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

The complex singlet extension CxSM of the Standard Model (SM) is a simple extension of the SM with two visible Higgs bosons in the spectrum and a Dark Matter (DM) candidate. In this paper we complete the computation of the next-to-leading (NLO) electroweak (EW) corrections to on-shell and non-loop-induced Higgs decays. Our calculations are implemented in the code EWsHDECAY which also includes the relevant QCD corrections. Performing an extensive parameter scan in the model and including all relevant theoretical and experimental single- and di-Higgs as well as DM constraints, we obtain a viable parameter sample. We find that current DM constraints are able to test the model in DM mass regions where collider searches are not sensitive. The relative EW corrections turn out to be large for scenarios with relatively large couplings, threshold effects or small leading-order (LO) widths. Otherwise, they are of typical EW size and can amount up to about 20-25%. The theory uncertainty derived from the change of the renormalization scheme dependence then is of a few per cent. While the NLO corrections applied in the constraints due to single- and di-Higgs searches impact the validity of specific parameter points, the overall shape of the allowed parameter region is not yet sensitive to the EW corrections. This picture will change with further increased experimental precision in the future and necessitates precise predictions on the theory side as presented in this paper.