Search forCPviolation inτ→ππ0ντdecay

We search for $\mathrm{CP}$ nonconservation in the decays of $\tau$ leptons produced via $e^{+}{e}^{-}$ annihilation at $\sqrt{s}\sim 10.6$ GeV. The method uses correlated decays of pairs of $\tau$ leptons, each decaying to the $\pi {\pi }^0{\nu }_{\tau }$ final state. The search is done within the framework of a model with a scalar boson exchange. In an analysis of a data sample corresponding to $12.2\times {10}^6$ produced $\tau$ pairs collected with the CLEO detector, we find no evidence of violation of $\mathrm{CP}$ symmetry. We obtain a limit on the imaginary part of the coupling constant parametrizing the relative contribution of diagrams that would lead to $\mathrm{CP}$ violation to be $-0.046<\mathrm{}\mathrm{Im}\left(\Lambda \right)<\mathrm{}0.022\mathrm{}$ at $90\%$ C.L. This result provides a restriction on $\mathrm{CP}$ nonconservation in tau lepton decays. As a cross-check, we study the decay angular distribution and perform a model-independent search for a $\mathrm{CP}$ violation effect of a scalar exchange in single $\overrightarrow{\tau }\pi {\pi }^0{\nu }_{\tau }$ decays. The limit on the imaginary part of the $\tau$ scalar coupling is $-0.033<\mathrm{}\mathrm{Im}\left(\Lambda \right)<\mathrm{}0.089\mathrm{}$ at 90% C.L.