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 $10.0{\mathrm{fb}}^{-1}$ of integrated luminosity from proton-antiproton collisions at $\sqrt{s}=1.96\mathrm{TeV}$ 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 $2.01\times {10}^{-5}$ for $Z\to {\pi }^0\gamma$, $1.46\times {10}^{-5}$ for $Z\to \gamma \gamma$, and $1.52\times {10}^{-5}$ for $Z\to {\pi }^0{\pi }^0$. The $Z\to {\pi }^0\gamma$ and $Z\to \gamma \gamma$ limits improve the most stringent results from other experiments by factors of 2.6 and 3.6, respectively. The $Z\to {\pi }^0{\pi }^0$ branching ratio limit is the first experimental result on this decay.

• Received 14 November 2013

DOI:https://doi.org/10.1103/PhysRevLett.112.111803