Search for new phenomena in events with twoZbosons and missing transverse momentum inpp¯collisions ats=1.96TeV

We present a search for new phenomena in events with two reconstructed $Z$ bosons and large missing transverse momentum, sensitive to processes $p\overline{p}\ensuremath{\rightarrow}{X}_{2}{X}_{2}\ensuremath{\rightarrow}ZZ{X}_{1}{X}_{1}$, where ${X}_{2}$ is an unstable particle decaying as ${X}_{2}\ensuremath{\rightarrow}Z{X}_{1}$ 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 $4.2\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ 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 $p\overline{p}\ensuremath{\rightarrow}{X}_{2}{X}_{2}\ensuremath{\rightarrow}ZZ{X}_{1}{X}_{1}$ ranging from 50 fb to 1 pb, depending on the masses of ${X}_{1}$ and ${X}_{2}$.