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

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