The first differential cross section measurements of $t\bar{t}$ produced with a $W$ boson in pp collisions

Measurements of inclusive $\ttW^\pm$ production cross sections performed by the ATLAS and CMS collaborations have consistently shown excesses of 20\%-70\% over theoretical predictions. These observations have lead to a growth in interest from the theory community over the last several years, leading to the realization that subleading electroweak corrections involving internal $tW\rightarrow tW$ scattering can be important for differential \ttW production cross section calculations. This thesis presents the first differential cross section measurements of the \ttW process using 138 fb$^{-1}$ of $pp$ collision data at $\sqrt{s}=13$ TeV collected by the ATLAS experiment. Of particular interest is the $N_\text{jets}$ distribution, a key input for the measurement of \ttH production in multi-lepton final states. Inclusive and differential cross sections are extracted at the particle level in \ll and \lll fiducial regions, both separated by total charge of the leptons as well as inclusively in charge with relative charge asymmetries. Charge-asymmetric enhancement in the \ttW \ll fiducial regions and charge-symmetric enhancement in the \lll region are observed. Excesses in the \ttW production cross section are localized to events with low jet multiplicity, high leptonic \HT, and high di-lepton invariant mass. Distributions are generally in good agreement with predictions of several Monte Carlo models.