Modeling uncertainties of $t\bar{t}W^\pm$ multilepton signatures

In light of recent discrepancies between the modeling of $t\bar{t} W^\pm$ signatures and measurements reported by the Large Hadron Collider (LHC) experimental collaborations, we investigate in detail theoretical uncertainties for multi-lepton signatures. We compare results from the state-of-the-art full off-shell calculation and its Narrow Width Approximation to results obtained from the on-shell $t\bar{t} W^\pm$ calculation, with approximate spin-correlations in top-quark and $W$ decays, matched to parton showers. In the former case double-, single-, and non-resonant contributions together with interference effects are taken into account, while the latter two cases are only based on the double resonant top-quark contributions. The comparison is performed for the LHC at $\sqrt{s} = 13$ TeV for which we study separately the multi-lepton signatures as predicted from the dominant NLO contributions at the perturbative orders $\mathcal{O}(\alpha_s^3\alpha^6)$ and $\mathcal{O}(\alpha_s\alpha^8)$. Furthermore, we combine both contributions and propose a simple way to approximately incorporate the full off-shell effects in the NLO computation of on-shell $pp\to t\bar{t} W^\pm$ matched to parton showers.