Search for Violation ofCPInvariance inτ±Decay

We report a comparison of the Dalitz-plot distributions of 1.6 million ${\tau }^{+}$ decays ($K^{+}\to {\pi }^{+}{\pi }^{+}{\pi }^{-}$) and an equal number of ${\tau }^{-}$ decays. No significant asymmetry has been found in any region of the plot. In terms of the difference in the slope parameters $a^{+}$ and $a^{-}$ for the odd-pion c.m.-energy spectra, the asymmetry is $\Delta =\frac{(a^{+}-a^{-})}{(a^{+}+a^{-})}=-0.0070\mathrm{}\pm 0.0053$. We also present a preliminary result for the slope parameter itself: $a=0.283\mathrm{}\pm 0.005$. New measurements of the ${\tau }^{\pm }$ decay rates and their difference confirm previous results.