Search forT-invariance violation inKμ3+decay

The transverse polarization of muons from the decay $K^{+}\to {\pi }^0{\mu }^{+}{\nu }_{\mu }$ was measured at Brookhaven National Laboratory. Having detected and measured 2.1 × ${10}^7$ ${\mu }^{+}\to e^{+}{\nu }_e{\overline{\nu }}_{\mu }$ decays we found that the $T$-violating component of muon polarization perpendicular to the $K^{+}$ decay plane $P_n=-0.0031\mathrm{}\pm 0.0053$. Combining this result with our result for $K_{\mu 3}^0$, we obtain as a measure of $T$- (and therefore $\mathrm{CP}$-) invariance violation $\mathrm{Im}\xi =-0.010\mathrm{}\pm 0.019$.