On the effective interactions of a light gravitino with matter fermions

If the gravitino is light and all the other supersymmetric particles are heavy, it can be considered the effective theory describing the interactions of its goldstino components with ordinary matter. To discuss the model-dependence of these interactions, in this paper is taken the simple case of spontaneously broken supersymmetry and only two chiral superfields, associated with the goldstino and a massless matter fermion. The four-point effective coupling involving two matter fermions and two goldstinos are derived by explicit integration of the heavy spin-0 degrees of freedom in the low-energy limit. Surprisingly, the result is not equivalent to the usual non-linear realization of supersymmetry, where a pair of goldstinos couples to the energy-momentum tensor of the matter field. The puzzle is solved by enlarging the non-linear realization to include a second independent couplings of this type up to this order in the low-energy expansion. The paper concludes by commenting on the interpretation of our results and on their possible phenomenological implications