Heavy flavour physics from lattice QCD

We study the semi-leptonic and non-leptonic decays of charmed D mesons. In the semi-leptonic case, using the lattice conserved current, we compute the form factors f0 and f+ at q2 = 0 and show them to be in good agreement with experimental observations. Nearest pole dominance gives a good description of the form factors for those points for which our calculations are reliable. The dependence of the conserved current matrix elements with the light quark mass is investigated. Computations using the local current are also performed. After renormalization, results are consistent with experiment, but not in such good agreement as the conserved current calculations. For non-leptonic decays into two pseudoscalar particles, final state interactions are shown to be negligible in our computations. We find that the lattice amplitudes of the various decay channels have large statistical errors and display a heavy dependence on the light quark mass. No clear information can be extracted. Following a method proposed in Nucl. Phys. B(Proc. Suppl.)4 1988:170 by E. Eichten, we investigate the treatment of heavy quarks on the lattice by calculating the B meson decay constant. The results show that it is necessary to have a statistical sample much greater than for similar calculations with light quarks to achieve comparable precision. Computations are carried out on a 20 x 10 x 10 x 40 lattice at β = 6.0 using Wilson fermions in the Quenched approximation. (author)