Indirect detection of gravitino dark matter including its three-body decays

It was recently pointed out that in supersymmetric scenarios with gravitino dark matter and bilinear R-parity violation, gravitinos with masses below Mw typically decay with a sizable branching ratio into the 3-body final states W^*+lepton and Z^*+neutrino. In this paper we study the indirect detection signatures of gravitino dark matter including such final states. First, we obtain the gamma ray spectrum from gravitino decays, which features a monochromatic contribution from the decay into photon+neutrino and a continuum contribution from the three-body decays. After studying its dependence on supersymmetric parameters, we compute the expected gamma ray fluxes and derive new constraints, from recent FERMI data, on the R-parity breaking parameter and on the gravitino lifetime. Indirect detection via antimatter searches, a new possibility brought about by the three-body final states, is also analyzed. For models compatible with the gamma ray observations, the positron signal is found to be negligible whereas the antiproton one can be significant.