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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, MDM ~ 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, sigmaₙ⁰--MDM. 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.
Arina et al. (Thu,) studied this question.