Abstract
The part-per-million measurement of the positive muon lifetime and determination of the Fermi constant by the MuLan experiment at the Paul Scherrer Institute is reviewed. The experiment used an innovative, time-structured, surface muon beam and a near-4\piπ, finely-segmented, plastic scintillator positron detector. Two in-vacuum muon stopping targets were used: a ferromagnetic foil with a large internal magnetic field, and a quartz crystal in a moderate external magnetic field. The experiment acquired a dataset of 1.6 \times 10^{12}1.6×1012 positive muon decays and obtained a muon lifetime \tau_{\mu} = 2\, 196\, 980.3(2.2)τμ=2196980.3(2.2)~ps (1.0~ppm) and Fermi constant G_F = 1.166\, 378\, 7(6) \times 10^{-5}F=1.1663787(6)×10−5 GeV^{-2}−2 (0.5~ppm). The thirty-fold improvement in \tau_{\mu}τμ has proven valuable for precision measurements in nuclear muon capture and the commensurate improvement in G_FF has proven valuable for precision tests of the standard model.
Highlights
The electromagnetic, strong, gravitational (G) and weak (GF ) couplings are the “calibration constants” of nature [1]
The construction of coincidence histograms with different thresholds and deadtimes was important for studying the distortions that arise from pulse pileup and gain changes
We note the precision determination of τμ is important to work on nuclear muon capture
Summary
The electromagnetic (αe), strong (αs), gravitational (G) and weak (GF ) couplings are the “calibration constants” of nature [1] Their magnitudes haven’t been determined by theory but rather are obtained from measurement. The energy-scale-dependent effective coupling αs governs the binding of protons and neutrons to form nuclei and the production of chemical elements in stars It controls the emergence of the two faces of the strong interaction: quark confinement at large distances and asymptotic freedom at short distances. This constant and the current-current weak interaction description have survived many decades as a very convenient, low-energy, effective theory. Their work opened the door for the MuLan experiment at PSI [5, 6], a part-per-million measurement of the muon lifetime τμ and determination of the Fermi constant GF – a thirty-fold improvement over earlier measurements
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