The polarimeter vector for $\tau \to 3\pi {\nu }_{\tau }$ decays

The polarimeter vector of the $\tau$ represents an optimal observable for the measurement of the $\tau$ spin. In this paper we present an algorithm for the computation of the $\tau$ polarimeter vector for the decay channels ${\tau }^{-}\to {\pi }^{-}{\pi }^{+}{\pi }^{-}{\nu }_{\tau }$ and ${\tau }^{-}\to {\pi }^{-}{\pi }^0{\pi }^0{\nu }_{\tau }$. The algorithm is based on a model for the hadronic current in these decay channels, which was fitted to data recorded by the CLEO experiment.