Glueball spectrum from an anisotropic lattice study

The spectrum of glueballs below 4 GeV in the SU(3) pure-gauge theory is investigated using Monte Carlo simulations of gluons on several anisotropic lattices with spatial grid separations ranging from 0.1 to 0.4 fm. Systematic errors from discretization and finite volume are studied, and the continuum spin quantum numbers are identified. Care is taken to distinguish single glueball states from two-glueball and torelon-pair states. Our determination of the spectrum significantly improves upon previous Wilson action calculations.</p

Analytic smearing of SU(3) link variables in lattice QCD

An analytic method of smearing link variables in lattice QCD is proposed and tested. The differentiability of the smearing scheme with respect to the link variables permits the use of modern Monte Carlo updating methods based on molecular dynamics evolution for gauge-field actions constructed using such smeared links. In examining the smeared mean plaquette and the static quark-antiquark potential, no degradation in effectiveness is observed as compared to link smearing methods currently in use, although an increased sensitivity to the smearing parameter is found.</p

Improved stochastic estimation of quark propagation with Laplacian Heaviside smearing in lattice QCD

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 multihadron 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 243×128 lattices with spatial spacing as∼0.12  fm and temporal spacing at∼0.034  fm for pion masses mπ≈390 and 240 MeV.</p

Extended hadron and two-hadron operators of definite momentum for spectrum calculations in lattice QCD

<p>Multihadron operators are crucial for reliably extracting the masses of excited states lying above multihadron thresholds in lattice QCD Monte Carlo calculations. The construction of multihadron operators with significant coupling to the lowest-lying multihadron states of interest involves combining single hadron operators of various momenta. The design and implementation of large sets of spatially-extended single-hadron operators of definite momentum and their combinations into two-hadron operators are described. The single hadron operators are all assemblages of gauge-covariantly-displaced, smeared quark fields. Group-theoretical projections onto the irreducible representations of the symmetry group of a cubic spatial lattice are used in all isospin channels. Tests of these operators on 243×128 and 323×256 anisotropic lattices using a stochastic method of treating the low-lying modes of quark propagation which exploits Laplacian Heaviside quark-field smearing are presented. The method provides reliable estimates of all needed correlations, even those that are particularly difficult to compute, such as ηη→ηη in the scalar channel, which involves the subtraction of a large vacuum expectation value. A new glueball operator is introduced, and the evaluation of the mixing of this glueball operator with a quark-antiquark operator, ππ, and ηη operators is shown to be feasible.</p

Nucleon, Δ, and Ω excited state spectra in Nf=2+1 lattice QCD

The energies of the excited states of the nucleon, Δ, and Ω are computed in lattice QCD, using two light quarks and one strange quark on anisotropic lattices. The calculation is performed at three values of the light quark mass, corresponding to pion masses mπ=392(4), 438(3), and 521(3) MeV. We employ the variational method with a large basis of interpolating operators enabling six energies in each irreducible representation of the lattice to be distinguished clearly. We compare our calculation with the low-lying experimental spectrum, with which we find reasonable agreement in the pattern of states. The need to include operators that couple to the expected multihadron states in the spectrum is clearly identified.</p

Group-theoretical construction of extended baryon operators in lattice QCD

The design and implementation of large sets of spatially extended, gauge-invariant operators for use in determining the spectrum of baryons in lattice QCD computations are described. Group-theoretical projections onto the irreducible representations of the symmetry group of a cubic spatial lattice are used in all isospin channels. The operators are constructed to maximize overlaps with the low-lying states of interest, while minimizing the number of sources needed in computing the required quark propagators. Issues related to the identification of the spin quantum numbers of the states in the continuum limit are addressed.</p

Lattice QCD determination of patterns of excited baryon states

Energies for excited isospin I=1/2 and I=3/2 states that include the nucleon and Δ families of baryons are computed using quenched, anisotropic lattices. Baryon interpolating field operators that are used include nonlocal operators that provide G2 irreducible representations of the octahedral group. The decomposition of spin 5/2 or higher spin states is realized for the first time in a lattice QCD calculation. We observe patterns of degenerate energies in the irreducible representations of the octahedral group that correspond to the subduction of the continuum spin 5/2 or higher. The overall pattern of low-lying excited states corresponds well to the pattern of physical states subduced to the irreducible representations of the octahedral group.</p

Novel quark-field creation operator construction for hadronic physics in lattice QCD

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.</p

Excited state nucleon spectrum with two flavors of dynamical fermions

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 243×64, spatial lattice spacing as≈0.11  fm, and temporal lattice spacing at=1/3as. 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.</p

Glueball spectrum and matrix elements on anisotropic lattices

The glueball-to-vacuum matrix elements of local gluonic operators in scalar, tensor, and pseudoscalar channels are investigated numerically on several anisotropic lattices with the spatial lattice spacing ranging from 0.1–0.2 fm. These matrix elements are needed to predict the glueball branching ratios in J/ψ radiative decays which will help identify the glueball states in experiments. Two types of improved local gluonic operators are constructed for a self-consistent check and the finite-volume effects are studied. We find that lattice spacing dependence of our results is very weak and the continuum limits are reliably extrapolated, as a result of improvement of the lattice gauge action and local operators. We also give updated glueball masses with various quantum numbers.</p