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

Abstract

We discuss the concept of handedness applied to $τ$ production in $e^+e^-$ annihilations with $τ$ decaying into $a_1ν_τ\to 3πν_τ$. The $a_1\to 3π$ decay is particularly interesting since it (together with $h_1\to 3π$) 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 $Λ\to Nπ$ is for weak decays. Apart from providing a new method for determining the $τ$ 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 $τ\to 3πν_τ$ decay will be very useful when looking for the similar asymmetry of jet handedness which can measure quark or gluon polarization.