Measurement of the Michel Parameter $\rho$ in Muon Decay

The TWIST Collaboration has measured the Michel parameter $\rho$ in normal muon decay, ${\mu }^{+}\to e^{+}{\nu }_e{\overline{\nu }}_{\mu }$. In the standard model, $\rho =3/4$. Deviations from this value imply mixing of left- and right-handed muon and electron couplings. We find $\rho =0.75080\pm 0.00032(\mathrm{stat})\pm 0.00097(\mathrm{syst})\pm 0.00023$, where the last uncertainty represents the dependence of $\rho$ on the Michel parameter $\eta$. This result sets new limits on the $W_L-W_R$ mixing angle in left-right symmetric models.

Figure 1

Measured positron momenta (solid lines) near the end point are compared to Monte Carlo simulations (dotted lines). The curves show surface muon set B and cloud muon spectra for $0.70<|\cos \theta |<0.74$.

Figure 2

Average momentum change of decay positrons through the target and detector materials as a function of momentum for data (solid circles) and Monte Carlo simulations (open circles), measured as described in the text.

Figure 3

Panel (a) shows the muon-decay spectrum (solid curve) from surface muon set B vs momentum, for events within $0.70<|\cos \theta |<0.84$, as well as the events within this angular region that pass the fiducial constraints (dot-dashed curve). The spectrum within $0.5<|\cos \theta |<0.7$ is similar. Panels (b) and (d) show the probability for reconstructing decays for the two angular ranges, as calculated by the Monte Carlo simulation. Panels (c) and (e) show the residuals for the same angular ranges from the fit of set B to the Monte Carlo standard spectrum plus derivatives.