Analysis of 17 898τ+Decays at Rest

The energy spectrum of the decay pions in ${\tau }^{+}$ decay was obtained from a sample of 17 898 events. It is found that the spectrum is adequately fitted by a squared matrix element of linear form, ${\mathrm{}\left|M\right|\mathrm{}}^2\propto 1+{\alpha }_{\tau }\times \left(\frac{M_{K}Q}{{m_{\pi }}^2}\right)Y$, with ${\alpha }_{\tau }=0.131\mathrm{}\pm 0.008$. No evidence for $\mathrm{CP}$ noninvariance is found for ${\tau }^{\pm }$ decays. A significant violation of the $\Delta I=\frac{1}{2}$ rule is observed for $K^{+}\to 3\pi$ decays. Comparison with several theoretical models for $K\to 3\pi$ decays shows fair agreement between experiment and theory.