The complete 2-loop QED contributions to the muon lifetime have been
calculated analytically in the Fermi theory. The exact result for the effects
of virtual and real photons, virtual electrons, muons and hadrons as well as
e+e- pair creation is
Delta Gamma^(2)=Gamma_0(alpha/pi)^2[(156815/5184)-(1036/27)zeta(2)
-(895/36)zeta(3)+(67/8)zeta(4)
+53zeta(2)ln(2)-(0.042+/-0.002)]
where Gamma_0 is the tree-level width. This eliminates the theoretical error
in the extracted value of the Fermi coupling constant, G_F, which was
previously the source of the dominant uncertainty. The new value is
G_F=(1.16637 +/- 0.00001) x 10^-5 GeV^-2
with the error being entirely experimental. Several experiments are planned
for the next generation of muon lifetime measurements and these can proceed
unhindered by theoretical uncertainties.Comment: 9 pages, LaTeX, uses sprocl.sty, amsmath.sty, amssymb.sty and
axodraw.sty. To appear in the Proceedings of the IVth International Symposium
on Radiative Corrections (RADCOR98), Barcelona, Spain, 8-12 September, 1998,
edited by J. Sol
