# The application of automated perturbation theory to lattice QCD

Thesis

Predictions of heavy quark parameters are an integral component of precision tests of the Standard Model of particle physics. Experimental measurements of electroweak processes involving heavy hadrons provide stringent tests of Cabibbo-Kobayashi-Maskawa (CKM) matrix unitarity and serve as a probe of new physics. Hadronic matrix elements parameterise the strong dynamics of these interactions and these matrix elements must be calculated nonperturbatively. Lattice quantum chromodynamics (QCD) provides the framework for nonperturbative calculations of QCD processes. Current lattices are too coarse to directly simulate b quarks. Therefore an effective theory, nonrelativistic QCD (NRQCD), is used to discretise the heavy quarks. High precision simulations are required so systematic uncertainties are removed by improving the NRQCD action. Precise simulations also require improved sea quark actions, such as the highly-improved staggered quark (HISQ) action. The renormalisation parameters of these actions cannot be feasibly determined by hand and thus automated procedures have been developed. In this dissertation I apply automated lattice pertubartion theory to a number of heavy quark calculations. I first review the fundamentals of lattice QCD and the construction of lattice NRQCD. I then motivate and discuss lattice perturbation theory in detail, focussing on the tools and techniques that I use in this dissertation. I calculate the two-loop tadpole improvement factors for improved gluons with improved light quarks. I then compute the renormalisation parameters of NRQCD. I use a mix of analytic and numerical methods to extract the one-loop radiative corrections to the higher order kinetic operators in the NRQCD action. I then employ a fully automated procedure to calculate the heavy quark energy shift at two-loops. I use this result to extract a new prediction of the mass of the b quark from lattice NRQCD simulations by the HPQCD collaboration. I also review the calculation of the radiative corrections to the chromo-magnetic operator in the NRQCD action. This computation is the first outcome of our implementation of background field gauge for automated lattice perturbation theory. Finally, I calculate the heavy-light currents for highly-improved NRQCD heavy quarks with massless HISQ light quarks and discuss the application of these results to nonperturbative studies by the HPQCD collaboration.