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

The TWIST Collaboration has measured the Michel parameter $\rho$ in normal muon decay, $\mu^+ \to e^+ \nu_e \bar{\nu}_{\mu}$. In the Standard Model, $\rho$ = 3/4. Deviations from this value require mixing of left- and right-handed muon and electron couplings in the muon-decay Lagrangian. We find $\rho$ = 0.75080 $\pm$ 0.00044(stat.) $\pm$ 0.00093(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.