Tau Neutrinos and Cross-Sections at DUNE

The high statistics and excellent resolution capabilities of DUNE's  $^{40}$Ar detector will allow us to make precision studies of oscillation parameters capable of explaining CP violation in the lepton sector, test interaction models, and of studying phenomena that have, until now, seemed too complex to measure, like $\nu_\tau$ detection and therefore, providing the completion of the 3-flavor neutrino paradigm. Good knowledge of the $\nu_\tau$ detection can impact a broad spectrum of open questions; how muon neutrinos oscillate into tau neutrinos with nearly maximal mixing \?, non-standard neutrino interactions, non-unitary constraints, energy dependence in neutrino mixing parameters, the extraction of the oscillation parameter, matter-antimatter asymmetry, look for an extra flavor (sterile neutrino) and the list continues. 

The $\nu_{\tau}$(N) and $\bar{\nu}_{\tau}$(N) cross-sections have large uncertainties as compared to the ones for $\nu_{\mu}$ and $\nu_{e}$, and some studies point out that the reason for these difference is due to the uncertainties in the nucleon structure functions. These nucleon structure functions are used to calculate the DIS cross-section by including kinematical corrections due to the $\tau$-lepton mass, and due to this mass inclusion, another two additional nucleon structure functions become non-negligible, $F_{4N}(x, Q^{2})$ and $F_{5N}(x, Q^{2})$. This presentation will show the semi-theoretical and experimental approach to the estimation of the $\nu_{\tau}$(N) and $\bar{\nu}_{\tau}$(N) cross-sections in DUNE for the DIS region. We aim to look over changes in Q$^{2}$, and the contributions of the additional nucleon structure functions $F_{4N}(x, Q^{2})$ and $F_{5N}(x, Q^{2})$.