Conservative Constraints on Dark Matter from the Fermi-LAT Isotropic
  Diffuse Gamma-Ray Background Spectrum
  We examine the constraints on final state radiation from Weakly Interacting
Massive Particle (WIMP) dark matter candidates annihilating into various
standard model final states, as imposed by the measurement of the isotropic
diffuse gamma-ray background by the Large Area Telescope aboard the Fermi
Gamma-Ray Space Telescope. The expected isotropic diffuse signal from dark
matter annihilation has contributions from the local Milky Way (MW) as well as
from extragalactic dark matter. The signal from the MW is very insensitive to
the adopted dark matter profile of the halos, and dominates the signal from
extragalactic halos, which is sensitive to the low mass cut-off of the halo
mass function. We adopt a conservative model for both the low halo mass
survival cut-off and the substructure boost factor of the Galactic and
extragalactic components, and only consider the primary final state radiation.
This provides robust constraints which reach the thermal production
cross-section for low mass WIMPs annihilating into hadronic modes. We also
reanalyze limits from HESS observations of the Galactic Ridge region using a
conservative model for the dark matter halo profile. When combined with the
HESS constraint, the isotropic diffuse spectrum rules out all interpretations
of the PAMELA positron excess based on dark matter annihilation into two lepton
final states. Annihilation into four leptons through new intermediate states,
although constrained by the data, is not excluded.
