  We use top quark pair production as a probe of top-philic non-resonant new
physics. Following a low energy effective field theory approach, we calculate
several key observables in top quark pair production at hadron colliders (e.g.,
total cross section, ttbar invariant mass distribution, forward-backward
asymmetry, spin correlations) including the interference of the Standard Model
with dimension-six operators. We determine the LHC reach in probing new physics
after having taken into account the Tevatron constraints. In particular, we
show that the gluon fusion process gg -> ttbar which remains largely
unconstrained at the Tevatron is affected by only one top-philic dimension-six
operator, the chromo-magnetic moment of the top quark. This operator can be
further constrained by the LHC data as soon as a precision of about 20% is
reached for the total ttbar cross-section. While our approach is general and
model-independent, it is particularly relevant to models of Higgs and top
compositeness, which we consider in detail, also in connection with ttbar ttbar
and ttbar bbbar production.
