We investigate the mass of the $1^{-+}$ exotic meson, created with hybrid interpolating fields. Access to light quark masses approaching 25 MeV is facilitated by the use of the Fat-Link Irrelevant Clover (FLIC) fermion action, and large ($20^3 \times 40$) lattices. Our results indicate that the $1^{-+}$ exotic exhibits significant curvature close to the chiral limit, and yield a $1^{-+}$ mass in agreement with the $\pi_1 (1600)$ candidate and exclusive of the $\pi_1 (1400)$.

The mass of the $1^{-+}$ exotic meson, created with hybrid interpolating fields, is explored at light quark masses approaching 25 MeV ($m_\pi / m_\rho \simeq 1/3$). Access to such light quark masses is facilitated by the use of the Fat-Link Irrelevant Clover (FLIC) fermion action. Additionally, we make use of large ($20^3 \times 40$) lattices to obtain good control of statistical and finite volume errors. Our results indicate that the $1^{-+}$ exotic exhibits significant curvature close the chiral limit, indicating previous linear extrapolations, far from the chiral regime, have overestimated the mass of the $1^{-+}$. We find for the first time in lattice studies a $1^{-+}$ mass in agreement with the $\pi_1 (1600)$ candidate. We also find a strangeness $\pm$1 $J^P = 1^-$ state with a mass close to 2 GeV.

Hybrid (exotic) mesons, which are important predictions of quantum chromodynamics (QCD), are states of quarks and anti-quarks bound by excited gluons. First principle lattice study of such states would help us understand the role of ``dynamical'' color in low energy QCD and provide valuable information for experimental search for these new particles. In this paper, we apply both improved gluon and quark actions to the hybrid mesons, which might be much more efficient than the previous works in reducing lattice spacing error and finite volume effect. Quenched simulations were done at $\beta=2.6$ and on a $\xi=3$ anisotropic $12^3\times36$ lattice using our PC cluster. We obtain $2013 \pm 26 \pm 71$ MeV for the mass of the $1^{-+}$ hybrid meson ${\bar q}qg$ in the light quark sector, and $4369 \pm 37 \pm 99$Mev in the charm quark sector; the mass splitting between the $1^{-+}$ hybrid meson ${\bar c}c g$ in the charm quark sector and the spin averaged S-wave charmonium mass is estimated to be $1302 \pm 37 \pm 99$ MeV. As a byproduct, we obtain $1438 \pm 32 \pm 57$ MeV for the mass of a P-wave $1^{++}$ ${\bar u}u$ or ${\bar d}d$ meson and $1499 \pm 28 \pm 65$ MeV for the mass of a P-wave $1^{++}$ ${\bar s}s$ meson, which are comparable to their experimental value 1426 MeV for the $f_1(1420)$ meson. The first error is statistical, and the second one is systematical. The mixing of the hybrid meson with a four quark state is also discussed.

The spectral properties of hybrid meson interpolating fields are investigated. The quantum numbers of the meson are carried by smeared-source fermion operators and highly-improved chromo-electric and -magnetic field operators composed with APE-smeared links. The effective masses of standard and hybrid operators indicate that the ground state meson is effectively isolated using both standard and hybrid interpolating fields. Focus is placed on interpolating fields in which the large spinor components of the quark and antiquark fields are merged. In particular, the effective mass of the exotic $1^{-+}$ meson is reported. Further, we report some values for excited mesonic states using a variational process.

The spectral properties of hybrid meson interpolating fields are investigated. The quantum numbers of the meson are carried by smeared-source fermion operators and highly-improved chromo-electric and -magnetic field operators composed with APE-smeared links. The effective masses of standard and hybrid operators indicate that the ground state meson is effectively isolated using both standard and hybrid interpolating fields. Focus is placed on interpolating fields in which the large spinor components of the quark and antiquark fields are merged. In particular, the effective mass of the exotic $1^{-+}$ meson is reported.

We use the non-relativistic expansion of QCD (NRQCD) on the lattice to study the lowest hybrid configuration contribution to the ground state of heavy S-wave mesons. Using lowest-order lattice NRQCD to create the heavy-quark propagators, we form a basis of ``unperturbed'' S-wave and hybrid states. We then apply the lowest-order coupling of the quark spin and chromomagnetic field at an intermediate time slice to create ``mixed'' correlators between the S-wave and hybrid states. From the resulting amplitudes, we extract the off-diagonal element of our two-state Hamiltonian. Diagonalizing this Hamiltonian gives us the admixture of hybrid configuration within the meson ground state. The present effort represents a continuation of previous work: the analysis has been extended to include lattices of varying spacings, source operators having better overlap with the ground states, and the pseudoscalar (along with the vector) channel. Results are presented for bottomonium ($\Upsilon$, $\eta_b^{}$) using three different sets of quenched lattices. We also show results for charmonium ($J/\psi$, $\eta_c^{}$) from one lattice set, although we note that the non-relativistic approximation is not expected to be very good in this case.

