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

If supersymmetry is dynamically broken at a low scale (MSUSY), 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 χ₁⁰ with mass m_χ₁⁰, which can decay into a photon (γ) plus a gravitino (̃ \~G). We study the detection of ${e}^{{-}}{e}⁺{→}{{χ}}₁⁰{{χ}}₁⁰{→}{γ}{ ̃ \~{}{}}{G}{γ}{ ̃ \~{}{}}{G}$ at the proposed Linear Collider, and find the range of the parameters ${M}SUSY$ and ${m}_{{{χ}}₁⁰}$ that can be accessible with a right-hand polarized electron beam at $√S=500$ GeV, with 50 ${fb}^{{-}1}$ integrated luminosity. We also discuss briefly the accessible range for current electron and hadron colliders.