G. P. Lepage

Effective lagrangians for bound state problems in QED, QCD, and other field theories

A renormalization group strategy for the study of bound states in field theory is developed. Our analysis is completely different from conventional analyses, based upon the Bethe-Salpeter equation, and it is far simpler. This is illustrated in state-of-the-art calculations for the ground state splittings in muonium and positronium.

Improved nonrelativistic QCD for heavy-quark physics.

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 site of nonperturbative contributions to the coupling constants.

High-precision determination of the pi, K, D, and D-s decay constants from lattice QCD

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).

High-Precision c and b Masses, and QCD Coupling from Current-Current Correlators in Lattice and Continuum QCD

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{sub c}(3 GeV,n{sub f}=4)=0.986(6) GeV, {alpha}{sub MS}(M{sub Z},n{sub f}=5)=0.1183(7), and m{sub b}(10 GeV,n{sub f}=5)=3.617(25) GeV. These are among the most accurate determinations by any method. We check our results using a nonperturbative determination of the mass ratio m{sub b}({mu},n{sub f})/m{sub c}({mu},n{sub f}); the two methods agree to within our 1% errors and taken together imply m{sub b}/m{sub c}=4.51(4). We also update our previous analysis of {alpha}{sub MS} from Wilson loops to account for revised values for r{sub 1} and r{sub 1}/a, finding a new value {alpha}{sub MS}(M{sub Z},n{sub f}=5)=0.1184(6); and we update our recent values for light-quark masses from the ratio m{sub c}/m{sub s}. Finally, in the Appendix, we derive a procedure for simplifying and accelerating complicated least-squares fits.

Highly improved staggered quarks on the lattice, with applications to charm physics

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

Update: Precision D_s decay constant from full lattice QCD using very fine lattices

We update our previous determination of both the decay constant and the mass of the D s 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 m Ds = 1.9691(32) GeV, in good agreement with experiment, and f Ds = 0.2480(25) GeV. Our result for f Ds is 1.6σ lower than the most recent experimental average determined from the D s leptonic decay rate and using V cs from Cabibbo-Kobayashi-Maskawa unitarity. Combining our f Ds with the experimental rate we obtain a direct determination of V cs = 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 η c , f ηc = 0.3947(24) GeV, as a calibration point for other lattice calculations.

Hadronic Wave Functions at Short Distances and the Operator Product Expansion

Abstract The operator product expansion, of appropriate products of quark fields, is used to find the anomalous dimensions which control the short distance behavior of hadronic wave functions. This behavior in turn controls the high- Q 2 limit of hadronic form factors. In particular, we relate each anomalous dimension of the nonsinglet structure functions to a corresponding logarithmic correction factor to the nominal α S ( Q 2 )/ Q 2 fall off of meson form factors. Unlike the case of deep inelastic lepton-hadron scattering, the operator product necessary here involves extra terms which do not contribute to forward matrix elements.

Constrained curve fitting

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

High-Precision Charm-Quark Mass from Current-Current Correlators in Lattice and Continuum QCD

We use lattice QCD simulations, with MILC configurations and HISQ

Lattice QCD on small computers

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