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.

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 for computing all elements of the lattice quark propagator is proposed. The method combines the spectral decomposition of the propagator, computing the lowest eigenmodes exactly, with noisy estimators which are 'diluted', i.e. taken to have support only on a subset of time, space, spin or colour. We find that the errors are dramatically reduced compared to traditional noisy estimator techniques.Comment: 24 pages, 18 figure

Hybrid bgb molecules in which the heavy bb pair is bound together by the excited gluon field g are studied using the Born-Oppenheimer expansion and quenched numerical simulations. The consistency of results from the two approaches reveals a simple and compelling physical picture for heavy hybrid states. PACS number(s): 11.15. Ha, 12.38.Gc, 12.39.Mk In addition to conventional hadrons, QCD predicts the existence of glueballs and hybrid states which contain excited gluon fields. Hybrid mesons with heavy bb quark pairs are the most amenable to theoretical treatment. They are also experimentally accessible: early results from the CUSB and CLEO collaborations [1,2] revealed a complex resonance structure between the BB threshold and 11.2 GeV in e + e − annihiliation, precisely where the lowest hybrid excitations are expected [3].In this work, we determine the masses of the lowest bgb states. Heavy hybrid mesons can be studied not only directly by numerical simulation, but also using the Born-Oppenheimer expansion which is our primary guidance for the development of a simple physical picture. The Born-Oppenheimer picture was introduced for the description of heavy hybrid states in Refs. [4,5] and was applied using hybrid potentials first calculated in lattice QCD in Ref. [6]. In this new study, we work to leading order in the expansion and neglect higher-order terms involving spin, relativistic, and retardation effects. We test the accuracy of the Born-Oppenheimer approach by comparison with high-precision results from simulations.Our hybrid meson simulations are the first to exploit anisotropic lattices with improved actions; preliminary reports on some of our results have appeared previously [7]. The hybrid meson mass uncertainties with improved anisotropic lattice technology are dramatically smaller than those obtained in recent isotropic lattice studies in the nonrelativistic formulation of lattice QCD (NRQCD) using the Wilson gauge action [8,9]. We report here our final analysis on four distinct hybrid bgb states. Although the effects of dynamical sea quarks are not included in our quenched simulations, we will comment on their impact on the hybrid spectrum. The mass of the lowest hybrid cgc state was determined recently [10] without NRQCD expansion for the slowly moving heavy quark and agrees with our Born-Oppenheimer results [3] (see caption of Fig. 1).The hybrid meson can be treated analogous to a diatomic molecule: the slow heavy quarks correspond to the nuclei and the fast gluon field corresponds to the electrons [4]. First, one treats the quark Q and antiquark Q as spatially-fixed color sources and determines the energy levels of the excited gluon field as a function of the QQ separation r; each of these excited energy levels defines an adiabatic potential V QgQ (r). The quark motion is then restored by solving the Schrödinger equation in each of these potentials. Conventional quarkonia are based on the lowest-lying static potential; hybrid quarkonium states emerge from the excited potentials. Once the st...

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.