This paper reports inclusive and differential measurements of the charge asymmetry in 20.3 fb of TeV collisions recorded by the ATLAS experiment at the Large Hadron Collider at CERN. Three differential measurements are performed as a function of the invariant mass, transverse momentum and longitudinal boost of the system. The pairs are selected in the single-lepton channels ( or ) with at least four jets, and a likelihood fit is used to reconstruct the event kinematics. A Bayesian unfolding procedure is performed to infer the asymmetry at parton level from the observed data distribution. The inclusive charge asymmetry is measured to be $A_{} = 0.009 \pm 0.005+$syst.). The inclusive and differential measurements are compatible with the values predicted by the Standard Model.

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