The standard model (SM) plus a real gauge-singlet scalar field dubbed darkon (SM+D) is the simplest model possessing a weakly interacting massive particle (WIMP) dark-matter candidate. The upper limits for the WIMP-nucleon elastic cross-section as a function of WIMP mass from the recent XENON10 and CDMS-II experiments rule out darkon mass ranges from 10 to (50,70,75) GeV for Higgs-boson masses of (120,200,350) GeV, respectively. This may exclude the possibility of the darkon providing an explanation for the gamma-ray excess observed in the EGRET data. We show that by extending the SM+D to a two-Higgs-doublet model plus a darkon the experimental constraints on the WIMP-nucleon interactions can be circumvented due to suppression occurring at some values of the product tan(alpha)tan(beta), with alpha being the neutral-Higgs mixing angle and tan(beta) the ratio of vacuum expectation values of the Higgs doublets. We also comment on the implication of the darkon model for Higgs searches at the LHC.
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