A new quark-field smearing algorithm is defined which enables efficient calculations of a broad range of hadron correlation functions. The technique applies a low-rank operator to define smooth fields that are to be used in hadron creation operators. The resulting space of smooth fields is small enough that all elements of the reduced quark propagator can be computed exactly at reasonable computational cost. Correlations between arbitrary sources, including multihadron operators can be computed a posteriori without requiring new lattice Dirac operator inversions. The method is tested on realistic lattice sizes with light dynamical quarks.

A new method of stochastically estimating the low-lying effects of quark propagation is proposed which allows accurate determinations of temporal correlations of single-hadron and multi-hadron operators in lattice QCD. The method is well suited for calculations in large volumes. Contributions involving quark propagation connecting hadron sink operators at the same final time can be handled in a straightforward manner, even for a large number of final time slices. The method exploits Laplacian Heaviside (LapH) smearing. ZN noise is introduced in a novel way, and variance reduction is achieved using judiciously-chosen noise dilution projectors. The method is tested using isoscalar mesons in the scalar, pseudoscalar, and vector channels, and using the two-pion system of total isospin I = 0, 1, 2 on large anisotropic 24 3 × 128 lattices with spatial spacing as ∼ 0.12 fm and temporal spacing at ∼ 0.034 fm for pion masses mπ ≈ 390 and 240 MeV.

Hadron Spectrum Collaboration)We present the first light-hadron spectroscopy on a set of N f = 2 + 1 dynamical, anisotropic lattices. A convenient set of coordinates that parameterize the two-dimensional plane of light and strange-quark masses is introduced. These coordinates are used to extrapolate data obtained at the simulated values of the quark masses to the physical light and strange-quark point. A measurement of the Sommer scale on these ensembles is made, and the performance of the hybrid Monte Carlo algorithm used for generating the ensembles is estimated.

We present a first N f = 2 lattice estimate of the hadronic coupling g12 which parametrises the strong decay of a radially excited B * meson into the ground state B meson at zero recoil. We work in the static limit of Heavy Quark Effective Theory (HQET) and solve a Generalised Eigenvalue Problem (GEVP), which is necessary for the extraction of excited state properties. After an extrapolation to the continuum limit and a check of the pion mass dependence, we obtain g12 = −0.17(4).

The elastic I = 1 p-wave ππ scattering amplitude is calculated together with the isovector timelike pion form factor using lattice QCD with N f = 2 + 1 dynamical quark flavors. Wilson clover ensembles generated by the Coordinated Lattice Simulations (CLS) initiative are employed at four lattice spacings down to a = 0.05 fm, several pion masses down to m π = 200 MeV, and spatial volumes of extent L = 3.1 − 5.5 fm. The set of measurements on these ensembles, which is publicly available, enables an investigation of systematic errors due to the finite lattice spacing and spatial volume. The ππ scattering amplitude is fit on each ensemble by a Breit-Wigner resonance lineshape, while the form factor is described better by a thrice-subtracted dispersion relation than the Gounaris-Sakurai parametrization.

The I = 1 p-wave and I = 2 s-wave elastic π-π scattering amplitudes are calculated from a first-principles lattice QCD simulation using a single ensemble of gauge field configurations with N f = 2 + 1 dynamical flavors of anisotropic clover-improved Wilson fermions. This ensemble has a large spatial volume V = (3.7fm) 3 , pion mass m π = 230MeV, and spatial lattice spacing a s = 0.11fm. Calculation of the necessary temporal correlation matrices is efficiently performed using the stochastic LapH method, while the large volume enables an improved energy resolution compared to previous work. For this single ensemble we obtain m ρ /m π = 3.350(24), g ρππ = 5.99(26), and a clear signal for the I = 2 s-wave. The success of the stochastic LapH method in this proof-of-principle large-volume calculation paves the way for quantitative study of the lattice spacing effects and quark mass dependence of scattering amplitudes using state-of-the-art ensembles.

We determine the parameter c SW required for O(a)-improvement of the three-flavor Wilson fermion action together with the tree-level Symanzik improved gauge action. The standard improvement condition is employed for a range of couplings. Additionally, we perform a check of the volume independence of c SW and provide a preliminary estimate of the lattice spacing at our largest values of the gauge coupling.

Highly excited states for isospin 1 2 baryons are calculated for the first time using lattice QCD with two flavors of dynamical quarks. Anisotropic lattices are used with two pion masses, mπ = 416(36) MeV and 578(29) MeV. The lowest four energies are reported in each of the six irreducible representations of the octahedral group at each pion mass. The lattices used have dimensions 24 3 ×64, spatial lattice spacing as ≈ 0.11 fm and temporal lattice spacing at = 1 3 as. Clear evidence is found for a 5 2 − state in the pattern of negative-parity excited states. This agrees with the pattern of physical states and spin 5 2 has been realized for the first time on the lattice.