The Critical Hopping Parameter in O(a) improved Lattice QCD

Abstract

We calculate the critical value of the hopping parameter, $κ_c$, in O(a) improved Lattice QCD, to two loops in perturbation theory. We employ the Sheikholeslami-Wohlert (clover) improved action for Wilson fermions. The quantity which we study is a typical case of a vacuum expectation value resulting in an additive renormalization; as such, it is characterized by a power (linear) divergence in the lattice spacing, and its calculation lies at the limits of applicability of perturbation theory. The dependence of our results on the number of colors $N$, the number of fermionic flavors $N_f$, and the clover parameter $c_{SW}$, is shown explicitly. We compare our results to non perturbative evaluations of $κ_c$ coming from Monte Carlo simulations.