Effect of longitudinal electron polarization in the measurement of the τ weak dipole moment in e+e- collisions

We show that certain CP-odd momentum correlations in the production and subsequent decay of τ pairs in e+e- collisions get enhanced when the electron beam is longitudinally polarized. Analytic expressions for these correlations are obtained when τ+τ- have a ''weak'' dipole form factor (WDFF) coupling to Z in the case of two-body decay modes of the τ. 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 10-17e cm for the real part of the τ WDFF and 3x10-17e cm for the imaginary part of the τ WDFF can be reached using π and ρ channels (which are the most sensitive channels) in τ decay, with 106 Z's likely to be available at the SLC at Stanford with e- polarization of 62%--75%