  Recent direct detection experiments of Dark Matter (DM), CoGeNT and DAMA
implicate a light DM of a few GeV. Such a light DM would generate a large
amount of anti-proton since suppression for anti-proton flux from DM
annihilation is ineffective. We discuss whether a light dark matter with mass
of 5-15 GeV, which is especially in favor of the recent experiments reported by
CoGeNT, is compatible with the anti-proton no excess in the cosmic-ray. In view
of the direct detection of DM and no anti-proton excess in the cosmic-ray both,
we show that a Dirac DM is favored than a scalar one since there is no s-wave
of the annihilation cross section for the Dirac DM. A large elastic cross
section for direct detection can be obtained through the additional light Higgs
exchange. We show an allowed region that simultaneously satisfies the DM relic
density, the elastic cross section favored by CoGeNT and also the constraint of
H_L Z Z coupling of the light Higgs boson by LEP.
