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The Next-to-Minimal Supersymmetric Extension of the Standard Model (NMSSM)with a Higgs sector containing five neutral and two charged Higgs bosons allowsfor a rich phenomenology. In addition, the plethora of parameters provides manysources of CP violation. In contrast to the Minimal Supersymmetric Extension,CP violation in the Higgs sector is already possible at tree-level. For areliable understanding and interpretation of the experimental results of theHiggs boson search, and for a proper distinction of Higgs sectors provided bythe Standard Model or possible extensions, the Higgs boson masses have to beknown as precisely as possible including higher-order corrections. In thispaper we calculate the one-loop corrections to the neutral Higgs boson massesin the complex NMSSM in a Feynman diagrammatic approach adopting a mixedrenormalization scheme based on on-shell and $\bar{DR}$ conditions. We studyvarious scenarios where we allow for tree-level CP-violating phases in theHiggs sector and where we also study radiatively induced CP violation due to anon-vanishing phase of the trilinear coupling $A_t$ in the stop sector. Theeffects on the Higgs boson phenomenology are found to be significant. Wefurthermore estimate the theoretical error due to unknown higher-ordercorrections by both varying the renormalization scheme of the top and bottomquark masses and by adopting different renormalization scales. The residualtheoretical error can be estimated to about 10%.

Higgs Boson Masses in the Complex NMSSM at One-Loop Level