  Searches for new physics in the top quark sector are of great theoretical
interest, yet some powerful avenues for discovery remain unexplored. We
characterize the expected statistical power of the LHC dataset to constrain the
single production of heavy top partners $T$ decaying to a top quark and a
photon or a top quark and a gluon. We describe an effective interaction which
could generate such production, though the limits apply to a range of
theoretical models. We find sensitivity to cross sections in the
$10^{2}-10^{5}$ fb range, for $T$ masses between 300 and 1000 GeV, depending on
decay mode.
