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

Abstract

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 ${\ensuremath{\chi}}_{1}^{0}$ with mass ${m}_{{\ensuremath{\chi}}_{1}^{0}}$, which can decay into a photon ($\ensuremath{\gamma}$) plus a gravitino ($\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{G}$). We study the detection of ${e}^{\ensuremath{-}}{e}^{+}\ensuremath{\rightarrow}{\ensuremath{\chi}}_{1}^{0}{\ensuremath{\chi}}_{1}^{0}\ensuremath{\rightarrow}\ensuremath{\gamma}\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{G}\ensuremath{\gamma}\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{G}$ at the proposed Linear Collider, and find the range of the parameters ${M}_{\mathrm{SUSY}}$ and ${m}_{{\ensuremath{\chi}}_{1}^{0}}$ that can be accessible with a right-hand polarized electron beam at $\sqrt{S}=500$ GeV, with 50 ${\mathrm{fb}}^{\ensuremath{-}1}$ integrated luminosity. We also discuss briefly the accessible range for current electron and hadron colliders.