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

TL;DR

This paper computes the two-loop additive mass renormalization in lattice QCD with improved actions, providing detailed perturbative results for various parameters to aid comparison with non-perturbative simulations.

Contribution

It presents the first two-loop calculation of the critical hopping parameter using clover fermions and Symanzik improved gluons, including dependence on multiple parameters.

Findings

Polynomial dependence on c_{SW} and Symanzik coefficients

Explicit dependence on N and N_f

Results applicable to improved perturbation theory methods

Abstract

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 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 c_{SW} (clover parameter) and cover a wide range of values for the Symanzik coefficients c_i. 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 kappa_c coming from Monte Carlo simulations, we employ an improved perturbation theory method applied to improved actions.