We present a detailed report of the method, setup, analysis and results of a precision measurement of the positive muon lifetime. The experiment was conducted at the Paul Scherrer Institute using a time-structured, nearly 100%-polarized, surface muon beam and a segmented, fast-timing, plastic scintillator array. The measurement employed two target arrangements; a magnetized ferromagnetic target with a ∼4 kG internal magnetic field and a crystal quartz target in a 130 G external magnetic field. Approximately 1.6 × 10 12 positrons were accumulated and together the data yield a muon lifetime of τµ(MuLan) = 2 196 980.3(2.2) ps (1.0 ppm), thirty times more precise than previous generations of lifetime experiments. The lifetime measurement yields the most accurate value of the Fermi constant GF (MuLan) = 1.166 378 7(6) × 10 −5 GeV −2 (0.5 ppm). It also enables new precision studies of weak interactions via lifetime measurements of muonic atoms.

The muon anomalous magnetic moment has been measured in a new experiment at Brookhaven. Polarized muons were stored in a superferric ring, and the angular frequency difference, v a , between the spin precession and orbital frequencies was determined by measuring the time distribution of highenergy decay positrons. The ratio R of v a to the Larmor precession frequency of free protons, v p , in the storage-ring magnetic field was measured. We find R 3.707 220͑48͒ 3 10 23. With m m ͞m p 3.183 345 47͑47͒ this gives a m 1 1 165 925͑15͒ 3 10 29 (613 ppm), in good agreement with the previous CERN measurements for m 1 and m 2 and of approximately the same precision.

We report a measurement of the positive muon lifetime to a precision of 1.0 parts per million (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 × 10 12 decays. Two different stopping target configurations were employed in independent data-taking periods. The combined results give τ µ + (MuLan) = 2196980.3(2.2) ps, more than 15 times as precise as any previous experiment. The muon lifetime gives the most precise value for the Fermi constant: GF (MuLan) = 1.1663788(7) × 10 −5 GeV −2 (0.6 ppm). It is also used to extract the µ − p singlet capture rate, which determines the proton's weak induced pseudoscalar coupling g P .A measurement of the positive muon lifetime, τ µ + , to high precision determines the Fermi constant, G F , according to the relationHere, ∆q represents well-known phase space and both QED and hadronic radiative corrections [1], and we assume that G F is universal for weak interactions. Strictly speaking, τ µ + determines a muon-decay-specific coupling, denoted G µ , which could be compared to other G F determinations as a test of the standard model [2]. Prior to 1999, the limitation on the precision of G F was dominated by the uncertainty on ∆q. Van Ritbergen and Stuart were the first to compute the secondorder QED radiative corrections in the massless electron limit, reducing the theoretical uncertainty to below 0.3 ppm [3], and well below the then-current experimental uncertainty. This development motivated a new generation of precision muon lifetime measurements, MuLan [4] and FAST [5]. More recently, Pak and Czarnecki extended the result in [3] to finite electron mass, which shifts the predicted decay rate 1/τ µ by -0.43 ppm; alternatively, it decreases G F by 0.21 ppm [6].In Ref.[4], we reported an 11 ppm measurement of τ µ + based on a relatively short commissioning run. This Letter reports the results from a 100 times larger data set, accumulated using the final setup of the experiment.The experiment is designed to stop muons in a target during a beam-on accumulation interval and measure the decay positrons-primarily from the µ + → e + ν eνµ decay mode-during a beam-off measurement period. The two running periods, R06 and R07, used different targets. More than 10 12 decays were recorded in each period.The experiment used the πE3 beamline at the Paul Scherrer Institute (PSI). During the run, positive muons from at-rest pion decay near the surface of the production target are directed to the experiment through two opposing vertical dipole magnets and a series of 15 magnetic quadrupole lenses. A velocity-selecting E × B separator is tuned to pass muons and reject positrons. A special feature of the beamline is a custom, 60-ns switching, 25-kV kicker [8]. When energized, the electric field across the 120-mm vertical gap and 1500-mm length displaces the muon beam by 46 mm at the exit and deflects it by 45 mrad onto a downstream collimator. The muon flux of ∼ 1...

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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(micro)=2.197 013(24) micros, is in excellent agreement with the previous world average. The new world average tau(micro)=2.197 019(21) micros determines the Fermi constant G(F)=1.166 371(6)x10(-5) GeV-2 (5 ppm). Additionally, the precision measurement of the positive-muon lifetime is needed to determine the nucleon pseudoscalar coupling g(P).