LAUSR

A bstractWe calculate the complete-NLO predictions for tt¯W±$$ t\overline{t}{W}^{\pm } $$ and tt¯tt¯$$ t\overline{t}t\overline{t} $$ production in proton-proton collisions at 13 and 100 TeV. All the non-vanishing contributions of Oαsiαj$$ \mathcal{O}\left({\alpha}_s^i{\alpha}^j\right) $$ with i + j = 3, 4 for tt¯W±$$ t\overline{t}{W}^{\pm } $$ and i + j = 4, 5 for tt¯tt¯$$ t\overline{t}t\overline{t} $$ are evaluated without any approximation. For tt¯W±$$ t\overline{t}{W}^{\pm } $$ we find that, due to the presence of tW → tW scattering, at 13(100) TeV the Oαsα3$$ \mathcal{O}\left({\alpha}_s{\alpha}^3\right) $$ contribution is about 12(70)% of the LO, i.e., it is larger than the so-called NLO EW corrections (the Oαs2α2$$ \mathcal{O}\left({\alpha}_s^2{\alpha}^2\right) $$ terms) and has opposite sign. In the case of tt¯tt¯$$ t\overline{t}t\overline{t} $$ production, large contributions from electroweak tt → tt scattering are already present at LO in the Oαs3α$$ \mathcal{O}\left({\alpha}_s^3\alpha \right) $$ and Oαs2α2$$ \mathcal{O}\left({\alpha}_s^2{\alpha}^2\right) $$ terms. For the same reason we find that both NLO terms of Oαs4α$$ \mathcal{O}\left({\alpha}_s^4\alpha \right) $$, i.e., the NLO EW corrections, and Oαs3α2$$ \mathcal{O}\left({\alpha}_s^3{\alpha}^2\right) $$ are large (±15% of the LO) and their relative contributions strongly depend on the values of the renormalisation and factorisation scales. However, large accidental cancellations are present (away from the threshold region) between these two contributions. Moreover, the NLO corrections strongly depend on the kinematics and are particularly large at the threshold, where even the relative contribution from Oαs2α3$$ \mathcal{O}\left({\alpha}_s^2{\alpha}^3\right) $$ terms amounts to tens of percents.