Low-energy Gravitino Interactions *

It is well known that the solution of the hierarchy problem in supersymmetric extensions of the Standard Model (SM) requires a mass splitting ∆m ∼ 1 TeV between ordinary particles and their superpartners. This requirement, however, leaves largely undetermined the supersymmetrybreaking scale √ F , or, equivalenty, the gravitino mass m3/2 = F/( √ 3MP ), MP being the Planck mass. The ratio ∆m /F is given by the coupling of the goldstino to the matter sector under consideration. If this coupling is gravitational, of order m3/2/MP , then ∆m is of order m3/2 and supersymmetry breaking takes place at the intermediate scale √ F ∼ 10 GeV. On the other hand, if the goldstino coupling to matter is of order 1, then √ F is comparable to the mass splitting ∆m, and the gravitino becomes superlight, with a mass of about 10 eV. In the absence of a theory of supersymmetry breaking, F should be treated as a free parameter. If the gravitino is superlight, then one expects a substantially different phenomenology from that characterizing the Minimal Supersymmetric Standard Model (MSSM). In this case, only the±3/2 gravitino helicity states can be safely omitted from the low-energy effective theory, when gravitational interactions are neglected. The ±1/2 helicity states, essentially described by the goldstino field, should instead be accounted for at low energy, because of their non-negligible coupling to matter. The lightest supersymmetric particle is the gravitino and peculiar experimental signatures can arise from the decay of the next-to-lightest supersymmetric particle into its ordinary partner plus a gravitino [1].