  Direct searches for dark matter (DM) by the LUX and PandaX-II Collaborations
employing xenon-based detectors have recently come up with the most stringent
limits to date on the spin-independent elastic scattering of DM off nucleons.
For Higgs-portal scalar DM models, the new results have precluded any
possibility of accommodating low-mass DM as suggested by the DAMA and CDMS II
Si experiments utilizing other target materials, even after invoking
isospin-violating DM interactions with nucleons. In the simplest model, SM+D,
which is the standard model plus a real singlet scalar named darkon acting as
the DM candidate, the LUX and PandaX-II limits rule out DM masses roughly from
4 to 450 GeV, except a small range around the resonance point at half of the
Higgs mass where the interaction cross-section is near the neutrino-background
floor. In the THDM II+D, which is the type-II two-Higgs-doublet model combined
with a darkon, the region excluded in the SM+D by the direct searches can be
recovered due to suppression of the DM effective interactions with nucleons at
some values of the ratios of Higgs couplings to the up and down quarks, making
the interactions significantly isospin-violating. However, in either model, if
the 125-GeV Higgs boson is the portal between the dark and SM sectors, DM
masses less than 50 GeV or so are already ruled out by the LHC constraint on
the Higgs invisible decay. In the THDM II+D, if the heavier $CP$-even Higgs
boson is the portal, theoretical restrictions from perturbativity, vacuum
stability, and unitarity requirements turn out to be important instead and
exclude much of the region below 100 GeV. For larger DM masses, the THDM II+D
has plentiful parameter space that corresponds to interaction cross-sections
under the neutrino-background floor and therefore is likely to be beyond the
reach of future direct searches without directional sensitivity.
