Tau Polarization in Tau-Neutrino Nucleon Scattering

We investigate the spin polarization of \tau^{\pm} leptons produced in \nu_{\tau} and \bar{\nu}_{\tau} nucleon scattering via charged currents. Quasi-elastic scattering, \Delta resonance production and deep inelastic scattering processes are studied. The polarization information is essential for measuring the \tau^{\pm} appearance rate in long baseline neutrino oscillation experiments, because the decay particle distributions depend crucially on the \tau^{\pm} spin. In this article, we calculate the spin density matrix of each process and estimate the spin polarization vector in medium and high neutrino energy interactions. We find that the produced \tau^{\pm}'s have high degree of polarization, and their spin direction depends non-trivially on the energy and the scattering angle of \tau^{\pm} in the laboratory frame.