Result of T-violating muon polarization measurement in the $K^+ to pi^0 mu^+ u$ decay

A search for T-violating muon polarization in the $K^+ to pi^0 mu^+ u$ decay has been performed at KEK using stopped kaons. A new improved limit was obtained, $P_T= -0.0017 pm 0.0023 (stat) pm 0.0011 (syst)$, corresponding to a 90 % confidence limit of $| P_T| < 0.0050$. The T-violating parameter was also determined to be Im$xi = -0.0053 pm 0.0071 (stat) pm 0.0036 (syst)$, and $|{rm Im}xi| < 0.016$ (90 % CL).