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The complex singlet extension CxSM of the Standard Model (SM) is a simpleextension of the SM with two visible Higgs bosons in the spectrum and a DarkMatter (DM) candidate. In this paper we complete the computation of thenext-to-leading (NLO) electroweak (EW) corrections to on-shell andnon-loop-induced Higgs decays. Our calculations are implemented in the codeEWsHDECAY which also includes the relevant QCD corrections. Performing anextensive parameter scan in the model and including all relevant theoreticaland experimental single- and di-Higgs as well as DM constraints, we obtain aviable parameter sample. We find that current DM constraints are able to testthe model in DM mass regions where collider searches are not sensitive. Therelative EW corrections turn out to be large for scenarios with relativelylarge couplings, threshold effects or small leading-order (LO) widths.Otherwise, they are of typical EW size and can amount up to about 20-25%. Thetheory uncertainty derived from the change of the renormalization schemedependence then is of a few per cent. While the NLO corrections applied in theconstraints due to single- and di-Higgs searches impact the validity ofspecific parameter points, the overall shape of the allowed parameter region isnot yet sensitive to the EW corrections. This picture will change with furtherincreased experimental precision in the future and necessitates precisepredictions on the theory side as presented in this paper.

Electroweak Corrections to Higgs Boson Decays in a Complex Singlet Extension of the SM and their Phenomenological Impact