Effect of longitudinal electron polarization in the measurement of the $\tau$ weak dipole moment in $e^{+}{e}^{-}$ collisions

Abstract

We show that certain CP-odd momentum correlations in the production and subsequent decay of tau pairs in $e^{+}{e}^{-}$ collisions get enhanced when the electron beam is longitudinally polarized. Analytic expressions for these correlations are obtained when ${\tau }^{+}{\tau }^{-}$ have a ``weak" dipole form factor (WDFF) coupling to $Z$ in the case of two-body decay modes of the $\tau$. Expressions of the variance of these correlations due to the standard model interactions are also presented. For $e^{+}{e}^{-}$ collisions at the $Z$ peak, a sensitivity of about $10^{-17}e$ cm for the real part of the $\tau$ WDFF and $3\times 10^{-17}e$ cm for the imaginary part of the $\tau$ WDFF can be reached using $\pi$ and $\rho$ channels (which are the most sensitive channels) in $\tau$ decay, with $10^{6}Z$'s likely to be available at the SLC at Stanford with $e^{-}$ polarization of 62\%-75\%.

Comments: 15 pages, latex, 3 tables and no figures, PRL-TH-94/7, UNIL-TP-2/94