Normal muon decay (µ⁺→ e⁺ ν_{e µ}) is an ideal process to investigate the electroweak interaction in the Standard Model. The reaction involves only leptons, obviating the need for uncertain strong interaction corrections, thus making it a clean probe of the theory's purely left-handed (V-A) structure. A high-precision determination of the parameters describing the muon decay spectral shape explores physics possibilities beyond the Standard Model, for example those involving right-handed interactions. The world's most precise such determination has been the goal of the TRIUMF Weak Interaction Symmetry Test (TWIST). The collaboration has recently completed its first phase by directly measuring the muon decay parameters ρ and δ, improving on the accepted Particle Data Group (PDG) values for the two spectral shape parameters by factors of 2.5 (ρ) and 2.9 (δ) [1, 2].
    The four so-called "Michel parameters" describe the distribution in energy and angle of positrons from polarized muon decay. The spectrum's isotropic part has a momentum dependence determined by ρ plus an additional small term proportional to a second parameter, η. The asymmetry is proportional to a third parameter ξ multiplied by the muon polarization, P_µ , while a fourth parameter, δ, determines its momentum dependence. Within the Standard Model, these parameters are predicted to be ρ = ¾, δ = ¾, ξ = 1, and η = 0.

   Beams of positive muons are used by TWIST since they can be produced with high polarization and high stopping density. The high intensity TRIUMF proton beam produces π⁺, some of which decay at rest at the surface of a production target to create a highly polarized "surface" muon beam with momentum 29.6 MeV/c, which is subsequently transported into a 2T superconducting solenoid. A schematic diagram of the TWIST spectrometer is shown in Figure 1.
   Most of the muon beam stops in a thin target, located at the center of a symmetric array of 56 low mass, high precision planar drift chambers. Limitations on final errors are dominated by systematic effects since the statistical precision is very high.
   The measured momentum and angle distribution of the decay positrons is shown in Figure 2. The drop in acceptance near |cosθ | = 0 is due to the poor reconstruction efficiency in that region. To extract the muon decay parameters, a two-dimensional fit is made to a fiducial region where the detector acceptance is essentially uniform, utilizing a blind analysis technique. The results are based on 6 × 10⁹ muon decays, spread over sixteen data sets. Four sets were analyzed for both ρ and δ. A fifth set of low polarized muons from pion decays in flight was also analyzed for ρ. The remaining data sets, combined with further MC simulations, were used to estimate the sensitivities to various systematic effects.
   TWIST's new measurement of ρ = 0.75080 ± 0.00032(stat.) ± 0.00097(syst.) ± 0.00023 (last uncertainty due to the current PDG error in η) sets an upper limit on the mixing angle of a possible heavier right-handed partner to the W boson, |ζ| < 0.030 at 90% c.l. Combining ρ with the new measurment of δ = 0.74964 ± 0.00066(stat.) ± 0.00112(syst.), and the PDG value of P_µ ξ δ /ρ, an indirect limit is set on P_µ ξ: 0.9960 < P_µ ξ ≤ ξ < 1.0040 with 90% c.l. The lower limit 0.9960 < P_µ ξ slightly improves the limit on the mass of the possible right-handed boson, W_R ≥ 420 GeV/c². Finally, an upper limit is found for the muon right-handed coupling probability, Q^µ_R<0.00184 at 90% c.l.
   Muon decay, combined with complement-ary measurements from experiments at higher energies and in nuclear beta decay, help our understanding of the asymmetry in the weak interaction's handedness and whether symmetry may be restored at higher energy scales. In the future phases of the experiment, TWIST aims to produce a direct measurement of P_µ ξ with a precision of few parts in 10⁴ and to increase its sensitivity to ρ and δ by approximately another factor of five.•

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