An investigation of the running coupling and meson masses in lattice QCD

We investigate a lattice determination of the running coupling defined in the MOM-tilde scheme to see if it is consistent with a power correction to the perturbative formula. We attempt a lattice determination of the masses of the a0, a1 and b1 flavour nonsinglet mesons. We then consider the mass differences between flavour singlet and nonsinglet mesons in the cases of the π, ρ, a1 and b1 mesons. Finally, we investigate the pion decay constant fπ using both quenched and unquenched lattice data. (author)