Search for Leptonic Charge Asymmetry in the Trilepton Final State of $t\bar{t}W^\pm$

A search for the leptonic charge asymmetry 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 reconstructed 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 reconstructed level into a charge-asymmetry value in a fiducial volume at particle level with the result of $-0.112 \pm 0.170$~(stat.)~$\pm \, 0.055$~(syst.). The Standard Model expectations for these two observables are calculated using Monte Carlo simulation with next-to-leading order plus parton shower precision in quantum chromodynamics and including next-to-leading order electroweak corrections. They are $-0.084 \, ^{+0.005}_{-0.003}$~(scale) $\pm\, 0.006$~(MC stat.) and $-0.063 \, ^{+0.007}_{-0.004}$~(scale) $\pm\, 0.004$~(MC stat.), respectively.