2-loop additive mass renormalization with clover fermions and Symanzik improved gluons

Abstract

We calculate the critical value of the hopping parameter, κc, in Lattice QCD, up to two loops in perturbation theory. We employ the Sheikholeslami-Wohlert (clover) improved action for Wilson fermions and the Symanzik improved gluon action for 4- and 6-link loops. 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. Our results are polynomial in cSW (clover parameter) and cover a wide range of values for the Symanzik coefficients ci. Furthermore, the dependence on the number of colors N and the number of fermionic flavors N f is shown explicitly. In order to compare our results to non perturbative evaluations of κc coming from Monte Carlo simulations, we employ an improved perturbation theory method applied to improved actions.