  The top quark seesaw mechanism offers a method for constructing a composite
Higgs field without the usual difficulties that accompany traditional
technicolor or topcolor theories. The focus of this article is to study the
phenomenology of the new physics required by this mechanism. After establishing
a set of criteria for a plausible top quark seesaw theory, we develop two
models, the first of which has a heavy weak singlet fermion with hypercharge
4/3 while the second has, in addition, a heavy weak singlet hypercharge -2/3
fermion. At low energies, these theories contain one or two Higgs doublets
respectively. We then derive the low energy effective Higgs potential in detail
for the two-doublet theory as well as study the likely experimental signatures
for both theories. A strong constraint on the one-doublet model is the measured
value of the rho parameter which permits the new heavy fermion to have a mass
of about 5-7 TeV, when the Higgs has a mass greater than 300 GeV. In the
two-doublet model, mixing of the new heavy Y=-2/3 fermion and the b quark
affects the prediction for R_b. In order to agree with the current limits on
R_b, the mass of this fermion should be at least 12 TeV. The mass of the heavy
Y=4/3 fermion in the two-doublet model is not as sharply constrained by
experiments and can be as light as 2.5 TeV.
