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High energy electrons and positrons from decaying dark matter can produce asignificant flux of gamma rays by inverse Compton off low energy photons in theinterstellar radiation field. This possibility is inevitably related with thedark matter interpretation of the observed PAMELA and FERMI excesses. The aimof this paper is providing a simple and universal method to constraint darkmatter models which produce electrons and positrons in their decay by using theFermi LAT gamma-ray observations in the energy range between 0.5 GeV and 300GeV. We provide a set of universal response functions that, once convolved witha specific dark matter model produce the desired constraint. Our responsefunctions contain all the astrophysical inputs such as the electron propagationin the galaxy, the dark matter profile, the gamma-ray fluxes of known origin,and the Fermi LAT data. We study the uncertainties in the determination of theresponse functions and apply them to place constraints on some specific darkmatter decay models that can well fit the positron and electron fluxes observedby PAMELA and Fermi LAT. To this end we also take into account prompt radiationfrom the dark matter decay. We find that with the available data decaying darkmatter cannot be excluded as source of the PAMELA positron excess.

Constraining Decaying Dark Matter with Fermi LAT Gamma-rays