Testing Gauge-Gravitino Coupling in Gauge-Mediated Supersymmetry Breaking Through Single Photon Events

We show that the process $e^{+}{e}^{-}\to \gamma +$ missing energy, arising from the pair production of neutralinos, can probe the $\gamma-\tilde\gamma- \gravitino$aswellasthe$Z-\tilde Z-\gravitino$ couplings in Gauge Mediated Supersymmetry Breaking models. This enables one to study the mutual relationship of the Goldstino couplings of the different gauginos, a feature whose testability has not been emphasized so far. The Standard Model backgrounds get suppresed with the use of a right polarized electron beam. The energy and angular distribution of the emitted photon can distinguish such models from the minimal supersymmetric theory and its variants.