Detailed Report of the MuLan Measurement of the Positive Muon Lifetime and Determination of the Fermi Constant

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 x 10^{12} positrons were accumulated and together the data yield a muon lifetime of tau_{mu}(MuLan) = 2196980.3(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 G_F (MuLan) = 1.1663787(6) x 10^{-5} GeV^{-2} (0.5 ppm). It also enables new precision studies of weak interactions via lifetime measurements of muonic atoms.