We construct an improved version of nonrelativistic QCD for use in lattice simulations of heavy quark physics, with the goal of reducing systematic errors from all sources to below 10%. We develop power counting rules to assess the importance of the various operators in the action and compute all leading order corrections required by relativity and finite lattice spacing. We discuss radiative corrections to tree level coupling constants, presenting a procedure that effectively resums the largest such corrections to all orders in perturbation theory. Finally, we comment on the size of nonperturbative contributions to the coupling constants.

We use perturbative Symanzik improvement to create a new staggered-quark action (HISQ) that has greatly reduced one-loop taste-exchange errors, no tree-level order a 2 errors, and no tree-level order (am) 4 errors to leading order in the quark's velocity v/c. We demonstrate with simulations that the resulting action has taste-exchange interactions that are at least 3-4 times smaller than the widely used ASQTAD action. We show how to estimate errors due to taste exchange by comparing ASQTAD and HISQ simulations, and demonstrate with simulations that such errors are no more than 1% when HISQ is used for light quarks at lattice spacings of 1/10 fm or less. The suppression of (am) 4 errors also makes HISQ the most accurate discretization currently available for simulating c quarks. We demonstrate this in a new analysis of the ψ − ηc mass splitting using the HISQ action on lattices where amc = 0.43 and 0.66, with full-QCD gluon configurations (from MILC). We obtain a result of 111(5) MeV which compares well with experiment. We discuss applications of this formalism to D physics and present our first high-precision results for Ds mesons.

We extend our earlier lattice-QCD analysis of heavy-quark correlators to smaller lattice spacings and larger masses to obtain new values for the c mass and QCD coupling, and, for the first time, values for the b mass: m c ð3 GeV; n f ¼ 4Þ ¼ 0:986ð6Þ GeV, MS ðM Z ; n f ¼ 5Þ ¼ 0:1183ð7Þ, and m b ð10 GeV; n f ¼ 5Þ ¼ 3:617ð25Þ GeV. These are among the most accurate determinations by any method. We check our results using a nonperturbative determination of the mass ratio m b ð; n f Þ=m c ð; n f Þ; the two methods agree to within our 1% errors and taken together imply m b =m c ¼ 4:51ð4Þ. We also update our previous analysis of MS from Wilson loops to account for revised values for r 1 and r 1 =a, finding a new value MS ðM Z ; n f ¼ 5Þ ¼ 0:1184ð6Þ; and we update our recent values for light-quark masses from the ratio m c =m s . Finally, in the Appendix, we derive a procedure for simplifying and accelerating complicated least-squares fits.

The spectrum of the Υ system is investigated using the Nonrelativistic Lattice QCD approach to heavy quarks and ignoring light quark vacuum polarization. We find good agreement with experiment for the Υ, Υ ′ , Υ ′′ and for the center of mass and fine structure of the χ b -states. The lattice calculations predict b b D-states with center of mass at (10.20 ± 0.07 ± 0.03)GeV. Fitting procedures aimed at extracting both ground and excited state energies are developed. We calculate a nonperturbative dispersion mass for the Υ(1S) and compare with tadpole-improved lattice perturbation theory.

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

We present a new determination of the Bs leptonic decay constant from lattice QCD simulations that use gluon configurations from MILC and a highly improved discretization of the relativistic quark action for both valence quarks. Our result, fB s = 0.225(4) GeV, is almost three times more accurate than previous determinations. We analyze the dependence of the decay constant on the heavy quark's mass and obtain the first empirical evidence for the leading 1/ √ m h dependence predicted by Heavy Quark Effective Theory (HQET). As a check, we use our analysis technique to calculate the mB s − mη b /2 mass difference. Our result agrees with experiment to within errors of 11 MeV (better than 2%). We discuss how to extend our analysis to other quantities in Bs and B physics, making 2%-precision possible for the first time. Lattice simulations of QCD have become essential for high-precision experimental studies of B-meson decays -studies that test our understanding and the limitations of the standard model of weak, electromagnetic and strong interactions, and also determine fundamental parameters, like the CKM matrix, in that model. Accurate theoretical calculations of QCD contributions to meson masses, decay constants, mixing amplitudes, and semileptonic form factors are critical for this program, and lattice simulation is the main tool for providing these calculations. A major complication for the lattice simulations has been the large mass of the b quark, which has necessitated the use of non-relativistic effective field theories like NRQCD to describe b dynamics in the simulations. The need for effective field theories has made it difficult to achieve better than 5-10% precision for many important quantities.Recently we overcame the analogous problem for c quarks by introducing a highly improved discretization of the relativistic quark action that gives accurate results even on quite coarse lattices: the Highly Improved Staggered-Quark (HISQ) discretization [1]. With this formalism, c quarks are analyzed in the same way as u, d, and s quarks, which greatly reduces the uncertainties in QCD simulations of D physics [2][3][4][5][6][7]. More recently we showed that the HISQ action can be pushed to much higher masses -indeed, very close to the b mass -using new lattices, from the MILC collaboration, with the smallest lattice spacing available today (a = 0.044 fm). This allowed us to extract a value for the b's MS mass that was accurate to better than 1%. Here we extend that work in a new analysis of the B s meson's leptonic decay constant f Bs , which produces the most accurate theoretical value to date.We also compute the mass difference m Bs − m η b /2, as an additional test of our analysis method. This difference is particularly sensitive to QCD dynamics because the leading (and uninteresting) dependence on the heavy quark's mass mostly cancels in the difference.It would be quite expensive to extend our new analysis directly to B-meson quantities, because of the added costs associated with very light valence and sea qua...

Tin 1 QCD light cone lUmiltonian is diagcmalized in adisrrete momentum spare baMs. Hit-spectra and w^wfunrtiuns for various coupling constants, numbers of color, arid baryon numb«-r are computed. Talk Presented to the Ohio Slate Workshop OnRflAiivistic A/amBody Physics, Columbus, Ohio, June 6 9J98H•

We use lattice QCD simulations, with MILC gluon configurations and HISQ c-quark propagators, to make very precise determinations of moments of charm-quark pseudoscalar, vector and axialvector correlators. These moments are combined with new four-loop results from continuum perturbation theory to obtain several new determinations of the MS mass of the charm quark and of the MS coupling. We find mc(3 GeV) = 0.986 (10) GeV, or, equivalently, mc(mc) = 1.268 (9) GeV, both for n f = 4 flavors; and α MS (3 GeV, n f = 4) = 0.251 (6), or, equivalently, α MS (MZ , n f = 5) = 0.1174 (12). The new mass agrees well with results from continuum analyses of the vector correlator using experimental data for e + e − annihilation (instead of using lattice QCD simulations). These lattice and continuum results are the most accurate determinations to date of this mass. Ours is also one of the most accurate determinations of the QCD coupling by any method.