  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.
