Prompt signals and displaced vertices in sparticle searches for next-to-minimal gauge-mediated supersymmetric models

We study the LHC phenomenology of the next-to-minimal model of gauge-mediated supersymmetry breaking, both for Run I and Run II. The Higgs phenomenology of the model is consistent with observations: a 125 GeV standard model-like Higgs which mixes with singlet-like state of mass around 90 GeV that provides a 2σ excess at LEP II. The model possesses regions of parameter space where a longer-lived lightest neutralino decays in the detector into a gravitino and a b-jet pair or a tau pair resulting in potential displaced vertex signatures. We investigate current bounds on sparticle masses and the discovery potential of the model, both via conventional searches and via searches for displaced vertices. The searches based on promptly decaying sparticles currently give a lower limit on the gluino mass 1080 GeV and could be sensitive up to 1900 GeV with 100 fb^{- 1}, whereas the current displaced vertex searches cannot probe this model due to b-quarks in the final state. We show how the displaced vertex cuts might be relaxed in order to improve signal efficiency, while simultaneously applied prompt cuts reduce background, resulting in a much better sensitivity than either strategy alone and motivating a fully fledged experimental study.