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We report on our recent comparison of various theoretical approaches topredict fiducial signatures for $pp\to t\bar{t}W$ in the $3\ell$ decay channelat $\mathcal{O}(\alpha_s^3\alpha^6)$ and $\mathcal{O}(\alpha_s\alpha^8)$. Thecomparison includes fixed-order predictions including full off-shell effects aswell as predictions based only on the double-resonant contributions byemploying the Narrow-Width-Approximation. Furthermore, we include parton-showermatched predictions using the MG5 and POWHEG-BOX frameworks.

Comparison of $t\bar{t}W$ theory predictions in the $3\ell$ channel