Definitions of the gauge-theory coupling in lattice and continuum quantum chromodynamics: Implications of change in the lattice action

We investigate various effects of a change in action for lattice QCD. The lattice scale parameter Λ/sub L/ depends on the action used and Λ/sub L//Λ/sub MOM/ is computed by the background-field method in the continuum limit for Manton's and the generalized Villain's (the heat-kernel) action. When comparing with results from Monte Carlo simulations we find evidence for sizable three-loop corrections to the lattice β function. Creutz's renormalization-group analysis is extended to Manton's and the heat-kernel action. The method produces good results with the actions we study. The static quark-antiquark potential we obtain, which is close in form to a phenomenological charmonium potential, exhibits an independence of the lattice action used. Finally, we present a discussion of the effects of changing the form of the action, relating these to a line of critical points that the theory may possess