  The hadronic light-by-light scattering contribution to the muon anomalous
magnetic moment can be estimated by computing constituent quark loops. Such an
estimate is very sensitive to the numerical values of the constituent quark
masses. These can be fixed by computing the hadronic vacuum polarization
contribution to the muon magnetic anomaly within the same model. In this
Letter, we demonstrate the stability of this framework against first-order
perturbative QCD corrections.
