Confronting recent AMS-02 positron fraction and Fermi-LAT extragalactic γ-ray background measurements with gravitino dark matter

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Recent positron flux fraction measurements in cosmic-rays (CR) made by the AMS-02 satellite confirm and extends the evidence on the existence of a new (yet unknown) source of high energy positrons. To explain this excess, we use the gravitino of bilinear R-parity violating SUSY models as a decaying Dark Matter candidate, as the source of those high energy particles. Being a long lived weak-interacting and spin 3/2 particle, it offers several particularities which makes it an attractive candidate. We compute the electron, positron and $\gamma$-ray\ fluxes produced by each gravitino decay channel at the Earth. Combining the flux from the different decay modes we can fit AMS-02 measurements of the positron fraction, as well as the electron and positron fluxes, with a gravitino mass in the range $1-2$ TeV and lifetimes of $\sim 1.0-0.8\times 10^{26}$ s. . Then, we study the viability of these scenarios through their implications in $\gamma$-ray observations. We set limits on the gravitino lifetime using the Extragalactic $\gamma$-ray Background recently reported by the {\it Fermi}-LAT Collaboration and a state-of-the-art model of its known contributors. These limits exclude the gravitino parameter space which provides an acceptable explanation of the AMS-02 data. Therefore, we conclude that the gravitino of bilinear R-parity violating models is ruled out as the unique primary source of electrons and positrons needed to explain the rise in the positron fraction.