Weak dipole moment of $τ$ in $e^+e^-$ collisions with longitudinally polarized electrons

It is pointed out that certain CP-odd momentum correlations in the production and subsequent decay of tau pairs in $e^+e^-$ collisions get enhanced when the $e^-$ is longitudinally polarized. Analytic expressions for these correlations are obtained for the single-pion decay mode of $τ$ when $τ^+τ^-$ have a ``weak" dipole form factor (WDFF) coupling to $Z$ . For $e^+e^-$ collisions at the $Z$ peak, a sensitivity of about 1-5$\times 10^{-17}$\mbox{$e$ cm} for the $τ$ WDFF can be reached using a {\em single} $τ^+τ^-$ decay channel, with $10^6\, Z$'s likely to be available at the SLC at Stanford with $e^-$ polarization of 62\%-75\%.

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