Multi-scale improved predictions for

We compare standard fixed-order NLO QCD predictions for the full off-shell $pp\to e^{+}{\nu }_e{\mu }^{-}{\bar{\nu }}_{\mu }{\tau }^{+}{\nu }_{\tau }b\bar{b}(j)+X$ processes in the multi-lepton decay channel with the results obtained using the MiNLO approach. The MiNLO method, now also implemented in the Helac-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 $pp\to e^{+}{\nu }_e{\mu }^{-}{\bar{\nu }}_{\mu }{\tau }^{+}{\nu }_{\tau }b\bar{b}+X$, $pp\to e^{+}{\nu }_e{\mu }^{-}{\bar{\nu }}_{\mu }{\tau }^{+}{\nu }_{\tau }b\bar{b}j+X$ and $pp\to e^{+}{\nu }_e{\mu }^{-}{\bar{\nu }}_{\mu }{\tau }^{+}{\nu }_{\tau }b\bar{b}jj$, with the aim of improving the description of the underlying $pp\to e^{+}{\nu }_e{\mu }^{-}{\bar{\nu }}_{\mu }{\tau }^{+}{\nu }_{\tau }b\bar{b}+X$ process.