K+Three-Body Leptonic Decay Modes

Abstract

The ${K_{\mu 3}}^{+}\to {\pi }^0+{\mu }^{+}+\nu$ and ${K_{e3\mathrm{}}}^{+}\to {\pi }^0+e^{+}+\nu$ decay-mode Dalitz-plot distributions were studied for lepton momenta below 120 $\frac{\mathrm{MeV}}{c}$, using an exposure of the Brookhaven 30-in. propane bubble chamber to a stopping beam of $K^{+}$ mesons. The vector momentum of the ${\pi }^0$ was obtained with a typical error of 5% by considering only those events in which both $\gamma$ rays from the ${\pi }^0$ decay converted to electron-positron pairs. Both decay modes are consistent with a pure vector interaction. 78 $K_{\mu 3}$ events yield the results, assuming $\xi$ to be independent of momentum transfer: $\mathrm{Re}\xi =-0.5\mathrm{}\pm 0.9$, $\left|\mathrm{Im}\xi \right|={{0.0}_{-0.0\mathrm{}}}^{+2.3\mathrm{}}$, and a discrimination of 150:1 against a second value of $\mathrm{Re}\xi =-5.3\mathrm{}\pm 0.7$. There were 90 $K_{e3\mathrm{}}$ events consistent with a constant form factor $f^{+}$, giving ${\lambda }_{+}={{-0.02\mathrm{}}_{-0.12\mathrm{}}}^{+0.08\mathrm{}}$.