We present a search for new phenomena in events with two reconstructed $Z$ bosons and large missing transverse momentum, sensitive to processes $p\overline{p}\to X_2{X}_2\to ZZ{X}_1{X}_1$, where $X_2$ is an unstable particle decaying as $X_2\to Z{X}_1$ and $X_1$ is undetected. The particles $X_1$ and $X_2$ may be, among other possibilities, fourth-generation neutrinos or supersymmetric particles. We study the final state in which one $Z$ boson decays to two charged leptons and the second decays hadronically. In data corresponding to an integrated luminosity of $4.2{\mathrm{fb}}^{-1}$ from proton-antiproton collisions recorded by the CDF II detector at the Tevatron, with center-of-mass energy of 1.96 TeV, we find agreement between data and standard-model backgrounds. We calculate 95% confidence level upper limits on the cross section of the process $p\overline{p}\to X_2{X}_2\to ZZ{X}_1{X}_1$ ranging from 50 fb to 1 pb, depending on the masses of $X_1$ and $X_2$.

• Received 5 December 2011

DOI:https://doi.org/10.1103/PhysRevD.85.011104