Search for the violation of time-reversal invariance inKμ30decays

The transverse polarization of muons from the decay $K_L^0\to {\pi }^{-}{\mu }^{+}{\nu }_{\mu }$ has been recently measured at Brookhaven National Laboratory. A cylindrically symmetric detector was employed with scintillation-counter hodoscopes detecting the charged decay products of the in-flight kaon decay and determining the orientation of the decay plane in the laboratory. Muons were brought to rest in an aluminum polarimeter where they precessed in 60-G magnetic field. The muon polarization was determined from the asymmetric emission of the positron in the muon decay (${\mu }^{+}\to e^{+}{\nu }_e{\overline{\nu }}_{\mu }$). With 12×${10}^6$ events collected the mean values measured for the two components of transverse polarization are $P_n^{\mathrm{lab}}=0.0017\mathrm{}\pm 0.0056$ for the component normal to the decay plane and $P_t^{\mathrm{lab}}=0.417\mathrm{}\pm 0.063$ for the component in the decay plane. For $\mathrm{Im}\xi$, where $\xi$ is the ratio of form factors describing $K_{\mu 3}$ decay, we have deduced a value of 0.009±0.030 which is not significantly different from the value 0.008, expected if time-reversal invariance is valid. We deduce that the average value of the ratio of the normal to transverse components of muon polarization in the kaon rest frame is given by ${〈\frac{P_n}{P_t}〉}^{\mathrm{c}.\mathrm{m}.\mathrm{}}=0.005\mathrm{}\pm 0.015$.