Prospects for measuring the mass of heavy, long-lived neutral particles that decay to photons

We describe a novel way to measure the mass of heavy, long-lived neutral particles that decay to photons using collider experiments. We focus on a Light Neutralino and Gravitino model in a Gauge Mediated Supersymmetry Breaking scenario where the neutralino has a long-lifetime (O(ns)) as it is not excluded by current experiments. To illustrate our method and give sensitivity estimates we use recent CDF results and a production mechanism where sparticles are produced via $\phi_{i} \rightarrow \widetilde{\chi}^{1}_{0} \widetilde{\chi}^{1}_{0} \rightarrow (\gamma \widetilde{G})(\gamma \widetilde{G})$ in which $\phi_{i}$ indicates a neutral scalar boson, $\widetilde{\chi}^{1}_{0}$ is the lightest neutralino and $\widetilde{G}$ is the gravitino, as a full set of background shapes and rates are available. Events can be observed in the exclusive photon plus Missing $E_{T}$ final state where one photon arrives at the detector with a delayed time of arrival. Surprisingly, a simple measurement of the slope of the delayed-time distribution with the full CDF dataset is largely insensitive to all but the $\widetilde{\chi}^{1}_{0}$ mass and allows for the possibility of determining its mass to approximately 25% of itself.