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 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 scalar singlet named darkon acting as the DM candidate, the
LUX and PandaX-II limits rule out DM masses from 5 GeV to about 330 GeV, except
a small range around the resonant point at half of the Higgs mass where the
interaction cross-section is near the neutrino-background floor. In the
THDMII+D, which extends the SM+D by the addition of another Higgs doublet, 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, which make the
interactions significantly isospin-violating. However, in either model, if the
125-GeV Higgs boson is the portal between the DM 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 THDMII+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 THDMII+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.