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We compute the one-loop corrections to \tth up to order$\mathcal{O}(\epsilon^2)$ in the dimensional regularization parameter. We applythe projector method to compute polarized amplitudes, which generalize masslesshelicity amplitudes to the massive case. We employ a semi-numerical strategy toevaluate the scattering amplitudes. We express the form factors through scalarintegrals analytically, and obtain separately integration by parts reductionidentities in compact form. We integrate numerically the corresponding masterintegrals with an enhanced implementation of the Auxiliary Mass Flow algorithm.Using a numerical fit method, we concatenate the analytic and the numericresults, to obtain fast and reliable evaluation of the scattering amplitude.This approach improves numerical stability and evaluation time. Our results areimplemented in the \texttt{Mathematica} package \texttt{TTH}.

One loop QCD corrections to $gg \to t\overline{t}H$ at $\mathcal{O}(\epsilon^2)$