Constraints on additional Z bosons.

Abstract

$Z$-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 ${\mathrm{SU}(2)}_{L}\ifmmode\times\else\texttimes\fi{}{\mathrm{SU}(2)}_{R}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ 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 ${Z}_{1}^{0}\ensuremath{-}{Z}_{2}^{0}$ mixing angle $\ensuremath{\theta}$ ($|\ensuremath{\theta}|l0.01$ 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 $\ensuremath{\theta}$ are correlated, the constraints are much stronger (${M}_{2}g500\ensuremath{-}1000$ GeV). The weak angle in the modified minimal subtraction scheme is well determined even allowing for extra $Z'\mathrm{s}$ and an arbitrary Higgs structure: ${sin}^{2}{\stackrel{^}{\ensuremath{\theta}}}_{W}({M}_{Z})={0.2334}_{\ensuremath{-}0.0011}^{+0.0008}$, for the models considered, where the uncertainties include ${m}_{t}$, compared to the SU(2)\ifmmode\times\else\texttimes\fi{}U(1) model value 0.2333\ifmmode\pm\else\textpm\fi{}0.0008. The 95%-C.L. upper limits on ${m}_{t}$ (${m}_{t}l182$ GeV for Higgs doublets and singlets only, and ${m}_{t}l310$ GeV for arbitrary Higgs representations) continue to hold in the presence of the extra $Z'\mathrm{s}$ considered. The implications of these results for ordinary and supersymmetric grand unification, atomic parity violation, charged-current universality, $R$ (${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$, 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.