We derive Feynman rules for the interactions of a single gravitino with (s)quarks and gluons/gluinos from an effective supergravity Lagrangian in non-derivative form and use them to calculate the hadroproduction cross sections and decay widths of single gravitinos. We confirm the results obtained previously with a derivative Lagrangian as well as those obtained with the non-derivative Lagrangian in the high-energy limit and elaborate on the connection between gauge independence and the presence of quartic vertices. We perform extensive numerical studies of branching ratios, total cross sections, and transverse-momentum spectra at the Tevatron and the LHC. From the latest CDF monojet cross section limit, we derive a new and robust exclusion contour in the gravitino-squark/gluino mass plane, implying that gravitinos with masses below $2cdot10^{-5}$ to $1cdot10^{-5}$ eV are excluded for squark/gluino-masses below 200 and 500 GeV, respectively. These limits are complementary to the one obtained by the CDF collaboration, $1.1cdot 10^{-5}$ eV, under the assumption of infinitely heavy squarks and gluinos. For the LHC, we conclude that SUSY scenarios with light gravitinos will lead to a striking monojet signal very quickly after its startup.
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