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

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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 ϕᵢ → χ¹₀ χ¹₀ → (γG)(γG) in which ϕᵢ indicates a neutral scalar boson, χ¹₀ is the lightest neutralino and 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 Eₜ 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 χ¹₀ mass and allows for the possibility of determining its mass to approximately 25% of itself.