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 (NMGMSB), 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 2$\sigma$ 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. We investigate current lower bounds on sparticle masses and the discovery potential of the model, both via conventional sparticle searches and via searches for displaced vertices. The strongest bound from searches for promptly decaying sparticles yields a lower limit on the gluino mass of 1080 GeV. An analysis of 100 fb$^{-1}$ from Run II, on the other hand, is expected to be sensitive up to 1900 GeV. The displaced vertex searches from Run I suffer from a very low signal efficiency, mainly due to the presence of $b-$quarks in the final state. We show how the displaced vertex cuts might be relaxed in order to improve signal efficiency, while simultaneous prompt objects can be used to cut down background. We find that a combined search strategy with both prompt and displaced cuts potentially has a far better sensitivity to this model than either set alone, motivating a fully fledged experimental study.