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

Abstract

We calculate the critical value of the hopping parameter, $κ_c$, in Lattice QCD, up to two loops in perturbation theory. We employ the Sheikholeslami-Wohlert (clover) improved action for fermions and the Symanzik improved gluon action with 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 $c_{SW}$ (clover parameter) and cover a wide range of values for the Symanzik coefficients $c_i$. The dependence on the number of colors N and the number of fermion flavors $N_f$ is shown explicitly. In order to compare our results to non perturbative evaluations of $κ_c$ coming from Monte Carlo simulations, we employ an improved perturbation theory method for improved actions.

20 pages, 8 figures, 14 tables. Phys. Rev. D77, Number 1 (2008)