Abstract: A search for forbidden and exotic Z boson decays in the diphoton mass spectrum is presented for the first time in hadron collisions, based on data corresponding to 10.0??fb-1 of integrated luminosity from proton-antiproton collisions at vs=1.96??TeV collected by the CDF experiment. No evidence of signal is observed, and 95% credibility level Bayesian upper limits are set on the branching ratios of decays of the Z boson to a photon and neutral pion (which is detected as a photon), a pair of photons, and a pair of neutral pions. The observed branching ratio limits are 2.01×10-5 for Z?p0?, 1.46×10-5 for Z???, and 1.52×10-5 for Z?p0p0. The Z?p0? and Z??? limits improve the most stringent results from other experiments by factors of 2.6 and 3.6, respectively. The Z?p0p0 branching ratio limit is the first experimental result on this decay.

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