K+Decay in Flight

From a sample of ${10}^5$ $K^{+}$ decays in flight the following branching ratios were obtained: $K_{\mu 2}=(63.24\mathrm{}\pm 0.44)\%$, $K_{\pi 2}=(21.18\mathrm{}\pm 0.28)\%$, $\tau (K^{+}\to {\pi }^{+}{\pi }^{+}{\pi }^{-})=(5.56\mathrm{}\pm 0.20)\%$, ${\tau }^{\prime }(K^{+}\to {\pi }^{+}{\pi }^0{\pi }^0)=(1.84\mathrm{}\pm 0.06)\%$, $K_{\mu 3}(3.33\mathrm{}\pm 0.16)\%$, and $K_{e3\mathrm{}}=(4.86\mathrm{}\pm 0.10)\%$. The phase-space distributions for three-body semileptonic modes were studied in detail from a second sample of ${10}^5$ decays. For 4017 $K^{+}\to {\pi }^0{e}^{+}\nu$ events, ${\lambda }_{+}=0.029\mathrm{}\pm 0.011$. Limits on scalar and tensor form factors of $\left|\frac{f_S}{f_{+}}\right|<\mathrm{}0.13\mathrm{}$ and $\left|\frac{f_T}{f_{+}}\right|<\mathrm{}0.75\mathrm{}$ (90% confidence) were obtained. For $K^{+}\to {\pi }^0{\mu }^{+}\nu$ a parametrized fit to 3900 events assuming ${\lambda }_{+}={\lambda }_{-}=+0.030\mathrm{}$ gave $\xi =-0.09\mathrm{}\pm 0.28$.