  Light fermionic/scalar dark matter (DM) (m_DM ~ 8 GeV) neutral under the
standard model can be responsible for the CDMS and CoGeNT signals, and the
Fermi-LAT gamma-ray excesses. In order to explain them in a relatively simple
framework, we have explored various DM annihilation and scattering processes,
discussing important phenomenological constraints coming from particle physics.
Assuming that the two independent observations have a common DM origin and the
processes arise through a common mediator, DM should annihilate into
tau/anti-tau lepton pairs through an s-channel, and scatter with nuclei through
a t-channel process. To avoid the p-wave suppression, a new Higgs-like scalar
field with a mass of O(1) TeV is necessary as a common mediator of both the
processes. We propose a supersymmetric model realizing the scenario.
