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We analyze the recently published Fermi-LAT diffuse gamma-ray measurements inthe context of leptonically annihilating or decaying dark matter (DM) with theaim to explain simultaneously the isotropic diffuse gamma-ray and the PAMELA,Fermi and HESS (PFH) anomalous $e^\pm$ data. Five different DMannihilation/decay channels $2e$, $2\mu$, $2\tau$, $4e$, or $4\mu$ (the lattertwo via an intermediate light particle $\phi$) are generated with PYTHIA. Wecalculate both the Galactic and extragalactic prompt and inverse Compton (IC)contributions to the resulting gamma-ray spectra. To find the Galactic ICspectra we use the interstellar radiation field model from the latest releaseof GALPROP. For the extragalactic signal we show that the amplitude of theprompt gamma-emission is very sensitive to the assumed model for theextragalactic background light. For our Galaxy we use the Einasto, NFW andIsothermal DM density profiles and include the effects of DM substructureassuming a simple subhalo model. Our calculations show that for theannihilating DM the extragalactic gamma-ray signal can dominate only if ratherextreme power-law concentration-mass relation $C(M)$ is used, while morerealistic $C(M)$ relations make the extragalactic component comparable orsubdominant to the Galactic signal. For the decaying DM the Galactic signalalways exceeds the extragalactic one. In the case of annihilating DM the PFHfavored parameters can be ruled out only if power-law $C(M)$ relation isassumed. For DM decaying into $2\mu$ or $4\mu$ the PFH favored DM parametersare not in conflict with the Fermi gamma-ray data. We find that, due to the(almost) featureless Galactic IC spectrum and the DM halo substructure,annihilating DM may give a good simultaneous fit to the isotropic diffusegamma-ray and to the PFH $e^\pm$ data without being in clear conflict with theother Fermi-LAT gamma-ray measurements.

Implications of the Fermi-LAT diffuse gamma-ray measurements on annihilating or decaying Dark Matter