Extending two-Higgs-doublet models by a singlet scalar field - the Case for Dark Matter

We extend the two-Higgs doublet models of Type I and Type II by adding a real gauge-singlet scalar S dark matter candidate (2HDMS models). We impose theoretical constraints deriving from perturbativity, stability, unitarity and correct electroweak symmetry breaking and require that the lightest CP-even Higgs, h, fit the LHC data for the $\sim 125.5$ GeV state at the $68\%$~C.L. after including existing constraints from LEP and B physics and LHC limits on the heavier Higgs bosons. We find that these models are easily consistent with the LUX and SuperCDMS limits on dark-matter-Nucleon scattering and the observed $\Omega h^2$ for S masses above about 55 GeV. At lower $m_S$, the situation is more delicate. For points with $m_S$ in the 6-25 GeV range corresponding to the CDMS~II and CRESST-II positive signal ranges, the dark-matter-Nucleon cross sections predicted by the Type I and Type II models more or less automatically fall within the $95\%-99\%$~C.L. signal region boundaries. Were it not for the LUX and SuperCDMS limits, which exclude all (almost all) such points in the case of Type I (Type II), this would be a success for the 2HDMS models. In fact, in the case of Type II there are a few points with 5.5 GeV $\leq m_S \leq$ 6.2 GeV that survive the LUX and SuperCDMS limits and fall within the CDMS~II 99\% C.L. signal region. Possibilities for dark matter to be isospin-violating in this 2HDMS context are also examined.