Calculation of the Lepage-Mackenzie scale for the lattice axial-vector and vector currents

We calculate the perturbative scales ${(q}^{\star })$ for the axial-vector and vector currents for the Wilson action, with and without tadpole improvement, using the formalism of Lepage and Mackenzie. The scale for the pseudoscalar density (times the mass) is computed as well. Contrary to naive expectation, tadpole improvement reduces $q^{\star }$ by only a small amount for the operators we consider. We also discuss the use of a nonperturbative coupling to calculate the perturbative scale.