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

TL;DR

This paper computes the critical hopping parameter in O(a) improved Lattice QCD to two-loop order using perturbation theory, providing insights into its dependence on various parameters and comparing with non-perturbative results.

Contribution

It presents a two-loop perturbative calculation of the critical hopping parameter in O(a) improved Lattice QCD, including parameter dependencies and comparison with Monte Carlo data.

Findings

Calculated $\kappa_c$ to two loops in perturbation theory.

Explicit dependence on $N$, $N_f$, and $c_{SW}$ shown.

Comparison with non-perturbative Monte Carlo results included.

Abstract

We calculate the critical value of the hopping parameter, $\kappa_c$, 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 $\kappa_c$ coming from Monte Carlo simulations.