Gamma-ray constraints on hadronic and leptonic activities of decaying dark matter

While the excess in cosmic-ray electrons and positrons reported by PAMELA and Fermi may be explained by dark matter decaying primarily into charged leptons, this does not necessarily mean that dark matter should not have any hadronic decay modes. In order to quantify the allowed hadronic activities, we derive constraints on the decay rates of dark matter into WW, ZZ, hh, qq and gg using the Fermi and HESS gamma-ray data. We also derive gamma-ray constraints on the leptonic e⁺e^-, μ⁺μ^- and τ⁺τ^- final states. We find that dark matter must decay primarily into μ⁺μ^- or τ⁺τ ^- in order to simultaneously explain the reported excess and meet all gamma-ray constraints.