Quasielastic production of polarized $\tau$ leptons in $\nu_{\tau}$ and $\bar{\nu}_{\tau}$ scattering from nucleons

The cross sections and polarization components of the $\tau$ leptons produced in the charged current induced quasielastic $\nu_\tau~(\bar\nu_\tau) - N$ scattering have been studied. The theoretical uncertainties arising due to the use of different vector form factors and the axial dipole mass in the axial vector form factor have been investigated. Due to the high mass of $\tau$ lepton, the contributions from the term containing pseudoscalar and second class current form factors are non-negligible and contribute to the uncertainty in the cross section and polarization observables as these form factors are not well known. In view of the currently proposed experiments by DUNE, SHiP and DsTau collaborations to study the production of $\tau$ lepton, an updated calculation of the cross sections and polarizations of tau leptons in the case of quasielastic production have been done and the numerical results have been presented along with a discussion of the theoretical uncertainties.