Heavy quark physics on the lattice with improved nonrelativistic actions
Hadrons containing heavy quarks, in particular b quarks, play an important role in high energy physics. Measurements of their electroweak interactions are used to test the Standard Model and search for new physics. For the comparison of experimental results with theoretical predictions, nonperturbative calculations of hadronic matrix elements within the theory of quantum chromodymanics are required. Such calculations can be performed from first principles by formulating QCD on a Euclidean spacetime grid and computing the path integral numerically. Including b quarks in lattice QCD calculations requires special techniques as the lattice spacing in present computations usually can not be chosen fine enough to resolve their Compton wavelength. In this work, improved nonrelativistic lattice actions for heavy quarks are used to perform calculations of the bottom hadron mass spectrum and of form factors for heavy-to-light decays. In heavy-to-light decays, additional complications arise at high recoil, when the momentum of the light meson reaches a magnitude comparable to the cutoff imposed by the lattice. Discretisation errors at high recoil can be reduced by working in a frame of reference where the heavy and light mesons move in opposite directions. Using a formalism referred to as moving nonrelativistic QCD (mNRQCD), the nonrelativistic expansion for the heavy quark can be performed around a state with an arbitrary velocity. This dissertation begins with a review of the fundamentals of lattice QCD. Then, the construction of effective Lagrangians for heavy quarks in the continuum and on the lattice is discussed in detail. A highly improved lattice mNRQCD action is derived and its effectiveness is demonstrated by nonperturbative tests involving both heavy-heavy and heavy-light mesons at several frame velocities. This mNRQCD action is then used in combination with a staggered action for the light quarks to calculate hadronic matrix elements relevant for rare B decays, including B --> K* gamma and B --> K l l. A major contribution to the uncertainty of the results also comes from statistical errors. The effectiveness of random-wall sources to reduce these errors is studied. As another application of a nonrelativistic heavy quark action, the spectrum of bottomonium is calculated and masses of several bottom baryons are predicted. In these computations, the light quarks are implemented with a domain wall action.