Study of the $Wtb$ Vertex Structure in Top Quark Decays with the ATLAS experiment and Future Prospects

In this thesis, the ATLAS sensitivity to the $Wtb$ vertex structure was studied in top quark decays. Measurements were performed on the polarization of $W^\pm$ bosons, derived from top quark pairs events ($t\bar{t}$) with single lepton and dilepton topologies. The results were obtained with data from $pp$ collisions at a center-of-mass energy of 7 TeV, collected by the ATLAS experiment at the Large Hadron Collider (LHC), corresponding to an integrated luminosity of 1.04 $\textrm{fb}^{-1}$. The measured fractions of the longitudinal, left-handed and right-handed helicities are $F_{\rm 0}= 0.67 \pm 0.07$, $F_{\rm L}= 0.32 \pm0.04$ and $F_{\rm R}= 0.01 \pm 0.05$, which can be translated into angular asymmetries yielding $A_{\rm +}= 0.53 \pm 0.02$ and $A_{\rm -}=-0.84 \pm 0.02$. These results are in good agreement with the Standard Model predictions, and correspond in the present date to the most precise published results. As the polarization of the $W^\pm$ bosons in top quark decays is sensitive to the Lorentz structure and couplings of the $Wtb$ vertex, the measurements were used to set limits on anomalous contributions to the $Wtb$ couplings. These results obtained at the LHC were compared with the expected results in a possible future linear collider, such as the International Linear Collider (ILC). The sensitivity to these anomalous couplings may largely surpass the one achievable by the LHC either in neutral or charged current processes.