This dissertation presents the results of a search in the exclusive photon plus missing transverse energy (gamma + E/_T) final state in proton antiproton collisions at center of mass energy of 1.96 TeV using the Collider Detector at Fermilab experiment. The strategy used here is to search for delayed photons coming from gauge mediated supersymmetric events with the exclusive production of ~X(0 1) -> gamma~G. In these models the ~X(0 1) is the lightest neutralino and has nanosecond lifetime before decaying to a photon (gamma) and gravitino (~G) which exits the detector unrecorded. In order to search for this process we select collisions that have a single photon plus missing transverse energy and little other activity in the detector and examine the arrival time of the photon. This arrival time is then compared against expectations from a data driven background of the standard model sources. In the data collected from the Fermilab Tevatron collider from December 2004 to June 2010, representing 6.3 fb^-1 of data, we observe 322 events in the photon arrival timing region from 2 nanoseconds to 7 nanoseconds with a data driven background prediction of 257 +/- 35. An excess of 65 events is observed, equivalent to a standard deviation (N_sigma) of 1.65 from the null hypothesis.

This dissertation presents a search for heavy, long-lived, neutral particles that decay to photons in proton anti-proton collisions with a center of mass energy of 1.96 TeV at the Collider Detector at Fermilab (CDF) experiment. Such particles are typical of models of Gauge Mediated Supersymmetry Breaking (GMSB). We select events with a single photon, missing transverse energy, and little other activity in the detector. We model the photon arrival time for Standard Model and non-collision sources using a data-driven method and consider photons which have a time of arrival at the detector which is significantly delayed relative to predictions. Using 6.3 fb^−1 of data collected from December 2004 to June 2010, we observe 322 events in the signal region compared to a background prediction of 287 ± 24 events. While the data are consistently above predictions, we report a model excess with a significance of 1.2 standard deviations from the null hypothesis.