Investigating the Supersymmetric Explanation of Anomalous CDF lepton(s) photon(s) Missing-$E_T$ Events

The recent excess over the Standard Model prediction in the \mu \gamma missing-E_T channel reported by CDF can be well-explained by resonant smuon production with a single dominant R-parity violating coupling \lambda'_{211}, in the context of models where the gravitino is the lightest supersymmetric particle. The slepton decays to the lightest neutralino and a muon followed by neutralino decaying to a gravitino and photon. The kinematical distributions are fitted well by our hypothesis and we use them to constrain the available parameter space. The model also provides an explanation for the ee\gamma\gamma missing-E_T event observed in Run I of the Tevatron by the CDF experiment. Our model predicts an excess of between 5 and 35 events in a \gamma missing-E_T channel at Run I. We provide predictions for signatures expected by the model at Run II.