  Ongoing LHC searches for the standard model Higgs Boson in WW or ZZ decay
modes strongly constrain the top-Higgs state predicted in many models with new
dynamics that preferentially affects top quarks. Such a state couples strongly
to top-quarks, and is therefore produced through gluon fusion at a rate that
can be greatly enhanced relative to the rate for the standard model Higgs
boson. As we discuss in this talk, a top-Higgs state with mass less than 300
GeV is excluded at 95% CL if the associated top-pion has a mass of 150 GeV, and
the constraint is even stronger if the mass of the top-pion state exceeds the
top-quark mass or if the top-pion decay constant is a substantial fraction of
the weak scale. These results have significant implications for theories with
strong top dynamics, such as topcolor-assisted technicolor, top-seesaw models,
and certain Higgsless models.
