  A recent study of gamma-ray data from the Galactic Center motivates the
investigation of light (~7-10 GeV) particle dark matter models featuring tau
lepton pairs as dominant annihilation final state. The Lepton-Specific
two-Higgs-doublet Model (2HDM-L) provides a natural framework where light,
singlet scalar dark matter can pair-annihilate dominantly into tau leptons. We
calculate the nucleon-dark matter cross section for singlet scalar dark matter
within the 2HDM-L framework, and compare with recent results from direct
detection experiments. We study how direct dark matter searches can be used to
constrain the dark matter interpretation of gamma ray observations, for
different dominant annihilation final states. We show that models exist with
the correct thermal relic abundance that could fit the claimed gamma-ray excess
from the Galactic Center region and have direct detection cross sections of the
order of what needed to interpret recent anomalous events reported by direct
detection experiments.
