Effective heavy-light meson energies in small-volume quenched QCD

We study effective energies of heavy-light meson correlation functions in lattice QCD and a small volume of (0.2 fm)^4 to non-perturbatively calculate their dependence on the heavy quark mass in the continuum limit. Our quenched results obtained here constitute an essential intermediate step of a first fully non-perturbative computation of the b-quark's mass in the static approximation that has recently been presented as an application of a new proposal to non-perturbatively renormalize the Heavy Quark Effective Theory. The renormalization constant and the improvement coefficients relating the renormalized current and subtracted quark mass are determined in the relevant parameter region at weak couplings, which allows to perform the numerical simulations at several, precisely fixed values of the renormalization group invariant heavy quark mass in a range from 3 GeV to 15 GeV.Comment: 24 pages including figures and tables, latex2e; version published in JHEP, small additions, results unchange

Perturbative two- and three-loop coefficients from large beta Monte Carlo

Perturbative coefficients for Wilson loops and the static quark self-energy are extracted from Monte Carlo simulations at large beta on finite volumes, where all the lattice momenta are large. The Monte Carlo results are in excellent agreement with perturbation theory through second order. New results for third order coefficients are reported. Twisted boundary conditions are used to eliminate zero modes and to suppress Z_3 tunneling.Comment: 6 pages, 5 figures. Contributions of Howard Trottier and Paul Mackenzie to Lattice '9

Analytical results for the confinement mechanism in QCD_3

We present analytical methods for investigating the interaction of two heavy quarks in QCD_3 using the effective action approach. Our findings result in explicit expressions for the static potentials in QCD_3 for long and short distances. With regard to confinement, our conclusion reflects many features found in the more realistic world of QCD_4.Comment: 24 pages, uses REVTe

Adjoint "quarks" on coarse anisotropic lattices: Implications for string breaking in full QCD

A detailed study is made of four dimensional SU(2) gauge theory with static adjoint ``quarks'' in the context of string breaking. A tadpole-improved action is used to do simulations on lattices with coarse spatial spacings $a_s$, allowing the static potential to be probed at large separations at a dramatically reduced computational cost. Highly anisotropic lattices are used, with fine temporal spacings $a_t$, in order to assess the behavior of the time-dependent effective potentials. The lattice spacings are determined from the potentials for quarks in the fundamental representation. Simulations of the Wilson loop in the adjoint representation are done, and the energies of magnetic and electric ``gluelumps'' (adjoint quark-gluon bound states) are calculated, which set the energy scale for string breaking. Correlators of gauge-fixed static quark propagators, without a connecting string of spatial links, are analyzed. Correlation functions of gluelump pairs are also considered; similar correlators have recently been proposed for observing string breaking in full QCD and other models. A thorough discussion of the relevance of Wilson loops over other operators for studies of string breaking is presented, using the simulation results presented here to support a number of new arguments.Comment: 22 pages, 14 figure

Chiral Symmetry Breaking and Cooling in Lattice QCD

Chiral symmetry breaking is calculated as a function of cooling in quenched lattice QCD. A non-zero signal is found for the chiral condensate beyond one hundred cooling steps, suggesting that there is chiral symmetry breaking associated with instantons. Quantitatively, the chiral condensate in cooled gauge field configurations is small compared to the value without cooling.Comment: 11 pages in REVTEX including 4 PS figures embedded using psfig.sty, uuencode

Non-perturbative Heavy Quark Effective Theory

We explain how to perform non-perturbative computations in HQET on the lattice. In particular the problem of the subtraction of power-law divergences is solved by a non-perturbative matching of HQET and QCD. As examples, we present a full calculation of the mass of the b-quark in the combined static and quenched approximation and outline an alternative way to obtain the B-meson decay constant at lowest order. Since no excessively large lattices are required, our strategy can also be applied including dynamical fermions.Comment: 27 pages including figures and tables, latex2e; version published in JHEP, typos corrected and 1 reference adde

Perturbative expansions from Monte Carlo simulations at weak coupling: Wilson loops and the static-quark self-energy

Perturbative coefficients for Wilson loops and the static-quark self-energy are extracted from Monte Carlo simulations at weak coupling. The lattice volumes and couplings are chosen to ensure that the lattice momenta are all perturbative. Twisted boundary conditions are used to eliminate the effects of lattice zero modes and to suppress nonperturbative finite-volume effects due to Z(3) phases. Simulations of the Wilson gluon action are done with both periodic and twisted boundary conditions, and over a wide range of lattice volumes (from $3^4$ to $16^4$) and couplings (from $\beta \approx 9$ to $\beta \approx 60$). A high precision comparison is made between the simulation data and results from finite-volume lattice perturbation theory. The Monte Carlo results are shown to be in excellent agreement with perturbation theory through second order. New results for third-order coefficients for a number of Wilson loops and the static-quark self-energy are reported.Comment: 36 pages, 15 figures, REVTEX documen

Numerical Stochastic Perturbation Theory for full QCD

We give a full account of the Numerical Stochastic Perturbation Theory method for Lattice Gauge Theories. Particular relevance is given to the inclusion of dynamical fermions, which turns out to be surprisingly cheap in this context. We analyse the underlying stochastic process and discuss the convergence properties. We perform some benchmark calculations and - as a byproduct - we present original results for Wilson loops and the 3-loop critical mass for Wilson fermions.Comment: 35 pages, 5 figures; syntax revise

Measurement of hybrid content of heavy quarkonia using lattice NRQCD

Using lowest-order lattice NRQCD to create heavy meson propagators and applying the spin-dependent 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 bottomonium spectrum. After diagonalization of the two-state Hamiltonian, we find the ground state of the $\Upsilon$ to show a $0.0035(1)c_B^2$ (with $c_B^2 \sim 1.5-3.1$) probability admixture of hybrid, $|b\bar{b}g>$.Comment: 11 pages, 4 figures, to appear in Phys Rev

Heavy Quarks on Anisotropic Lattices: The Charmonium Spectrum

We present results for the mass spectrum of $c{\bar c}$ mesons simulated on anisotropic lattices where the temporal spacing $a_t$ is only half of the spatial spacing $a_s$. The lattice QCD action is the Wilson gauge action plus the clover-improved Wilson fermion action. The two clover coefficients on an anisotropic lattice are estimated using mean links in Landau gauge. The bare velocity of light $\nu_t$ has been tuned to keep the anisotropic, heavy-quark Wilson action relativistic. Local meson operators and three box sources are used in obtaining clear statistics for the lowest lying and first excited charmonium states of $^1S_0$, $^3S_1$, $^1P_1$, $^3P_0$ and $^3P_1$. The continuum limit is discussed by extrapolating from quenched simulations at four lattice spacings in the range 0.1 - 0.3 fm. Results are compared with the observed values in nature and other lattice approaches. Finite volume effects and dispersion relations are checked.Comment: 36 pages, 6 figur