51 000τ−Decays

Abstract

An analysis has been made of 51 000 $K^{-}\to {\pi }^{-}{\pi }^{-}{\pi }^{+}$ decays in flight in the Berkeley 25-in. hydrogen bubble chamber. After corrections for detection efficiency and Coulomb interactions, the projections of the pion spectra have been fitted with expansions in the Dalitz variables $X$ and $Y$. In addition, maximum-likelihood fits to the entire Dalitz plot have been made. The decay distribution is well described by $1+aY$, where the slope $a=0.247\mathrm{}\pm 0.009$. Comparison of this slope with that derived from a world compilation of 28 000 ${\tau }^{+}$ decays shows no evidence for $\mathrm{CP}$ violation. An isospin analysis of the rates and slopes of $\tau$, ${\tau }^{\prime }$, and of $K_2^{}{}_{}{}^0\to 3\pi$ decays, requires, in addition to the dominant $\Delta I=\frac{1}{2}$ amplitude, $\Delta I=\frac{3}{2}$ amplitudes into both $I=1\mathrm{}$ and $I=2\mathrm{}$ three-pion final states. No detectable $\Delta I=\frac{5}{2}$ or $\Delta I=\frac{7}{2}$ amplitudes are required.