Antiproton Limits on Decaying Gravitino Dark Matter

We derive 95% CL lower limits on the lifetime of decaying dark matter in the channels $Z\nu$, $W\ell$ and $h\nu$ using measurements of the cosmic-ray antiproton flux by the PAMELA experiment. Performing a scan over the allowed range of cosmic-ray propagation parameters we find lifetime limits in the range of $8 \times 10^{28}$s to $5 \times 10^{25}$s for dark matter masses from roughly 100 GeV to 10 TeV. We apply these limits to the well-motivated case of gravitino dark matter in scenarios with bilinear violation of R-parity and find a similar range of lifetime limits for the same range of gravitino masses. Converting the lifetime limits to constraints on the size of the R-parity violating coupling we find upper limits in the range of $10^{-8}$ to $8 \times 10^{-13}$.