  If there is new physics associated with the top quark, it could show up as
anomalous couplings of the top quark to weak gauge bosons, such as $Z\ttbar$
and $W\tbbar$ vector and axial-vector couplings. We use the processes
$\ttbar\to Z^0Z^0$, $\ttbar\to W^+W^-$, and $\ttbar\to Z^0H$ to obtain the
unitarity constraints on these anomalous couplings, and combine these
constraints with those from precision electroweak data. The unitarity
constraints can impose additional limits on the anomalous couplings when the
scale of new physics is as low as 2 TeV. A nonzero measurement of such an
anomalous coupling leads to an upper limit on the new physics scale from the
unitarity condition.
