  LHC searches for the standard model Higgs Boson in WW or ZZ decay modes place
strong constraints on the top-Higgs state predicted in many models with new
dynamics preferentially affecting top quarks. Such a state couples strongly to
top-quarks, and is therefore produced through gluon fusion at a rate enhanced
relative to the rate for the standard model Higgs boson. 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.
