High scale validity of two-Higgs-doublet scenarios with a real scalar singlet dark matter

We study the high-scale validity of two kinds of two Higgs doublet models (2HDM), namely, type-II and type-X, but with a scalar SU(2) singlet dark matter (DM) candidate in addition in each case. The additional quartic couplings involving the DM particle in the scalar potential in both the scenarios bring in additional constraints from the requirement of perturbative unitarity and vacuum stability. DM relic density and direct search constraints play a crucial role in this analysis as the perturbative unitarity of the DM-Higgs portal couplings primarily decide the high scale validity of the model. We find that, within the parameter regions thus restricted, the type-II scenario must have a cutoff at around <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msup><a:mrow><a:mn>10</a:mn></a:mrow><a:mrow><a:mn>6</a:mn></a:mrow></a:msup><a:mtext> </a:mtext><a:mtext> </a:mtext><a:mi>GeV</a:mi></a:mrow></a:math>, while the type-X scenario admits of validity up to the Planck scale. However, only those regions which are valid up to about <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msup><c:mn>10</c:mn><c:mn>8</c:mn></c:msup><c:mtext> </c:mtext><c:mtext> </c:mtext><c:mi>GeV</c:mi></c:math> in type-X 2HDM is amenable to detection at the High-luminosity LHC (up to <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:mn>3000</e:mn><e:mtext> </e:mtext><e:mtext> </e:mtext><e:msup><e:mi>fb</e:mi><e:mrow><e:mo>−</e:mo><e:mn>1</e:mn></e:mrow></e:msup></e:mrow></e:math>), while most of the parameter space of the type-II scenario mentioned above is likely to be detectable.