The case for three-body decaying dark matter

Fermi-LAT has confirmed the excess in cosmic positron fraction observed by PAMELA, which could be explained by dark matter annihilating or decaying in the center of the galaxy. Most existing models postulate that the dark matter annihilates or decays into final states with two or four leptons, which would produce diffuse gamma ray emissions that are in tension with data measured by Fermi-LAT. We point out that the tension could be alleviated if the dark matter decays into three-body final states with a pair of leptons and a missing particle. Using the goldstino decay in a certain class of supersymmetric theories as a prime example, we demonstrate that simultaneous fits to the total e⁺+e^- and the fractional e⁺/e^- fluxes from Fermi-LAT and PAMELA could be achieved for a 2 TeV parent particle and a 1 TeV missing particle, without being constrained by gamma-ray measurements. By studying different effective operators giving rise to the dark matter decay, we show that this feature is generic for three-body decaying dark matter containing a missing particle. Constraints on the hadronic decay widths from the cosmic anti-proton spectra are also discussed.