Complete 2-loop Quantum Electrodynamic Contributions to the Muon   Lifetime in the Fermi Model
  The complete 2-loop quantum electrodynamic corrections to the muon lifetime are calculated in the Fermi theory. The exact result for the effects of virtual and real photons, virtual electrons, muons as well as e+e- pair creation is   Delta Gamma_QED   = Gamma_0(alpha/pi)^2[(156815/5184)-(1036/27)zeta(2)-(895/36)zeta(3)   +(67/8)zeta(4)+53zeta(2)ln(2)]   = Gamma_0(alpha/pi)^2(6.743)   where Gamma_0 is the tree-level width. The theoretical error in the value of the Fermi coupling constant, G_F, is now rendered negligible compared to the experimental uncertainty coming from the measurement of the muon lifetime. The overall error in G_F is then roughly halved giving   G_F = (1.16637 +/- 0.00001) x 10^(-5) GeV^(-2). 
Timo van Ritbergen and Robin G. Stuart