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 $α^3$ and state-of-the-art hadronic contributions based on dispersive methods. Radiative corrections and finite-electron-mass effects are parametrized by the correction factor $Δq$ in $τ_μ^{-1}=G_F^2m_μ^5(1+Δq)/(192π^3)$, for which we obtain $Δq=(-4\, 384\, 678 \pm 34)\times 10^{-9}$. This reduces the uncertainty associated with $Δq$ by an order of magnitude compared to the previous prediction at order $α^2$. We use our results to provide an updated value of the Fermi coupling constant, $G_F=1.166\,378\, 59 \, (59) \times 10^{-5} \, \mathrm{GeV}^{-2}$. Further improvements will require better measurements of the muon lifetime and mass.