The three-loop β-function of QCD with the clover action

We calculate, to 3 loops in perturbation theory, the bare beta-function of QCD, formulated on the lattice with the clover fermionic action. The dependence of our result on the number of colors N, the number of fermionic flavors N-f, as well as the clover parameter c(SW), is shown explicitly. A direct outcome of our calculation is the two-loop relation between the bare coupling constant go and the one renormalized in the (MS) over bar scheme. Further, we can immediately derive the three-loop correction to the relation between the lattice A-parameter and go, which is important in checks of asymptotic scaling. For typical values of c(SW), this correction is found to be very pronounced. (C) 2002 Elsevier Science B.V. All rights reserved.