Search for Heavy, Long-Lived Neutralinos that Decay to Photons at CDF II Using Photon Timing

We present the results of the first hadron collider search for heavy, long-lived neutralinos that decay via lightest neutralino to gamma gravitino in gauge-mediated supersymmetry breaking models. Using an integrated luminosity of $570\pm 34p{b}^{-1}$ of $p\bar{p}$ collisions at $\sqrt{s}=1.96$ TeV, we select $\gamma$+jet+missing transverse energy candidate events based on the arrival time of a high-energy photon at the electromagnetic calorimeter as measured with a timing system that was recently installed on the CDF II detector. We find 2 events, consistent with the background estimate of 1.3$\pm$0.7 events. While our search strategy does not rely on model-specific dynamics, we set cross section limits and place the world-best 95% C.L. lower limit on the neutralino mass of 101 GeV at lifetime = 5 ns.