Kl3+Decay Rates

An experiment has been performed at the Brookhaven Cosmotron to study $K^{+}\to {\pi }^0{l}^{+}\nu$. A spark-chamber-magnet system was triggered on any charged particle leaving the target after a $K^{+}$ had stopped. Separation between ${\pi }^{+}$ and ${\mu }^{+}$ was performed using momentum and range. Positrons were identified by shower production. On the basis of 300 $K_{e3\mathrm{}}$ and 350 $K_{\mu 3}$ events in the momentum range 100 to 220 MeV/c, we found ratios $\frac{K_{e3\mathrm{}}}{\left(\mathrm{all} K^{+}\right)}=0.044\mathrm{}\pm 0.004$, $\frac{K_{\mu 3}}{\left(\mathrm{all} K^{+}\right)}=0.035\mathrm{}\pm 0.0030$. The positron spectrum was consistent with a constant form factor. The ratio of constant form factors $\xi =\frac{f_{-}}{f_{+}}$ determined from the $\frac{K_{e3\mathrm{}}}{K_{\mu 3}}$ branching ratio was $\xi =+1.0\mathrm{}\pm 0.3$.