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Recent measurements of the $pp\to t\bar{t}W^\pm$ process in multi-leptonfinal states, as performed by the ATLAS collaboration in the context of theHiggs boson studies in the $t\bar{t}H$ channel, have shown discrepanciesbetween theoretical predictions and experimental data. Such discrepancies havebeen observed both in the overall normalisation as well as in the modelling ofthe $t\bar{t}W^\pm$ process. With the goal of understanding and resolving themodelling issues within the SM $t\bar{t}W^\pm$ process we report on thestate-of-the-art NLO QCD computation for this process. Specifically, wecalculate higher-order corrections to the $e^+ \nu_e \,\mu^-\bar{\nu}_\mu \,e^+ \nu_e \, b\bar{b}$ and $e^- \bar{\nu}_e \, \mu^+ {\nu}_\mu \, e^-\bar{\nu}_e \, b\bar{b}$ final state at the LHC with $\sqrt{s}=13$ TeV. In thecomputation off-shell top quarks are described by Breit-Wigner propagators,furthermore, double-, single- as well as non-resonant top-quark contributionsalong with all interference effects are consistently incorporated at the matrixelement level. Results at NLO QCD accuracy are presented in the form offiducial integrated and differential cross sections for two selectedrenormalisation and factorisation scale choices and three different PDF sets.The impact of the top quark off-shell effects on the $t\bar{t}W^\pm$ crosssection is also examined by an explicit comparison to the narrow-widthapproximation.

The simplest of them all: $t\bar{t} W^\pm$ at NLO accuracy in QCD