about twice as large as the phenomenologically fitted displays

[en] It is emphasized in the 2015 NSAC Long Range Plan that 'understanding the structure of hadrons in terms of QCD's quarks and gluons is one of the central goals of modern nuclear physics.' Over the last three decades, lattice QCD has developed into a powerful tool for ab initio calculations of strong-interaction physics. Up until now, it is the only theoretical approach to solving QCD with controlled statistical and systematic errors. Since 1985, we have proposed and carried out first-principles calculations of nucleon structure and hadron spectroscopy using lattice QCD which entails both algorithmic development and large-scale computer simulation. We started out by calculating the nucleon form factors -- electromagnetic, axial-vector, ?NN, and scalar form factors, the quark spin contribution to the proton spin, the strangeness magnetic moment, the quark orbital angular momentum, the quark momentum fraction, and the quark and glue decomposition of the proton momentum and angular momentum. The first round of calculations were done with Wilson fermions in the 'quenched' approximation where the dynamical effects of the quarks in the sea are not taken into account in the Monte Carlo simulation to generate the background gauge configurations. Beginning in 2000, we have started implementing the overlap fermion formulation into the spectroscopy and structure calculations. This is mainly because the overlap fermion honors chiral symmetry as in the continuum. It is going to be more and more important to take the symmetry into account as the simulations move closer to the physical point where the u and d quark masses are as light as a few MeV only. We began with lattices which have quark masses in the sea corresponding to a pion mass at ~ 300 MeV and obtained the strange form factors, charm and strange quark masses, the charmonium spectrum and the D_s meson decay constant f_D__s, the strangeness and charmness, the meson mass decomposition and the strange quark spin from the anomalous Ward identity. Recently, we have started to include multiple lattices with different lattice spacings and different volumes including large lattices at the physical pion mass point. We are getting quite close to being able to calculate the hadron structure at the physical point and to do the continuum and large volume extrapolations, which is our ultimate aim. We have now finished several projects which have included these systematic corrections. They include the leptonic decay width of the ρ, the πN sigma and strange sigma terms, and the strange quark magnetic moment. Over the years, we have also studied hadron spectroscopy with lattice calculations and in phenomenology. These include Roper resonance, pentaquark state, charmonium spectrum, glueballs, scalar mesons a_0(1450) and σ(600) and other scalar mesons, and the 1"-"+ meson. In addition, we have employed the canonical approach to explore the first-order phase transition and the critical point at finite density and finite temperature. We have also discovered a new parton degree of freedom -- the connected sea partons, from the path-integral formulation of the hadronic tensor, which explains the experimentally observed Gottfried sum rule violation. Combining experimental result on the strange parton distribution, the CT10 global fitting results of the total u and d anti-partons and the lattice result of the ratio of the momentum fraction of the strange vs that of u or d in the disconnected insertion, we have shown that the connected sea partons can be isolated. In this final technical report, we shall present a few representative highlights that have been achieved in the project.

[en] Highlights: → We propose a method to compute the polarization for a multi-dimensional random distribution. → We apply the method to the eigenemodes of the Dirac operator in pure glue QCD. → We compute the chiral polarization for these modes and study its scale dependence. → We find that in a finite volume there is a scale where the polarization tendency changes. → We study the continuum limit of this chiral polarization scale. - Abstract: We propose a framework for quantitative evaluation of dynamical tendency for polarization in an arbitrary random variable that can be decomposed into a pair of orthogonal subspaces. The method uses measures based on comparisons of given dynamics to its counterpart with statistically independent components. The formalism of previously considered X-distributions is used to express the aforementioned comparisons, in effect putting the former approach on solid footing. Our analysis leads to the definition of a suitable correlation coefficient with clear statistical meaning. We apply the method to the dynamics induced by pure-glue lattice QCD in local left-right components of overlap Dirac eigenmodes. It is found that, in finite physical volume, there exists a non-zero physical scale in the spectrum of eigenvalues such that eigenmodes at smaller (fixed) eigenvalues exhibit convex X-distribution (positive correlation), while at larger eigenvalues the distribution is concave (negative correlation). This chiral polarization scale thus separates a regime where dynamics enhances chirality relative to statistical independence from a regime where it suppresses it, and gives an objective definition to the notion of 'low' and 'high' Dirac eigenmode. We propose to investigate whether the polarization scale remains non-zero in the infinite volume limit, in which case it would represent a new kind of low energy scale in QCD.

[en] We report the first lattice QCD calculation of the glue spin in the nucleon. The lattice calculation is carried out with valence overlap fermions on 2+1 flavor DWF gauge configurations on four lattice spacings and four volumes including an ensemble with physical values for the quark masses. The glue spin S_G in the Coulomb gauge in the MSbar scheme is obtained with the 1-loop perturbative matching. We find the results fairly insensitive to lattice spacing and quark masses. We also find that the proton momentum dependence of S_G in the range 0≤ p <1.5 GeV is very mild, and we determine it in the large momentum limit to be S_G= 0.251(47)(16) at the physical pion mass in the MSbar scheme at μ^2= 10 GeV^2. If the matching procedure in large momentum effective theory is neglected, S_G is equal to the glue helicity measured in high-energy scattering experiments.

[en] We present the N_f=2+1 clover fermion lattice QCD calculation of the nucleon strangeness form factors. We evaluate disconnected insertions using the Z(4) stochastic method, along with unbiased subtractions from the hopping parameter expansion. We find that increasing the number of nucleon sources for each configuration improves the signal significantly. We obtain G_M^s(0)=-0.017(25)(07), where the first error is statistical, and the second is the uncertainties in Q² and chiral extrapolations. This is consistent with experimental values, and has an order of magnitude smaller error.

[en] We employ dimension-4 operators to improve the local vector and axial-vector currents and calculate the nucleon isovector axial coupling $g$${{}^3}_A$ with overlap valence on 2 + 1-flavor domain wall fermion (DWF) sea. Using the equality of $g$${{}^3}_A$ from the spatial and temporal components of the axial-vector current as a normalization condition, we find that $g$${{}^3}_A$ is increased by a few percent towards the experimental value. Here, the excited-state contamination has been taken into account with three time separations between the source and sink. The improved axial charges $g$${{}^3}_A$ (24I) = 1.22 (4) (3) and $g$${{}^3}_A$ (32I) = 1.21 (3)(3) are obtained on a 24³ × 64 lattice at pion mass of 330 MeV and a 32³ × 64 lattice at pion mass 300 MeV and are increased by 3.4% and 1.7% from their unimproved values, respectively. We have also used clover fermions on the same DWF configurations and find the same behavior for the local axial charge as that with overlap fermions.