O(a) improved QCD: The 3-loop beta-function, and the critical hopping parameter

Abstract

We calculate the 3-loop 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 , and 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 turns out to be very pronounced. We also calculate the critical value of the hopping parameter, κ c , in the clover action, to two loops in perturbation theory. This quantity is an additive renormalization; as such, it exhibits a linear divergence in the lattice spacing. We compare our results to non perturbative evaluations of κ c coming from MC simulations.