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Subleading EW corrections and spin-correlation effects in $t\bar{t}W$ multi-lepton signatures

Recently a slight tension between data and predictions has been reported in $t\bar{t}W$ production by both the CMS and ATLAS collaborations. We revisit the theoretical predictions for this process, focussing on the following two effects. We disentangle various effects that lead to asymmetries among the leptonic decay products of the (anti-)top quarks and $W$ bosons, for which we find that the spin correlations in the top-quark pair are the dominant source. We also discuss the impact of the large, formally subleading, electroweak corrections to $t\bar{t}W$ production at the LHC. We find that this effect changes the $t\bar{t}W$ cross section significantly in the signature phase-space regions, and should therefore be included differentially in the theory to data comparisons.