Tau polarization effects in $\nu_\tau / \bar{\nu}_\tau$-tungsten interactions at the LHC energies

Recent studies have demonstrated that the tau produced in charged current neutrino deeply inelastic interactions at the GeV -- TeV neutrino energy range is not fully polarized. In this paper we investigate the impact of the tau polarization on the pions generated in its decay. In particular, we consider tau neutrino - tungsten interactions at the LHC energies and estimate the associated pion momentum, energy and angular distributions. The contribution of the $F_5$ is also investigated. Our results indicate that the pion properties are sensitive to the tau polarization state as well as to the magnitude of $F_5$.
Comment: 10 pages, 7 figures, accepted for publication in Physical Review D