The Spectrum from Lattice NRQCD

I review recent results for heavy-heavy spectroscopy using Lattice NRQCD. The NRQCD collaboration reports that spin-independent splittings for the $\Upsilon$ are scaling for a sensible range of $\beta$ values in the quenched approximation. Spin-dependent splittings are not, if the scale is set by spin-independent splittings. Results which include higher order spin-dependent relativistic and discretisation corrections show differences from previous (NRQCD collaboration) results without these. As expected, the differences are small for $\Upsilon$ but rather large for charmonium. New results from the SESAM collaboration for $\Upsilon$ spectroscopy on configurations with Wilson dynamical fermions show good agreement with previous results on HEMCGC configurations with staggered dynamical fermions.Comment: 10 pages, Latex. 10 figures, 7 in postscript. Review for Tsukuba worksho

A review of heavy-heavy spectroscopy

Calculations of the heavy-heavy spectrum present a good opportunity for precision tests of QCD using lattice techniques. All methods make use of a non-relativistic expansion of the action and its systematic improvement to remove lattice artefacts. There was convincing demonstration this year that these methods work and that the associated perturbation theory is well-behaved. Comparison to experimental results yields an accurate value for the lattice spacing, a, a key result in the determination of \alpha_{s}, and (for the first time this year) the mass of the b quark (4.7(1) GeV).Comment: talk at Lattice'93, Dallas. 6 pages of latex espcrc2.sty needed and figures on reques

Latest Results from Heavy Quark Simulations

The status of b-bbar and c-cbar calculations, numerical and analytic, are reviewed. The extraction of alpha_s and quark masses from spectrum calculations is discussed. The NRQCD and Improved Heavy Wilson formulations of heavy quarks are compared, and recent calculations using a Heavy Staggered formulation are discussed.Comment: 15 pages, latex, 9 postscript figures, self-unpacking uuencoded compressed file, requires espcrc2.sty (included) and epsf.sty. Contribution to Lattice '9

Heavy Meson Spectroscopy at Beta=6.0

We present results of a quenched calculation of the heavy-light and quarkonium spectrum using the tadpole improved clover action. We resolve completely the triplet chi P-states in quarkonium systems, and obtain evidence for fine structure of the heavy-light P-states. Approximate scaling of the hyperfine splittings is observed, producing results that are significantly below experiment.Comment: Contribution to Lattice 97 proceedings: 3 pages, 7 postscript figures, LaTeX2e, uses espcrc2.st

Results on improved KS dynamical configurations: spectrum, decay constants, etc

The MILC Collaboration has been producing ensembles of lattice configurations with three dynamical flavors for the past few years. There are now results for three lattice spacings for a variety of light and strange quark masses, ranging down to $m_l=0.1 m_s$, where $m_s$ is the dynamical strange quark mass and $m_l$ is the common mass of the $u$ and $d$ quarks. Recently, the Fermilab, HPQCD, MILC and UKQCD collaborations have presented a summary of results obtained using these lattices. Compared with quenched results, these new calculations show great improvement in agreement with experiment. This talk addresses the technical improvements that make these calculations possible and provides additional details of calculations not presented in the initial summary. We demonstrate that a wide range of hadronic observables can now be calculated to 2--3% accuracy.Comment: 10 pages, 17 figures (16 in color), Lattice2003(plenary), Plenary talk presented at Lattice 2003, Tsukuba, Japan, July 15-19. Also presented at Lattice Hadron Physics workshop, Cairns, Australia, July 22-30, 200

A precise determination of the Bc mass from dynamical lattice QCD

We perform a precise calculation of the mass of the B_c meson using unquenched configurations from the MILC collaboration including 2+1 flavours of improved staggered quarks. Lattice NRQCD and the Fermilab formalism are used to describe the b and c quarks respectively. We find the mass of the B_c meson to be 6.304(16) GeVComment: Talk presented at Lattice2004(heavy), Fermilab, June 21-26. 3 pages, 2 figure

Quarkonium spin structure in lattice NRQCD

Numerical simulations of the quarkonium spin splittings are done in the framework of lattice nonrelativistic quantum chromodynamics (NRQCD). At leading order in the velocity expansion the spin splittings are of $O(M_Q v^4)$, where $M_Q$ is the renormalized quark mass and $v^2$ is the mean squared quark velocity. A systematic analysis is done of all next-to-leading order corrections. This includes the addition of $O(M_Q v^6)$ relativistic interactions, and the removal of $O(a^2 M_Q v^4)$ discretization errors in the leading-order interactions. Simulations are done for both S- and P-wave mesons, with a variety of heavy quark actions and over a wide range of lattice spacings. Two prescriptions for the tadpole improvement of the action are also studied in detail: one using the measured value of the average plaquette, the other using the mean link measured in Landau gauge. Next-to-leading order interactions result in a very large reduction in the charmonium splittings, down by about 60% from their values at leading order. There are further indications that the velocity expansion may be poorly convergent for charmonium. Prelimary results show a small correction to the hyperfine splitting in the Upsilon system.Comment: 16 pages, REVTEX v3.1, 5 postscript figures include

Non-Perturbative Improvement of the Anisotropic Wilson QCD Action

We describe the first steps in the extension of the Symanzik O($a$) improvement program for Wilson-type quark actions to anisotropic lattices, with a temporal lattice spacing smaller than the spatial one. This provides a fully relativistic and computationally efficient framework for the study of heavy quarks. We illustrate our method with accurate results for the quenched charmonium spectrum.Comment: LATTICE98(improvement), 3 pages, 4 figure

Lattice QCD on Small Computers

We demonstrate that lattice QCD calculations can be made $10^3$--$10^6$ times faster by using very coarse lattices. To obtain accurate results, we replace the standard lattice actions by perturbatively-improved actions with tadpole-improved correction terms that remove the leading errors due to the lattice. To illustrate the power of this approach, we calculate the static-quark potential, and the charmonium spectrum and wavefunctions using a desktop computer. We obtain accurate results that are independent of the lattice spacing and agree well with experiment.Comment: 15 pages, 3 figs incl as LaTex pictures Minor additions to tables and tex

Tadpole renormalization and relativistic corrections in lattice NRQCD

We make a comparison of two tadpole renormalization schemes in the context of the quarkonium hyperfine splittings in lattice NRQCD. Improved gauge-field and NRQCD actions are analyzed using the mean-link $u_{0,L}$ in Landau gauge, and using the fourth root of the average plaquette $u_{0,P}$. Simulations are done for $c\bar c$, $b\bar c$, and $b\bar b$ systems. The hyperfine splittings are computed both at leading and at next-to-leading order in the relativistic expansion. Results are obtained at lattice spacings in the range of about 0.14~fm to 0.38~fm. A number of features emerge, all of which favor tadpole renormalization using $u_{0,L}$. This includes much better scaling behavior of the hyperfine splittings in the three quarkonium systems when $u_{0,L}$ is used. We also find that relativistic corrections to the spin splittings are smaller when $u_{0,L}$ is used, particularly for the $c\bar c$ and $b\bar c$ systems. We also see signs of a breakdown in the NRQCD expansion when the bare quark mass falls below about one in lattice units. Simulations with $u_{0,L}$ also appear to be better behaved in this context: the bare quark masses turn out to be larger when $u_{0,L}$ is used, compared to when $u_{0,P}$ is used on lattices with comparable spacings. These results also demonstrate the need to go beyond tree-level tadpole improvement for precision simulations.Comment: 14 pages, 7 figures (minor changes to some phraseology and references