  Effective interactions involving both the top quark and the Higgs field are
among the least constrained of all possible (gauge invariant) dimension-six
operators in the Standard Model. Such a handful of operators, in particular the
top quark chromomagnetic dipole moment, might encapsulate signs of the new
physics responsible for electroweak symmetry breaking. In this work, we compute
the contributions of these operators to inclusive Higgs and t tbar h
production. We argue that: i) rather strong constraints on the overall size of
these operators can already be obtained from the current limits/evidence on
Higgs production at the LHC; ii) t tbar h production will provide further key
information that is complementary to t tbar measurements, and the possibility
of discriminating among different contributions by performing accurate
measurements of total and differential rates.
