High Precision Lattice QCD: Perturbations in a Non-Perturbative World
The High-Precision QCD collaboration has embarked on a ground-breaking survey of strongly interacting Standard Model phenomenology from lattice QCD using the improved staggered action for light quarks, NRQCD for the heavy quarks and one-loop Symanzik improved gluons. This program requires one- and two-loop perturbative renormalisations of action parameters, matrix elements and currents. The current techniques for lattice perturbation theory are very cumbersome and inflexible, built for individual one-loop applications. Very few two-loop results are known, even for the simplest actions. A new method for performing perturbative calculations in Lattice QCD is presented. The combination of easily determining Feynman rules for arbitrary actions and automated diagram generation has enabled the calculation of six related three-loop quantities for several different actions including the most highly improved, ``Asqtad'' that is being used for the most realistic lattice simulations ever. The necessity of choosing an appropriate scheme and scale for lattice expansions is demonstrated. Further improvements to the scaling in the quark sector are investigated and a new action with three times smaller errors is obtained. The connection between the lattice and continuum couplings is determined to two-loops for these actions which is a pre-requisite for any future perturbative calculations. Third-order Wilson loops up to 2x2 are calculated for the first time which can be used to determine the strong coupling constant at energies relevant to simulations and to experimenters. The quark mass is renormalised to one-loop in order to determine the mass of the strange quark and compare to sum rules.
Lattice QCD; Perturbation Theory; multi-loop; strange quark mass; staggered quarks; alpha_s
dissertation or thesis