Toward a 0.5 ppm measurement of $G_F$*

The weak coupling constant, $G_F,$ is determined most precisely from the mean life of the positive muon, $\tau_\mu$. Advances in theory have reduced the theoretical uncertainty on $G_F$ as calculated from $\tau_\mu$ to a few tenths of a ppm. The remaining uncertainty on $G_F$ is entirely experimental, and is dominated by the uncertainty on $\tau_\mu$. The MuLan experiment is designed to measure the muon lifetime to a precision of 1 ppm, a twenty-fold improvement over the previous generation of experiments. We report an intermediate result, $\tau_\mu=2.197013(24)$ $\mathrm{\mu s}$ (11 ppm), which is in excellent agreement with the previous world average. The mean life was measured using a pulsed surface muon beam stopped in a ferromagnetic target, surrounded by a symmetric scintillator detector array. The new world average $\tau_\mu=2.197019(21)$ $\mathrm{\mu s}$ determines the Fermi constant $G_F = 1.166371(6) \times 10^{-5}$ $\mathrm{GeV}^{-2}$ (5 ppm). Since the intermediate measurement, the detector was instrumented with waveform digitizers, the muon beam rate and beam extinction were increased, and two data sets were acquired on different targets, each containing over $10^{12}$ muon decays. These data will lead to a new determination of $G_F$ to 0.5 ppm.