We report on a lattice determination of the mass of the exotic $1^{-+}$ hybrid meson using an improved Kogut-Susskind action. Results from both quenched and dynamical quark simulations are presented. We also compare with earlier results using Wilson quarks at heavier quark masses. The results on lattices with three flavors of dynamical quarks show effects of sea quarks on the hybrid propagators which probably result from coupling to two meson states. We extrapolate the quenched results to the physical light quark mass to allow comparison with experimental candidates for the $1^{-+}$ hybrid meson. The lattice result remains somewhat heavier than the experimental result, although it may be consistent with the $\pi_1(1600)$.

We study hybrid mesons from the clover and improved gauge actions at $\beta=2.6$ on the anisotropic $12^3\times36$ lattice using our PC cluster. We estimate the mass of $1^{-+}$ light quark hybrid as well as the mass of the charmonium hybrid. The improvement of both quark and gluonic actions, first applied to the hybrid mesons, is shown to be more efficient in reducing the lattice spacing and finite volume errors.

We summarize our measurement of the mass of the exotic $1^{-+}$ hybrid meson using an improved Kogut-Susskind action. We show results from both quenched and dynamical quark simulations and compare with results from Wilson quarks. Extrapolation of these results to the physical quark mass allows comparison with experimental candidates for the $1^{-+}$ hybrid meson.

We study hybrid mesons from the clover and improved gauge actions at $\beta=2.6$ on the anisotropic $12^3\times36$ lattice using our PC cluster. We estimate the mass of $1^{-+}$ light quark hybrid as well as the mass of the charmonium hybrid. The improvement of both quark and gluonic actions, first applied to the hybrid mesons, is shown to be more efficient in reducing the lattice spacing and finite volume errors.

Hybrid (exotic) mesons, which are important predictions of quantum chromodynamics (QCD), are states of quarks and anti-quarks bound by excited gluons. First principle lattice study of such states would help us understand the role of ``dynamical'' color in low energy QCD and provide valuable information for experimental search for these new particles. In this paper, we apply both improved gluon and quark actions to the hybrid mesons, which might be more efficient than the previous works in reducing lattice spacing error and finite volume effect. Quenched simulations were done at $\beta=2.6$ and on a $\xi=3$ anisotropic $12^3 \times 36$ lattice using our PC cluster. We obtain $2013 \pm 26 \pm 71$ MeV for the mass of the $1^{-+}$ hybrid meson ${\bar q}qg$ in the light quark sector, and $4369 \pm 37 \pm 99$Mev in the charm quark sector; the mass splitting between the $1^{-+}$ hybrid meson ${\bar c}c g$ in the charm quark sector and the spin averaged S-wave charmonium mass is estimated to be $1302 \pm 37 \pm 99$ MeV. As a byproduct, we obtain $1438 \pm 32 \pm 57$ MeV for the mass of a P-wave $1^{++}$ ${\bar u}u$ or ${\bar d}d$ meson and $1499\pm 28 \pm 65$ MeV for the mass of a P-wave $1^{++}$ ${\bar s}s$ meson, which are comparable to their experimental value 1426 MeV for the $f_1(1420)$ meson. The first error is statistical, and the second one is systematical. The mixing of the hybrid meson with a four quark state is also discussed.

We discuss the allowed decays of a hybrid meson in the heavy quark limit. We deduce that an important decay will be into a heavy quark non-hybrid state and a light quark meson, in other words, the de-excitation of an excited gluonic string by emission of a light quark-antiquark pair. We discuss the study of hadronic decays from the lattice in the heavy quark limit and apply this approach to explore the transitions from a spin-exotic hybrid to $\chi_b \eta$ and $\chi_b S$ where $S$ is a scalar meson. We obtain a signal for the transition emitting a scalar meson and we discuss the phenomenological implications.

We examine the chiral corrections to exotic meson masses calculated in lattice QCD. In particular, we ask whether the non-linear chiral behavior at small quark masses, which has been found in other hadronic systems, could lead to large corrections to the predictions of exotic meson masses based on linear extrapolations to the chiral limit. We find that our present understanding of exotic meson decay dynamics suggests that open channels may not make a significant contribution to such non-linearities whereas the virtual, closed channels may be important.

