Complete 2-loop quantum electrodynamic contributions to the muon lifetime in the Fermi model

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

Gauge Invariance and the Unstable Particle

It is shown how to construct exactly gauge-invariant S-matrix elements for processes involving unstable gauge particles such as the $Z^0$ boson. The results are applied to derive a physically meaningful expression for the cross-section $\sigma(e^+e^-\to Z^0Z^0)$ and thereby provide a solution to the long-standing problem of the unstable particle.Comment: 8 pages LaTeX. Uses aipproc.sty and epsfig.sty. Talk presented at 1st Latin American Symposium on High-energy Physics, SILAFAE-I, Merida, November 1--5, 199

Gauge Invariance in the Process e+e−→νˉee−W+→νˉee−udˉe^+e^-\to \bar \nu_e e^-W^+\to\bar\nu_e e^-u\bar d

The process $e^+e^-\rightarrow \bar \nu_e e^-W^+ \rightarrow\bar\nu_e e^-u\bar d$ is considered as an example of the problems associated with maintaining gauge invariance in matrix elements involving unstable particles. It is shown how to construct a matrix element that correctly treats width effects for the intermediate unstable $W$ boson and that is both $SU(2)_L$ and $U(1)_{\rm e.m.}$ gauge-invariant. $SU(2)_L$ gauge-invariance is maintained by Laurent expansion in kinematic invariants and $U(1)_{\rm e.m.}$ gauge-invariance is enforced by means of a projection operator under which the exact matrix element is invariant.Comment: Case of $SU(2)_L$ gauge-invariance addressed. Substantial changes in text. 9 pages LaTeX, also available from via anonymous ftp from ftp://feynman.physics.lsa.umich.edu/pub/preprints/UM-TH-96-02.p