UnusualZ0decays in supersymmetry with a superlight gravitino

Supergravity theory with a superlight gravitino (of mass $\sim m_W^2{M}_{\mathrm{Pl}}^{-1\mathrm{}}$) leads to many interesting $Z^0$ decay modes which are not present in the standard model or in the usual supergravity theory. We discuss the signals associated with two such decay modes, $Z^0\to \mathrm{Sf}\overline{f}, \mathrm{Pf}\overline{f}$, where $S\left(P\right)\mathrm{}$ is a massless scalar (pseudoscalar) particle present in this theory, and $f$ is a quark or a lepton. Lack of observation of this mode in the current measurements at the CERN $e^{+}{e}^{-}$ collider LEP leads to a lower bound on the gravitino mass of ${10}^{-14\mathrm{}}$ GeV. Such decays will be observable with ${10}^6$ $Z^0\text{'}\mathrm{s}$ at LEP if the gravitino mass is less than ${10}^{-13\mathrm{}}$ GeV.