Limits on Light Gravitino Production and New Processes with Large Missing Transverse Energy in $\mathit{p}\overline{\mathit{p}}$ Collisions at $\sqrt{\mathit{s}}=1.8\mathrm{}\mathrm{TeV}$

Events collected by the Collider Detector at Fermilab (CDF) with an energetic jet plus large missing transverse energy can be used to search for physics beyond the standard model. We see no deviations from the expected backgrounds and set upper limits on the production of new processes. We consider in addition the production of light gravitinos and set a limit at $95\%$ confidence level on the breaking scale $\sqrt{F}\ge 217\mathrm{GeV}$, which excludes gravitino masses smaller than $1.1\times {10}^{-5\mathrm{}}\mathrm{eV}{/c}^2$.