Critical mass of Wilson fermions: A comparison of perturbative and Monte Carlo results

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 to our results; this shifts them quite favorably towards the nonperturbative values.