Measurement of the Muon Polarization Vector inK+→π0+μ++ν

We have studied the decay $K^{+}\to {\pi }^0+{\mu }^{+}+\nu \left(K_{\mu 3}\right)$ in a spark-chamber experiment at the Bevatron. The data consist of 3133 events with $\mu -e$ decays and complete kinematics for $K_{\mu 3}^{}{}_{}{}^{+}$. We determined the muon polarization vector from the angular distribution of the decay electrons and related this measurement to a determination of the vector form-factor ratio, $\xi =\frac{f_{-}}{f_{+}}$. The data are statistically consistent with the assumption that $\xi$ does not depend on momentum transfer. Assuming $\xi$ constant, our result is $\xi =\left(\frac{-0.9+0.5\mathrm{}}{-0.4\mathrm{}}\right)+i(-0.3\mathrm{}\pm 0.5)$. If we analyze the data imposing the constraint that $\xi$ be real, we find $\xi =-0.95\mathrm{}\pm 0.3$. The muon polarization along the direction predicted by these values for $\xi$ is 0.9±0.1. In a calibration experiment, we find the muon longitudinal polarization in the decay $K^{+}\to {\mu }^{+}+\nu$ to be -1.0±0.1.