Singlet scalar and 2HDM extensions of the Standard Model: CP-violation and constraints from $(g-2)_\mu$ and $e$EDM

We study popular scalar extensions of the Standard Model, namely the singlet extension, the 2-Higgs doublet model (2HDM) and its extension by a singlet scalar. We focus on the contributions of the added scalars to the anomalous magnetic moment of the muon, $(g-2)_\mu$ in the presence of CP-violation, and the electric dipole moment of the electron ($e$EDM) in these models. In the absence of CP-violation, CP-even and CP-odd scalars contribute with an opposite sign to the anomalous magnetic moment of the muon and as a result these models generally require very light scalars to explain the observed discrepancy in $(g-2)_\mu$. We study the effect of CP-violation on the anomalous magnetic moment of the muon and its compatibility with the $e$EDM constraints. We show that given the current status of the global set of constraints applied on all values of $\cot\beta$, in the CP-violating scalar extensions, there exist no viable parameter space in agreement with both $a_\mu$ and $e$EDM bounds.