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We provide the two-loop corrections to the Higgs boson masses of theCP-violating NMSSM in the Feynman diagrammatic approach with vanishing externalmomentum at ${\cal O} (\alpha_t \alpha_s)$. The adopted renormalization schemeis a mixture between $\overline{\text{DR}}$ and on-shell conditions.Additionally, the renormalization of the top/stop sector is provided both forthe $\overline{\text{DR}}$ and the on-shell scheme. The calculation isperformed in the gaugeless limit. We find that the two-loop correctionscompared to the one-loop corrections are of the order of 5-10\%, depending onthe top/stop renormalization scheme. The theoretical error on the Higgs bosonmasses is reduced due to the inclusion of these higher order corrections.

Two-Loop Contributions of the Order $\mathcal{O}(\alpha_t\alpha_s)$ to the Masses of the Higgs Bosons in the CP-Violating NMSSM