Multi-scale improved predictions for $$pp\to t\overline{t}{W }^{+}+X$$

A bstract We compare standard fixed-order NLO QCD predictions for the full off-shell $$pp\to {e}^{+}{\nu}_{e}{\mu }^{-}{\overline{\nu }}_{\mu }{\tau }^{+}{\nu}_{\tau }b\overline{b }\left(j\right)+X$$ processes in the multi-lepton decay channel with the results obtained using the M i NLO approach. The M i NLO method, now also implemented in the H elac -NLO framework, provides a dynamic determination of the renormalization and factorization scale settings by identifying the most likely branching histories of the additional jets through an inverse k T -clustering algorithm. The inclusion of Sudakov form factors accounts for the large logarithms that arise in the presence of widely separated scales. We perform a dedicated comparison of the two approaches at both the integrated and differential (fiducial) cross-section levels for the LHC Run II energy of $$\sqrt{s}=13$$ TeV. Finally, we present the merging of the full off-shell predictions for $$pp\to {e}^{+}{\nu}_{e}{\mu }^{-}{\overline{\nu }}_{\mu }{\tau }^{+}{\nu}_{\tau }b\overline{b }+X$$ , $$pp\to {e}^{+}{\nu}_{e}{\mu }^{-}{\overline{\nu }}_{\mu }{\tau }^{+}{\nu}_{\tau }b\overline{b }j+X$$ and $$pp\to {e}^{+}{\nu}_{e}{\mu }^{-}{\overline{\nu }}_{\mu }{\tau }^{+}{\nu}_{\tau }b\overline{b }jj$$ , with the aim of improving the description of the underlying $$pp\to {e}^{+}{\nu}_{e}{\mu }^{-}{\overline{\nu }}_{\mu }{\tau }^{+}{\nu}_{\tau }b\overline{b }+X$$ process.