Single-photon signals at CERN LEP in supersymmetric models with a light gravitino

Abstract

We study the single-photon signals expected at CERN LEP in models with a very light gravitino ${(m}_{\mathrm{G\ifmmode \tilde{}\else \~{}\fi{}}}\ensuremath{\lesssim}{10}^{\ensuremath{-}3}\mathrm{eV})$. The dominant process is neutralino-gravitino production ${(e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\chi}\mathrm{G\ifmmode \tilde{}\else \~{}\fi{}})$ with subsequent neutralino decay via $\ensuremath{\chi}\ensuremath{\rightarrow}\ensuremath{\gamma}\mathrm{G\ifmmode \tilde{}\else \~{}\fi{}}$, giving a $\ensuremath{\gamma}+{\mathrm{E}}_{\mathrm{miss}}$ signal. We first calculate the cross section at arbitrary center-of-mass energies and provide new analytic expressions for the differential cross section valid for general neutralino compositions. We then consider the constraints on the gravitino mass from LEP 1 and LEP 161 single-photon searches, and possible such searches at the Fermilab Tevatron. We show that it is possible to evade the stringent LEP 1 limits and still obtain an observable rate at LEP 2, in particular, in the region of parameter space that may explain the CDF $\mathrm{ee}\ensuremath{\gamma}\ensuremath{\gamma}{+E}_{T,\mathrm{miss}}$ event. As diphoton events from neutralino pair production would not be kinematically accessible in this scenario, the observation of whichever photonic signal will discriminate among the various light-gravitino scenarios in the literature. We also perform a Monte Carlo simulation of the expected energy and angular distributions of the emitted photon, and of the missing invariant mass expected in the events. Finally we specialize the results to the case of a recently proposed one-parameter no-scale supergravity model.