Polarization and Handedness in Tau -> 3 Pi + Neutrino Decay Produced in e+e- Annihilations

We discuss the concept of handedness applied to $\tau$ production in $e^+e^-$ annihilations with $\tau$ decaying into $a_1\nu_\tau \to 3\pi\nu_\tau$. The $a_1\to 3\pi$ decay is particularly interesting since it (together with $h_1\to 3\pi$) is the lightest hadronic decay in which the helicity of the initial state can be determined from the distribution of the final particle momenta. Thus it is the first example of a helicity self-analysing strong decay, as $\Lambda\to N\pi$ is for weak decays. Apart from providing a new method for determining the $\tau$ polarization from the parity conserving part in the weak decay, this reaction provides a very instructive and useful demonstration of the handedness asymmetry as a measure of parton polarization. Thus we believe that experience gained from analyses of handedness in $\tau\to 3\pi\nu_\tau$ decay will be very useful when looking for the similar asymmetry of jet handedness which can measure quark or gluon polarization.