Muon lifetime and Fermi constant: an update

Abstract

We present an updated prediction for the lifetime of the muon including a detailed analysis of all relevant uncertainties. Our prediction includes QED corrections up to order ${\alpha }^3$ and state-of-the-art hadronic contributions based on dispersive methods. Radiative corrections and finite-electron-mass effects are parametrized by the correction factor $\Delta q$ in ${\tau }_{\mu }^{-1}=G_F^2{m}_{\mu }^5(1+\Delta q)/(192{\pi }^3)$, for which we obtain $\Delta q=(-4384678\pm 34)\times 10^{-9}$. This reduces the uncertainty associated with $\Delta q$ by an order of magnitude compared to the previous prediction at order ${\alpha }^2$. We use our results to provide an updated value of the Fermi coupling constant, $G_F=1.16637859(59)\times 10^{-5}{\mathrm{GeV}}^{-2}$. Further improvements will require better measurements of the muon lifetime and mass.

Comments: 7 pages