  The top quark may hold the key to new physics associated with the electroweak
symmetry-breaking sector, given its large mass and enhanced coupling to the
Higgs sector. We systematically categorize generic interactions of a new
particle that couples to the top quark and a neutral particle, which is assumed
to be heavy and stable, thus serving as a candidate for cold dark matter. The
experimental signatures for new physics involving top quarks and its partners
at the Large Hadron Collider (LHC) may be distinctive, yet challenging to
disentangle. We optimize the search strategy at the LHC for the decay of the
new particle to a top quark plus missing energy and propose the study of its
properties, such as its spin and couplings. We find that, at 14 TeV with an
integrated luminosity of 100 fb^-1, a spin-zero top partner can be observed at
the 5-sigma level for a mass of 675 GeV. A spin-zero particle can be
differentiated from spin-1/2 and spin-1 particles at the 5-sigma level with a
luminosity of 10 fb^-1.
