Measurement of the total and differential cross-sections of $t\bar{t}W$ production in $pp$ collisions at $\sqrt{s}=13$ TeV with the ATLAS detector

Measurements of inclusive and differential production cross-sections of a top-quark-top-antiquark pair in association with a $W$ boson ($t\bar{t}W$) are presented. They are performed by targeting final states with two same-sign or three isolated leptons (electrons or muons) and are based on $\sqrt{s}=13$ TeV proton-proton collision data with an integrated luminosity of 140 fb${}^{-1}$, recorded from 2015 to 2018 with the ATLAS detector at the Large Hadron Collider. The inclusive $t\bar{t}W$ production cross-section is measured to be $880\pm 80$ fb, compared to a reference theoretical prediction of $745\pm 50\text{(scale)}\pm 13\text{(2-loop approx.)}\pm 19\text{(PDF,}{\alpha }_{\text{S}})$ fb. Differential cross-section measurements characterise this process in detail for the first time. Several particle-level observables are compared with a variety of theoretical predictions, which generally agree well with the normalised differential cross-section results. Additionally, the relative charge asymmetry of $t\bar{t}{W}^{+}$ and $t\bar{t}{W}^{-}$ is measured inclusively to be $A_{\mathrm{C}}^{\mathrm{r}\mathrm{e}\mathrm{l}}=0.33\pm 0.05$, in very good agreement with the theoretical prediction of $0.322\pm 0.003(\mathrm{s}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{e})\pm 0.007(\mathrm{P}\mathrm{D}\mathrm{F})$, as well as differentially.