Constraints on Light WIMP candidates from the Isotropic Diffuse
  Gamma-Ray Emission
  Motivated by the measurements reported by direct detection experiments, most
notably DAMA, CDMS-II, CoGeNT and Xenon10/100, we study further the constraints
that might be set on some light dark matter candidates, M_DM ~ few GeV, using
the Fermi-LAT data on the isotropic gamma-ray diffuse emission. In particular,
we consider a Dirac fermion singlet interacting through a new Z' gauge boson,
and a scalar singlet S interacting through the Higgs portal. Both candidates
are WIMP (Weakly Interacting Massive Particles), i.e. they have an annihilation
cross-section in the pbarn range. Also they may both have a spin-independent
elastic cross section on nucleons in the range required by direct detection
experiments. Although being generic WIMP candidates, because they have
different interactions with Standard Model particles, their phenomenology
regarding the isotropic diffuse gamma-ray emission is quite distinct. In the
case of the scalar singlet, the one-to-one correspondence between its
annihilation cross-section and its spin-independent elastic scattering
cross-section permits to express the constraints from the Fermi-LAT data in the
direct detection exclusion plot, sigma_n^0--M_DM. Depending on the
astrophysics, we argue that it is possible to exclude the singlet scalar dark
matter candidate at 95 % CL. The constraints on the Dirac singlet interacting
through a Z' are comparatively weaker.
