The polarimeter vector for $\tau \rightarrow 3 \pi\nu_{\tau}$ 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 $\tau^{-} \rightarrow \pi^{-}\pi^{+}\pi^{-}\nu_{\tau}$ and $\tau^{-} \rightarrow \pi^{-}\pi^{0}\pi^{0}\nu_{\tau}$. 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.