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.