Measurement of the Positive Muon Lifetime and Determination of the Fermi Constant to Part-per-Million Precision

We report a measurement of the positive muon lifetime to a precision of 1.0 ppm; it is the most precise particle lifetime ever measured. The experiment used a time-structured, low-energy muon beam and a segmented plastic scintillator array to record more than $2\times {10}^{12}$ decays. Two different stopping target configurations were employed in independent data-taking periods. The combined results give ${\tau }_{{\mu }^{+}}(\mathrm{MuLan})=2196980.3(2.2)\mathrm{ps}$, more than 15 times as precise as any previous experiment. The muon lifetime gives the most precise value for the Fermi constant: $G_F(\mathrm{MuLan})=1.1663788(7)\times {10}^{-5}{\mathrm{GeV}}^{-2}$ (0.6 ppm). It is also used to extract the ${\mu }^{-}p$ singlet capture rate, which determines the proton’s weak induced pseudoscalar coupling $g_P$.

Figure 1

Diagram of the experiment. Muons are transported to the AK-3 or quartz disk targets through a vacuum beam pipe, which is lined on the inside with 0.1-mm-thick AK-3 foils polarized in the azimuthal direction. 170 pairs of triangular scintillator detectors, each read out individually, surround the target. The Halbach magnetic ring is used only for the quartz disk. A wire chamber (EMC) is placed at the rear to monitor the beam profile when the targets are opened.

Figure 2

Lifetime measurement summary. The MuLan R06 and R07 results are plotted separately to illustrate the consistency. The vertical shaded band is centered on the MuLan weighted average with a width equal to the combined uncertainty.