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 Nf, as well as the clover parameter cSW, is shown explicitly. A direct outcome of our calculation is the two-loop relation between the bare coupling constant g0 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 g0, which is important in checks of asymptotic scaling. For typical values of CSW, this correction is found to be very pronounced. © 2002 Elsevier Science B.V. All rights reserved.