Search for long-lived parents of $Z^0$ bosons in $p\overline{p}$ collisions at $\sqrt{s}=1.8\mathrm{}\mathrm{TeV}$

We search for new long-lived particles which decay to $Z^0$ bosons by looking for $Z^0\to e^{+}{e}^{-}$ decays with displaced vertices. We find no evidence for parent particles of the $Z^0$ with long lifetimes in $90{\mathrm{pb}}^{\mathrm{-}1}$ of data from the CDF experiment at Fermilab. We set a cross section limit as a function of the lifetime of the parent particle for both a generic $Z^0$ parent and a fourth-generation, charge $-\frac{1}{3}$ quark that decays into $Z^{0}b.\mathrm{}$