Perturbative improvement of lattice gauge action with staggered quarks

Realistic unquenched Lattice QCD including dynamical fermions has become available thanks to the use of highly improved staggered quarks and other newly developed techniques. While these calculations yielded excellent agreement with experiments, unquenched studies of the static quark potential at short distances show larger discretization errors than in quenched simulations. At leading order in perturbation theory these errors arise from $O(\alpha_s a^2)$ corrections to the couplings in the lattice gauge action ($\alpha_s$ is the QCD coupling and $a$ is the lattice spacing); fermion loop contributions to these couplings have not previously been available. In this thesis, fermion loop contributions to O($\alpha_s a^2$) improvement of the gauge action are calculated. The approach developed by L\uscher and Weisz is adopted and reviewed in detail. It is observed that dynamical contributions are large and hence could be the source of the large scaling violations in previous simulations of the unquenched static potential."