The Critical Mass of Wilson Fermions: A Comparison of Perturbative and Monte Carlo Results

TL;DR

This paper compares perturbative and Monte Carlo methods to determine the critical hopping parameter in Lattice QCD with Wilson fermions, highlighting the limitations of perturbation theory and the effectiveness of tadpole improvement.

Contribution

It provides a two-loop perturbative calculation of $oldsymbol{ ext{kappa}_c}$ and compares it with non-perturbative Monte Carlo results, demonstrating the impact of tadpole improvement.

Findings

Perturbative results are significantly shifted by tadpole improvement.

Non-perturbative Monte Carlo results differ from perturbative calculations.

Tadpole improvement brings perturbative estimates closer to Monte Carlo values.

Abstract

We calculate the critical value of the hopping parameter, $\kappa_c$, in Lattice QCD with Wilson fermions, to two loops in perturbation theory. This quantity is an additive renormalization; as such, it is characterized not only by the standard caveats regarding the asymptotic nature of perturbative results, but also by a linear divergence in the lattice spacing. Consequently, our calculation tests rather stringently the limits of applicability of perturbation theory. We compare our results to non perturbative evaluations of $\kappa_c$ coming from Monte Carlo simulations. Finally, we apply a tadpole improvement technique on our results; this shifts them quite favourably towards the non perturbative values.