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 Nf, and 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 M̄S scheme. Further, we can immediately derive the three-loop correction to the relation between the lattice Λ-parameter and g0, which turns out to be very pronounced. We also calculate the critical value of the hopping parameter, Κc, 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 Κc coming from MC simulations.