Detecting a Light Gravitino at Linear Collider to Probe the SUSY Breaking Scale

If supersymmetry is dynamically broken at a low scale ($M_{susy}$), 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 $\chi^0_1$ with mass $m_{\chi^0_1}$, which can decay into a photon ($\gamma$) plus a gravitino ($\widetilde{G}$). We study the detection of $e^{-}e^{+}\rightarrow \chi^0_1 \chi^0_1 \rightarrow \gamma\widetilde{G}\gamma\widetilde{G}$ at the proposed Linear Collider, and find the range of the parameters $M_{susy}$ and $m_{\chi^0_1}$ that can be accessible with a right-hand polarized electron beam at $\sqrt{S}=500$\,GeV, with 50\,${\rm fb}^{-1}$ integrated luminosity. We also discuss briefly the accessible range for current electron and hadron colliders.