Precise measurement of parity violation in polarized muon decay

We present a new high precision measurement of parity violation in the weak interaction, using polarized muon decay. The TWIST Collaboration has measured $P_{\mu }^{\pi }\xi$, where $P_{\mu }^{\pi }$ is the polarization of the muon in pion decay and $\xi$ describes the intrinsic asymmetry in muon decay. We find $P_{\mu }^{\pi }\xi =1.00084\pm 0.00029(\mathrm{stat}.{)}_{-0.00063}^{+0.00165}(\mathrm{syst}.)$, in good agreement with the standard model prediction of $P_{\mu }^{\pi }=\xi =1$. Our result is a factor of 7 more precise than the pre-TWIST value, setting new limits in left-right symmetric electroweak extensions to the standard model.

Figure 1

Proton and M13 beam lines at TRIUMF. Surface muons were selected from the muon production target and transported to a muon stopping target at the center of the TWIST detector. The properties of the muon beam were measured by a pair of time expansion chambers (TECs) near the entrance of the detector.

Figure 2

Measurement of the nominal muon beam (a) position and (b) convergence using the TECs. The $x$ and $y$ coordinates are orthogonal to the muon beam direction. The position $x=y=0$ corresponds to the symmetry axis of the solenoidal magnetic field. The correlation between $y$ and ${\theta }_y$ demonstrates that the muon beam is converging in this plane.

Figure 3

A cross section of the TWIST detector array, including an example event. Proportional chambers (PCs) provided timing information and drift chambers (DCs) determined the position of particles. The angle between the decay positron and the beam direction is $\theta =\pi -{\theta }_s$.

Figure 4

(a) Number of events as a function of time relative to the proton beam. The spectrum shape corresponds to the pion lifetime. (b) The resulting forward-backward asymmetry of the decay positrons.

Figure 5

Muon beam improvements. (a) The beam was steered onto the solenoid symmetry axis ($x=y=0$), and (b) a vertical average angle of $\approx 20\mathrm{mrad}$ was removed. This reduced the transverse momentum of the beam inside the spectrometer, as measured by the mean position of the beam at each pair of planes (c) and (d).

Figure 6

Distribution of pulse widths corresponding to ionization in the proportional chambers immediately before the target (PC 5 and PC 6). The muons in each quadrant predominantly stopped in the material indicated. The distribution was compared to simulation, confirming that region 1 contained an enriched sample of muons stopping in the metal target.

Figure 7

Reconstructed decay positron spectrum for the simulation of a single data set. The accepted events are inside the fiducial region defined by the total momentum ($p$), the transverse momentum ($p_t$), the longitudinal momentum ($p_z$), and the cosine of the angle ($\cos \theta$). The cuts are symmetric for upstream and downstream.

Figure 8

Spectrum slice in $\cos \theta$ for a single data set and its simulation. The simulation’s end point momentum is $\sim 0.01\mathrm{MeV}/c$ greater than data. The data spectra were calibrated so that the end point for all angle slices agreed with the simulation.

Figure 9

The transverse magnetic field component $B_x$ from Opera (dashed and dash-dotted lines), and the simulated evolution of the muon beam polarization due to the magnetic field (solid line). The on-axis field is nonzero for $z\approx -100\mathrm{cm}$ due to the asymmetry of the solenoid’s field.

Figure 10

Example of an exponential fit to the forward-backward asymmetry from set 87. The vertical scale factor is arbitrary.

Figure 11

Summary of the result of this experiment together with previous $P_{\mu }^{\pi }\xi$ results [8, 31].

Figure 12

Allowed regions (90% confidence) for the $W_2$ mass and mixing angle in (a) manifest and (b) generalized LRS models. We include new limits using only $P_{\mu }^{\pi }\xi$, and $P_{\mu }^{\pi }\xi$ combined with $\rho$ and $\delta$ from [11].