Constraints on additionalZbosons

$Z$-pole, $W$-mass, and weak neutral-current (WNC) data as well as direct collider limits are used to constrain the mass and mixing of possible heavy $Z_2$ bosons with couplings expected in grand unified theories and ${\mathrm{SU}\mathrm{}\left(2\right)\mathrm{}}_L\times {\mathrm{SU}\mathrm{}\left(2\right)\mathrm{}}_R\times \mathrm{U}\mathrm{}\left(1\right)\mathrm{}$ models. The data now enable the top-quark mass and $Z_2$ properties to be limited simultaneously. The indirect ($Z$-pole, $M_W$, WNC) data stringently constrain the $Z_1^0-Z_2^0$ mixing angle $\theta$ ($\left|\theta \right|<\mathrm{}0.01\mathrm{}$ in most cases). For models with arbitrary Higgs representations, the limits on the $Z_2$ mass $M_2$ from indirect and direct constraints are rather weak (typically 160-400 GeV), but in specific models in which $M_2$ and $\theta$ are correlated, the constraints are much stronger ($M_2>500-1000\mathrm{}$ GeV). The weak angle in the modified minimal subtraction scheme is well determined even allowing for extra $Z\text{'}\mathrm{s}$ and an arbitrary Higgs structure: ${sin}^2{\hat{\theta }}_W\left(M_Z\right)={0.2334}_{-0.0011\mathrm{}}^{+0.0008\mathrm{}}$, for the models considered, where the uncertainties include $m_t$, compared to the SU(2)×U(1) model value 0.2333±0.0008. The 95%-C.L. upper limits on $m_t$ ($m_t<182\mathrm{}$ GeV for Higgs doublets and singlets only, and $m_t<310\mathrm{}$ GeV for arbitrary Higgs representations) continue to hold in the presence of the extra $Z\text{'}\mathrm{s}$ considered. The implications of these results for ordinary and supersymmetric grand unification, atomic parity violation, charged-current universality, $R$ ($e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$, hadrons) below the $Z$ pole, and superstring theories are discussed. A nongauge model in which the $Z_2$ has the same couplings as the ordinary $Z$ is included for comparison.