Constraining decaying dark matter with FERMI-LAT gamma rays

High energy electrons and positrons from decaying dark matter can produce a significant flux of gamma rays by inverse Compton off low energy photons in the interstellar radiation field. This possibility is inevitably related with the dark matter interpretation of the observed PAMELA and FERMI excesses. We will describe a simple and universal method to constrain dark matter models which produce electrons and positrons in their decay by using the FERMI-LAT gammaray observations in the energy range between 0.5GeV and 300 GeV, by exploiting universal response functions that, once convolved with a specific dark matter model, produce the desired constraint. The response functions contain all the astrophysical inputs. We discuss the uncertainties in the determination of the response functions and apply them to place constraints on some specific dark matter decay models that can well fit the positron and electron fluxes observed by PAMELA and FERMI LAT, also taking into account prompt radiation from the dark matter decay. With the available data decaying dark matter cannot be excluded as source of the PAMELA positron excess.