Colin Morningstar

Glueball spectrum from an anisotropic lattice study

away all of the other unwanted states. An additional smallvolume simulation is done to assist in this identification and to study the systematic errors from finite volume. Finally, discretization errors are treated by extrapolating the energies to the continuum limit and determining the continuum spin quantum numbers. The end result is a nearly complete survey of the glueball spectrum in the pure gauge theory below 4 GeV. We find a total of 13 glueballs; two other tentative candidates are also located. With the exception of the light glueballs in the 0 11 sector, our results significantly improve upon those from previous studies @2‐4# of the complete lowlying glueball spectrum. This paper is organized as follows. The details of the simulations, including the construction of the glueball operators, the generation of the gauge-field configurations, the extraction of energies from Monte Carlo estimates of the correlation functions, and the lattice spacing determinations in terms of the hadronic scale r 0, are described in Sec. II. All of our energy estimates in terms of the inverse temporal lattice spacing are presented in this section. In Sec. III, the differentiation of single glueball states from two-glueball and torelon-pair states is discussed. Systematic errors from finite volume are studied in Sec. IV. The removal of lattice spacing errors, including the extrapolations to the continuum limit and the identification of the continuum spin quantum numbers, is described in Sec. V. We also discuss the problematical scalar states in this section and cite ongoing efforts to reduce their discretization errors. Section VI presents a discussion of the spectrum, and our findings are summarized with an outline of future work in the concluding Sec. VII.

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.

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/{psi} 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.

Efficient glueball simulations on anisotropic lattices

Monte Carlo results for the low-lying glueball spectrum using an improved, anisotropic action are presented. Ten simulations at lattice spacings ranging from 0.2 to 0.4 fm and two different anisotropies have been performed in order to demonstrate the advantages of using coarse, anisotropic lattices to calculate glueball masses. Our determinations of the tensor (2 11 ) and pseudovector (1 12 ) glueball masses are more accurate spacing should be the inverse of the energy of the states of interest; thus, for glueballs, a temporal cutoff larger than 1.5 GeV allows resolution from accessible statistics of the correlator over a few time slices. Meanwhile, the scale for the spatial lattice should be set by the size of the wave func- tion of the state; a spatial grid separation in the range 0.2-0.4 fm would seem reasonable. Since we propose to use lattices in which the temporal lattice spacing is small, improvement of the discretization in this direction is not needed. Thus, a lattice action which couples only nearest-neighbor time slices can be used. The transfer matrix corresponding to such an action is Hermitian and positive definite; all of our effective masses must con- verge to their plateau values monotonically from above. This ensures the validity of variational techniques which mini- mize the effective masses at small temporal separations. Such techniques are very effective in diminishing the excited-state contributions to the glueball correlation func- tions and are crucial for efficient extraction of ground-state masses. In this paper, we demonstrate the increased efficiency of glueball simulations using these actions on anisotropic lat- tices. We present results for the masses of three of the lighter SU~3! glueball states, the scalar (0 11 ), the tensor (2 11 ), and the pseudovector (1 12 ). The masses of the first-excited states in the scalar and tensor channels were also examined. Ten simulations at lattice spacings ranging from 0.2 to 0.4 fm were performed, enabling reliable extrapolations to the continuum limit ~although the mass of the scalar glueball was somewhat problematic!. The results are compared to previous simulation data obtained using the Wilson action and we find that more accurate determinations of the tensor and pseudovector glueball masses have been achieved. A comparison of efficiencies is also made. Lastly, finite- volume effects are shown to be small. The new action used in our simulations is described in Sec. II. The details of the glueball simulations, including the construction of the glueball operators, the generation of the gauge-field configurations, and the analysis of the Monte Carlo data, are given in Sec. III. The hadronic scale r 0 is used to relate our results at different values of the coupling b and the aspect ratio j. The determination of this scale in

Fine structure of the QCD string spectrum.

Using advanced lattice methods in quantum chromodynamics, three distinct scales are established in the excitation spectrum of the gluon field around a static quark-antiquark pair as the color source separation R is varied. On the shortest length scale, the excitations are consistent with states created by local gluon field operators arising from a multipole operator product expansion. An intermediate crossover region below 2 fm is identified with a dramatic rearrangement of the level orderings. On the largest length scale of 2-3 fm, the spectrum agrees with that expected for stringlike excitations. The energies nearly reproduce asymptotic pi/R string gaps, but exhibit a fine structure, providing important clues for developing an effective bosonic string description.

First results from 2+1 dynamical quark flavors on an anisotropic lattice: Light-hadron spectroscopy and setting the strange-quark mass

We present the first light-hadron spectroscopy on a set of

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

{N}_{f}=2+1

Constrained curve fitting

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.

Light hadron spectroscopy using domain wall valence quarks on an Asqtad sea

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.

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

We survey techniques for constrained curve fitting, based upon Bayesian statistics, that offer significant advantages over conventional techniques used by lattice field theorists.