ar X iv : h ep - l at / 0 11 02 11 v 1 2 9 O ct 2 00 1 The three - loop β - function of QCD with the clover action

The three-loop β-function of QCD with the clover action. Abstract We calculate, to 3 loops in perturbation theory, the bare β-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 g 0 and the one renormalized in the MS scheme. Further, we can immediately derive the three-loop correction to the relation between the lattice Λ-parameter and g 0 , which is important in checks of asymptotic scaling. For typical values of c SW , this correction is found to be very pronounced.