NLO QCD predictions for off-shell $t\bar{t}W$ production in association with a light jet at the LHC

In view of the persisting tension between theoretical predictions and the LHC data for the $pp \to t\bar{t}W^\pm$ production process, we present the state-of-the-art full off-shell NLO QCD result for $pp \to t\bar{t}W^+\, j+X$. We concentrate on the multi-lepton decay channel at the LHC with $\sqrt{s}= 13$ TeV. In our calculation off-shell top quarks and gauge bosons are described by Breit-Wigner propagators, furthermore, double-, single- as well as non-resonant top-quark contributions along with all interference effects are consistently incorporated at the matrix element level. We present results for both integrated and differential fiducial cross sections for various renormalisation and factorisation scale settings and different PDF sets. With a fairly inclusive choice of cuts and regardless of the scale and PDF choice, non-flat differential ${\cal K}$-factors are obtained for many observables that we have examined. Since from an experimental point of view, both processes $pp \to t\bar{t}W^\pm j+X$ and $pp\to t\bar{t}W^\pm +X$ consist of similar final states we investigate the effect of additional jet activity on the integrated and differential fiducial cross sections. For this purpose, the normalised differential distributions for $pp \to e^+\nu_e\, \mu^-\bar{\nu}_\mu\, \tau^+\nu_\tau\, b\bar{b} \,j+X$ and $pp \to e^+\nu_e\, \mu^-\bar{\nu}_\mu\, \tau^+\nu_\tau\, b\bar{b} +X$ are compared. The theoretical results for the latter process are also recalculated.