Three-Body Decays ofK0Mesons

Abstract

We have measured the time distributions of the ${\pi }^{+}{e}^{-}\overline{\nu }$, ${\pi }^{-}{e}^{+}\nu$, and ${\pi }^{+}{\pi }^{-}{\pi }^0$ modes from initially pure $K^0\text{'}\mathrm{s}$ in a spark-chamber experiment performed at the Bevatron. From 1079 $K_{e3\mathrm{}}$ events between 0.2 and 7 $K_S$ lifetimes, we find $\mathrm{Re}X=-0.070\mathrm{}\pm 0.036$, $\mathrm{Im}X={0.107}_{-0.074\mathrm{}}^{+0.092\mathrm{}}$. This result is consistent with $X=0\mathrm{}$ (relative probability = 0.25). From 148 $K\to {\pi }^{+}{\pi }^{-}{\pi }^0$ events in the same fiducial volume, we get $\mathrm{Re}W=-0.05\mathrm{}\pm 0.17$ and $\mathrm{Im}W={0.39}_{-0.37\mathrm{}}^{+0.35\mathrm{}}$. ("$W$" is variously known as ${\eta }^{+-0\mathrm{}}$ and $x+iy$.) Our results are consistent with $W=0\mathrm{}$ (relative probability = 0.30).