An Improved Determination of the Fermi Coupling Constant, G_F

TL;DR

This paper provides a precise analytic calculation of the complete 2-loop QED corrections to muon decay, significantly reducing the theoretical uncertainty in determining the Fermi coupling constant, G_F.

Contribution

It presents the first full analytic expression for 2-loop QED effects in muon decay, eliminating the previous theoretical error in G_F determination.

Findings

Reduced the theoretical error in G_F to purely experimental

Provided an exact 2-loop QED correction formula for muon lifetime

Enhanced the precision of G_F measurement to (1.16637 +/- 0.00001) x 10^-5 GeV^-2

Abstract

Over 40 years after the calculation of the 1-loop QED corrections to the muon lifetime, new theoretical developments have made it possible to obtain an analytic expression for the complete 2-loop QED contributions 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 The overall error has been roughly halved and is now entirely experimental. Several experiments are planned for the next generation of muon lifetime measurements and these can proceed unhindered by theoretical uncertainties.