Detecting a light gravitino at a linear collider to probe the SUSY-breaking scale

If supersymmetry is dynamically broken at a low scale ($M_{\mathrm{SUSY}}$), within a few orders of magnitude of the weak scale, then the lightest supersymmetric partner is the gravitino and the next-to-lightest supersymmetric partner is a neutralino ${\chi }_1^0$ with mass $m_{{\chi }_1^0}$, which can decay into a photon ($\gamma$) plus a gravitino ($\tilde{G}$). We study the detection of $e^{-}{e}^{+}\to {\chi }_1^0{\chi }_1^0\to \gamma \tilde{G}\gamma \tilde{G}$ at the proposed Linear Collider, and find the range of the parameters $M_{\mathrm{SUSY}}$ and $m_{{\chi }_1^0}$ that can be accessible with a right-hand polarized electron beam at $\sqrt{S}=500\mathrm{}$ GeV, with 50 ${\mathrm{fb}}^{-1\mathrm{}}$ integrated luminosity. We also discuss briefly the accessible range for current electron and hadron colliders.