Complete O(N_f alpha²) Weak Contributions to the Muon Lifetime

The complete O(N_f alpha^2) weak contributions to the muon lifetime, denoted as Delta r^(2), are calculated in the MS-bar renormalization scheme. These come from 2-loop Feynman diagrams containing a loop formed by complete generations of massless fermions. They form an independent, gauge-invariant set of corrections that, because of the large number of light fermions in the Standard Model, is expected to make a significant contribution. In the MS-bar renormalization scheme with mu'= (pi e^gamma)^(1/2) mu = M_Z and for a Higgs mass, M_H, in the range 100-1000 GeV the contribution varies from -0.55x10^-4 to -1.54x10^-4 for each massless generation of fermions.