Search for leptonic charge asymmetry in $t\bar{t}W$ production in final states with three leptons at $\sqrt{s}=13$ TeV

A search for the leptonic charge asymmetry ($A_{\text{c}}^{\mathrm{\ell }}$) of top-quark$-$antiquark pair production in association with a $W$ boson ($t\bar{t}W$) is presented. The search is performed using final states with exactly three charged light leptons (electrons or muons) and is based on $\sqrt{s}=13$ TeV proton$-$proton collision data collected with the ATLAS detector at the Large Hadron Collider at CERN during the years 2015$-$2018, corresponding to an integrated luminosity of 139 fb${}^{-1}$. A profile-likelihood fit to the event yields in multiple regions corresponding to positive and negative differences between the pseudorapidities of the charged leptons from top-quark and top-antiquark decays is used to extract the charge asymmetry. At reconstruction level, the asymmetry is found to be $-0.123\pm 0.136$ (stat.) $\pm 0.051$ (syst.). An unfolding procedure is applied to convert the result at reconstruction level into a charge-asymmetry value in a fiducial volume at particle level with the result of $-0.112\pm 0.170$ (stat.) $\pm 0.054$ (syst.). The Standard Model expectations for these two observables are calculated using Monte Carlo simulations with next-to-leading-order plus parton shower precision in quantum chromodynamics and including next-to-leading-order electroweak corrections. They are $-0.084{}_{-0.003}^{+0.005}$ (scale) $\pm 0.006$ (MC stat.) and $-0.063{}_{-0.004}^{+0.007}$ (scale) $\pm 0.004$ (MC stat.) respectively, and in agreement with the measurements.