Detailed report of the MuLan measurement of the positive muon lifetime and determination of the Fermi constant

Abstract

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 $\ensuremath{\sim}4\text{ }\text{ }\mathrm{kG}$ internal magnetic field and a crystal quartz target in a 130 G external magnetic field. Approximately $1.6\ifmmode\times\else\texttimes\fi{}{10}^{12}$ positrons were accumulated and together the data yield a muon lifetime of ${\ensuremath{\tau}}_{\ensuremath{\mu}}(\mathrm{\text{MuLan}})=2196980.3(2.2)\text{ }\text{ }\mathrm{ps}$ (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 ${G}_{F}(\mathrm{\text{MuLan}})=1.1663787(6)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\text{ }\text{ }{\mathrm{GeV}}^{\ensuremath{-}2}$ (0.5 ppm). It also enables new precision studies of weak interactions via lifetime measurements of muonic atoms.