State-of-the-art cross sections for $t\bar{t}H$: NNLO+NNLL+EW predictions

The most precise theoretical predictions for the total cross section for the associated production of a Higgs boson with a top-antitop quark pair at the LHC, first presented in \cite{Balsach:2025tth}, are reported. The calculation combines NNLO QCD corrections that include an approximation of the two-loop virtual contribution, with soft-gluon resummation at NNLL accuracy in two independent frameworks (SCET and direct QCD), and complete NLO electroweak corrections.