K+Three-Body Leptonic Decay Modes

Abstract

The ${{K}_{\ensuremath{\mu}3}}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}+{\ensuremath{\mu}}^{+}+\ensuremath{\nu}$ and ${{K}_{e3}}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}+{e}^{+}+\ensuremath{\nu}$ 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 ${\ensuremath{\pi}}^{0}$ was obtained with a typical error of 5% by considering only those events in which both $\ensuremath{\gamma}$ rays from the ${\ensuremath{\pi}}^{0}$ decay converted to electron-positron pairs. Both decay modes are consistent with a pure vector interaction. 78 ${K}_{\ensuremath{\mu}3}$ events yield the results, assuming $\ensuremath{\xi}$ to be independent of momentum transfer: $\mathrm{Re}\ensuremath{\xi}=\ensuremath{-}0.5\ifmmode\pm\else\textpm\fi{}0.9$, $|\mathrm{Im}\ensuremath{\xi}|={{0.0}_{\ensuremath{-}0.0}}^{+2.3}$, and a discrimination of 150:1 against a second value of $\mathrm{Re}\ensuremath{\xi}=\ensuremath{-}5.3\ifmmode\pm\else\textpm\fi{}0.7$. There were 90 ${K}_{e3}$ events consistent with a constant form factor ${f}^{+}$, giving ${\ensuremath{\lambda}}_{+}={{\ensuremath{-}0.02}_{\ensuremath{-}0.12}}^{+0.08}$.