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.

We determine D and D(s) decay constants from lattice QCD with 2% errors, 4 times better than experiment and previous theory: f(D(s))=241(3) MeV, f(D)=207(4) MeV, and fD(s))/f(D)=1.164(11). We also obtain f(K)/f(pi)=1.189(7) and (f(D(s))/f(D))/(f(K)/f(pi))=0.979(11). Combining with experiment gives V(us)=0.2262(14) and V(cs)/V(cd) of 4.43(41). We use a highly improved quark discretization on MILC gluon fields that include realistic sea quarks, fixing the u/d, s, and c masses from the pi, K, and eta(c) meson masses. This allows a stringent test against experiment for D and D(s) masses for the first time (to within 7 MeV).

We give results for the Upsilon spectrum from lattice QCD using an improved version of the NRQCD action for b quarks which includes radiative corrections to kinetic terms at O(v 4 ) in the velocity expansion. We also include for the first time the effect of up, down, strange and charm quarks in the sea using 'second generation' gluon field configurations from the MILC collaboration. Using the Υ 2S − 1S splitting to determine the lattice spacing, we are able to obtain the 1P − 1S splitting to 1.4% and the 3S − 1S splitting to 2.4%. Our improved result for M (Υ) − M (η b ) is 70(9) MeV and we predict M (Υ ) − M (η b ) = 35(3) MeV. We also calculate π, K and ηs correlators using the Highly Improved Staggered Quark action and perform a chiral and continuum extrapolation to give values for Mη s (0.6893(12) GeV) and fη s (0.1819(5) GeV) that allow us to tune the strange quark mass as well as providing an independent and consistent determination of the lattice spacing. Combining the NRQCD and HISQ analyses gives m b /ms = 54.7(2.5) and a value for the heavy quark potential parameter of r1 = 0.3209(26) fm.

We update our previous determination of both the decay constant and the mass of the Ds meson using the Highly Improved Staggered Quark formalism. We include additional results at two finer values of the lattice spacing along with improved determinations of the lattice spacing and improved tuning of the charm and strange quark masses. We obtain mD s = 1.9691(32) GeV, in good agreement with experiment, and fD s = 0.2480(25) GeV. Our result for fD s is 1.6σ lower than the most recent experimental average determined from the Ds leptonic decay rate and using Vcs from CKM unitarity. Combining our fD s with the experimental rate we obtain a direct determination of Vcs = 1.010(22), or alternatively 0.990 +0.013 −0.016 using a probability distribution for statistical errors for this quantity which vanishes above 1. We also include an accurate prediction of the decay constant of the ηc, fη c = 0.3947(24) GeV, as a calibration point for other lattice calculations.