Signals of a superlight gravitino at hadron colliders when the other superparticles are heavy

If the gravitino (G) is very light and all the other supersymmetric particles are above threshold, supersymmetry may still be found at colliders, by looking at processes with only gravitinos and ordinary particles in the final state. We compute here the cross-sections for some distinctive signals at hadron colliders: photon plus missing energy, induced by (q antiquark -> G G photon), and jet plus missing energy, induced by (q antiquark -> G G g), (q g -> G G q), and (g g -> G G g). From the present Tevatron data, we estimate the bound m_{3/2} > 2.7 10^-5 eV on the gravitino mass, corresponding to the bound sqrt{F} > 335 GeV on the supersymmetry-breaking scale. We foresee that the upgraded Tevatron and the LHC will be sensitive to values of m_{3/2} up to 4.9 10^-5 eV and 1.2 10^-3 eV, corresponding to sqrt{F} up to 450 GeV and 2.2 TeV, respectively.