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 1.6×10¹² positrons were accumulated and together the data yield a muon lifetime of τ_μ(MuLan)=2196980.3(2.2) ps (1.0 ppm), 30 times more precise than previous generations of lifetime experiments. The lifetime measurement yields the most accurate value of the Fermi constant GF(MuLan)=1.1663787(6)×10^-5 GeV^-2 (0.5 ppm). It also enables new precision studies of weak interactions via lifetime measurements of muonic atoms.