Using lowest-order lattice NRQCD to create heavy meson propagators and applying the spin-flip interaction, $c_B^{} \frac{-g}{2m_q}\vec\sigma\cdot\vec{B}$, at varying intermediate time slices, we compute the off-diagonal matrix element of the Hamiltonian for the quarkonium-hybrid two-state system. Thus far, we have results for one set of quenched lattices with an interpolation in quark mass to match the $J^{PC}=1^{--}$ bottomonium spectrum. After diagonalization of the two-state Hamiltonian, we find the ground state of bottomonium to show a $0.0035(1)c_B^2$ (with $c_B^2 \sim 1.5-3.1$) probability admixture of hybrid, $|Q\bar{Q}g>$.

Surface critical phenomena and the related onset of Goldstone modes represent fundamental properties of the confining flux in Quantum Chromodynamics. New ideas on surface roughening and their implications for lattice studies of quark confinement and string formation are presented. Problems with a simple string description of the large Wilson surface are discussed.

Recent lattice simulation studies of heavy-quark hybrid mesons in which the quark and antiquark are bound together by an excited gluon field are summarized.

We present non-perturbative results for the spectrum of heavy quarkonia. Using an anisotropic formulation of Lattice QCD we achieved an unprecedented control over statistical and systematic errors. We also study relativistic corrections to the leading order predictions for heavy hybrids and conventional bound states.

The status of lattice determinations of quarkonia and hybrid meson spectra is presented and compared with experiment. Both quenched and unquenched results are discussed. Hybrid meson decays are considered.

We present a quenched calculation of lowest bottomonium hybrid states on an anisotropic lattice with Landau mean-link tadpole improvement, using the improved NRQCD Hamiltonian. We investigate the quark-spin s=0,1 sectors, which contain both the non-exotic 1-- and the exotic 1-+, and demonstrate their degeneracy in the case of the lowest order Hamiltonian. Both states are found at around 1.6 GeV above the Upsilon ground state. We examine the spin-splitting for several hybrid states that is due to the magnetic moment term in the NRQCD Hamiltonian, all other terms having negligible effect. The spin splittings are well resolved outside errors and are surprisingly large, and we investigate their dependence on the strength of the magnetic term. We calculate one contribution to these splittings using the Born-Oppenheimer picture for hybrids and show that the observed size of the effect is plausibly explained by mixing with hybrid states with more than one constituent gluon.

The spectrum of heavy-quark hybrids is studied in the leading Born-Oppenheimer (LBO) approximation and using leading-order NRQCD simulations with an improved gluon action on anisotropic lattices. The masses of four hybrid states are obtained from our simulations for lattice spacings 0.1 fm and 0.2 fm and are compared to the LBO predictions obtained using previously-determined glue-excited static potentials. The consistency of results from the two approaches reveals a compelling physical picture for heavy-quark hybrid states.

After a brief introduction to hybrid and glueball source operators, summarize recent lattice results for these particles.

We study in detail the spectrum of heavy quarkonia with different orbital angular momentum along with their radial and gluonic excitations. Using an anisotropic formulation of Lattice QCD we achieved an unprecedented control over statistical errors and were able to study systematic errors such as lattice spacing artefacts, finite volume effects and relativistic corrections. First results on the spin structure in heavy hybrids are also presented.

I review the results from lattice gauge theory for the masses of exotic hybrid mesons.

Hybrid b-bar-gb molecules in which the heavy b-bar-b pair is bound together by the excited gluon field g are studied using the Born-Oppenheimer expansion and numerical simulations. The consistency of results from the two approaches reveals a simple and compelling physical picture for heavy hybrid states.

We report on a study of heavy hybrid states using the NRQCD approach on coarse and asymmetric lattices, where we discard vacuum polarisation effects and neglect all spin-correction terms. We find a clear hybrid signal on all our lattices ($a_s= 0.15 ... 0.47$ fm). We have studied in detail the lattice spacing artefacts, finite volume effects and mass dependence. Within the above approximations we predict the hybrid excitation in Charmonium to be 1.323(13) GeV above its ground state. The bottomonium hybrid was found to be 1.542(8) GeV above its ground state.

