Phenomenology of a<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>Z</mml:mi></mml:mrow><mml:mrow><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>coupling only to third-family fermions

The phenomenology of an additional $U(1)$ neutral gauge boson ${Z}^{\ensuremath{'}}$ coupled to the third family of fermions is discussed. One might expect such a particle to contribute to processes where taus, $b$ and $t$ quarks are produced. Precision data from CERN LEP1 put severe constraints on the mixing and heavy-boson mass. We find that the effects of such a particle could not be observed at hadronic colliders, be it at the Fermilab Tevatron or the CERN LHC, because of the QCD background. At LEP2 and future ${e}^{+}{e}^{\ensuremath{-}}$ linear colliders, one could instead hope to observe such effects, in particular, for $b\overline{b}$ final states.