Two-loop contributions of the order Oαtαs 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 $$ \mathcal{O}\left({\alpha}_t{\alpha}_s\right) $$ . The adopted renormalization scheme is a mixture between $$ \overline{\mathrm{DR}} $$ and on-shell conditions. Additionally, the renormalization of the top/stop sector is provided both for the $$ \overline{\mathrm{DR}} $$ 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.