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 $\hat{I}{\pm }^3$ and state-of-the-art hadronic contributions based on dispersive methods. Radiative corrections and finite-electron-mass effects are parametrized by the correction factor $\hat{I}”q$ in $\ddot{I}{„}_{\hat{I}}{¼}^{-1}=G_F^2{m}_{\hat{I}}{¼}^5(1+\hat{I}”q)/(192\ddot{I}{€}^3)$, for which we obtain $\hat{I}”q=(-4384678\pm 34)\times 10^{-9}$. This reduces the uncertainty associated with $\hat{I}”q$ by an order of magnitude compared to the previous prediction at order $\hat{I}{\pm }^2$. 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.

7 pages

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