The energies of glue in the presence of a static quark-antiquark pair are calculated for separations r ranging from 0.1 fm to 4 fm and for various quark-antiquark orientations on the lattice. Our simulations use an improved gauge-field action on anisotropic space-time lattices. Discretization errors and finite volume effects are studied. We find that the spectrum does not exhibit the expected onset of the universal pi/r Goldstone excitations of the effective QCD string, even for r as large as 4 fm. Our results cast serious doubts on the validity of treating glue in terms of a fluctuating string for r below 2 fm. Retardation effects in the Upsilon system are also studied by comparing level splittings from the Born-Oppenheimer approximation with those directly obtained in simulations.

We repeat our original simulations of the hybrid meson spectrum using the clover action, as a check on lattice artifacts. Our results for the 1-+ masses do not substantially change. We present preliminary results for the wave function of the 1-+ state in Coulomb gauge.

We present results for the hybrid meson spectrum produced by gluonic excitations in full QCD using Wilson fermions. For the spin-exotic mesons with J^{PC}=1^{-+}, 0^{+-}, and 2^{+-} we find the lightest state to be 1^{-+} with a mass of 1.9(2) GeV. Results obtained for orbitally excited mesons are also presented.

We report on a study of heavy hybrid states using the NRQCD approach on coarse and asymmetric lattices, where we discard vacuum polarisation effects and neglect all spin-correction terms. We find a clear hybrid signal on all our lattices ($a_s= 0.15 ... 0.47$ fm). We have studied in detail the lattice spacing artefacts, finite volume effects and mass dependence. Within the above approximations we predict the hybrid excitation in Charmonium to be 1.323(13) GeV above its ground state. The bottomonium hybrid was found to be 1.542(8) GeV above its ground state.

We present a quenched lattice calculation for the lowest lying $b \bar b g$-hybrid states in the framework of NRQCD using the leading order Hamiltonian up to ${\cal O}(mv^2)$. We demonstrate the existence of a nearly degenerate rotational band of states with an excitation energy approximately 1.6 GeV above the $\Upsilon$ ground state. This lies around the $B \bar B_J^*$-threshold but well above the $B \bar B$-threshold. Therefore a heavy hybrid signal may well be detected if the centre-of-mass energy in B-factories is raised a few hundred MeV to coincide with other resonances above the 4S state. Our prediction is consistent with most phenomenological models and lattice calculations carried out in the static limit.

The hybrid quarkonium states are studied using the Born-Oppenheimer expansion. The first step in this expansion is the determination of the energy levels of the gluons in the presence of a static quark-antiquark pair as a function of the quark-antiquark separation. The spectrum of such gluonic excitations is determined from first principles using lattice QCD.

A comprehensive determination of the rich, low-lying spectrum of gluonic excitations in the presence of a static quark-antiquark pair is presented. Our results are obtained from several simulations on anisotropic lattices using an improved action and a large set of gluonic operators. The hybrid quarkonium states are studied in the quenched approximation using the Born-Oppenheimer expansion and nonrelativistic lattice QCD.

We have studied the O(mv^6) effects in NRQCD on the spectrum of heavy quarkonia and compare our results for different lattices (quenched and dynamical). We also report on an investigation into hybrid states within the framework of NRQCD. This suggests that the lowest lying hybrid is around the B^* \bar B threshold and 3 standard deviations above the B \bar B.

A review of new results from lattice simulations of glueballs and heavy-quark hybrid mesons is presented.

We use lattice methods to evaluate from first principles the spectrum of hybrid mesons produced by gluonic excitations in quenched QCD with quark masses near the strange quark mass. For the spin-exotic mesons with $J^{PC}=1^{-+},\ 0^{+-}$, and $2^{+-}$ which are not present in the quark model, we determine the lightest state to be $1^{-+}$ with mass of 2.0(2) GeV.

Hybrid mesons, made from a quark, an antiquark and gluons, can have quantum numbers inaccessible to conventional quark-antiquark states. Confirmation of such states would give information on the role of "dynamical" color in low energy QCD. We present preliminary results for hybrid meson masses using light Wilson valence quarks.

We discuss in general the construction of gauge-invariant non-local meson operators on the lattice. We use such operators to study the $P$- and $D$-wave mesons as well as hybrid mesons in quenched QCD, with quark masses near the strange quark mass. The resulting spectra are compared with experiment for the orbital excitations. For the states produced by gluonic excitations (hybrid mesons) we find evidence of mixing for non-exotic quantum numbers. We give predictions for masses of the spin-exotic hybrid mesons with $J^{PC}=1^{-+},\ 0^{+-}$, and $2^{+-}$.