Improved Measurement of the Positive-Muon Lifetime and Determination of the Fermi Constant

The mean life of the positive muon has been measured to a precision of 11 ppm using a low-energy, pulsed muon beam stopped in a ferromagnetic target, which was surrounded by a scintillator detector array. The result, ${\tau }_{\mu }=2.197013(24)\mu \mathrm{s}$, is in excellent agreement with the previous world average. The new world average ${\tau }_{\mu }=2.197019(21)\mu \mathrm{s}$ determines the Fermi constant $G_F=1.166371(6)\times {10}^{-5}{\mathrm{GeV}}^{-2}$ (5 ppm). Additionally, the precision measurement of the positive-muon lifetime is needed to determine the nucleon pseudoscalar coupling $g_P$.

Figure 1

Data from a subset of the MuLan detectors, illustrating the accumulation and measurement periods and the background mainly caused by incomplete extinction. The fit region used for the whole data set starts as $1\mu \mathrm{s}$ (thick red line). The residuals divided by their uncertainty (i.e., in standard deviations) are shown in the upper inset panel.

Figure 2

Diagram of the experiment with several detector elements removed. Muons enter through the beam pipe vacuum window and traverse the EMC and a helium bag (not shown) before stopping in the AK-3 target. Decay positrons are recorded by the coincidence of inner and outer scintillators in one triangular segment; the outer scintillators are visible. Two example decay trajectories are shown.