Dark matter particles that annihilate each other or decay with long lifetimes can be constrained by data in various wavebands. Here we apply this method to supersymmetric weakly interacting massive particles (10-1000 GeV neutralinos and gravitinos) by using observations of the diffuse X-ray and γ-ray backgrounds. Our work treats these predicted lightest supersymmetric particles as cold dark matter that clumps into galaxy halos and affects the intensity of the background radiation in a way that can be calculated using exact general relativistic cosmological models. We are able to set firm lower bounds on the decay lifetimes of neutralinos and gravitinos. These are of orders 1-10~6 Gyr and 10-100 Gyr, respectively, depending on rest mass. Unlike decaying vacua and eV-scale neutrinos and axions (which we have constrained elsewhere by similar methods), our results imply that weakly interacting massive particles (WIMPs) are viable dark matter candidates.
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