Nonexotic neutral gauge bosons

We study theoretical and experimental constraints on electroweak theories including a new color-singlet and electrically neutral gauge boson. We first note that the electric charges of the observed fermions imply that any such $Z^{\prime }$ boson may be described by a gauge theory in which the Abelian gauge groups are the usual hypercharge along with another $U\left(1\right)\mathrm{}$ component in a kinetic-diagonal basis. Assuming that the observed quarks and leptons have generation-independent $U\left(1\right)\mathrm{}$ charges, and that no new fermions couple to the standard model gauge bosons, we find that their $U\left(1\right)\mathrm{}$ charges form a two-parameter family consistent with anomaly cancellation and viable fermion masses, provided there are at least three right-handed neutrinos. We then derive bounds on the $Z^{\prime }$ mass and couplings imposed by direct production and Z-pole measurements. For generic charge assignments and a gauge coupling of electromagnetic strength, the strongest lower bound on the $Z^{\prime }$ mass comes from Z-pole measurements, and is of the order of 1 TeV. If the new $U\left(1\right)\mathrm{}$ charges are proportional to $B-L,$ however, there is no tree-level mixing between the Z and $Z^{\prime },$ and the best bounds come from the absence of direct production at CERN LEP II and the Fermilab Tevatron. If the $U\left(1\right)\mathrm{}$ gauge coupling is one or two orders of magnitude below the electromagnetic one, these bounds are satisfied for most values of the $Z^{\prime }$ mass.