Two-loop additive mass renormalization with clover fermions and Symanzik improved gluons
A. Skouroupathis, M. Constantinou, and H. Panagopoulos

We calculate the critical value of the hopping parameter, $\kappa_c$, 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 $c_{\rm SW}$ (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 $\kappa_c$ coming from Monte Carlo simulations, we employ an improved perturbation theory method for improved actions. \medskip {\bf Keywords:} Lattice QCD, Lattice perturbation theory, Hopping parameter, Improved actions. \medskip {\bf PACS numbers:} 11.15.Ha, 12.38.Gc, 11.10.Gh, 12.38.Bx

© 2008 The American Physical Society.