P-odd observables at the $\Upsilon$ peak

We study the $\gamma$-Z interference in the process $e^+ e^-\to \Upsilon \to \tau^+ \tau^-$ as a means to measure the neutral current coupling of the b-quark. The helicity amplitudes are calculated from resonant and background diagrams and the spin density matrix of the final state is discussed. The spin analyzer of the $\tau$'s is illustrated with the decays $\pi \nu$ and $\rho \nu \to (\pi \pi) \nu$. With $10^8 \Upsilon$ a sensitivity to $g_V^b$ of a few per cent could be reachable.