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Prospects of Searches for Gauge Mediated Supersymmetry with h^0 -> χ_1^0 χ_1^0 production in the Time-Delayed Photon + MET Final State at the Tevatron

We propose a search for direct production and decay of the lightest supersymmetric Higgs boson to two neutralinos in gauge mediated models at the Fermilab Tevatron. We focus on the final state where each neutralino decays to photon and light gravitino with a lifetime of order O(ns). In the detector this will show up as a photon with a time-delayed signature and missing E_T. We estimate that using the photon timing system at CDF, and the full 10/fb data sample, that the sensitivity can be within a factor of three in some regions of parameter space for direct production of the Higgs.