  Working in the framework of the Standard Model Effective Field Theory, we
study chirality-flipping couplings of the top quark to Higgs and gauge bosons.
We discuss in detail the renormalization group evolution to lower energies and
investigate direct and indirect contributions to high- and low-energy
CP-conserving and CP-violating observables. Our analysis includes constraints
from collider observables, precision electroweak tests, flavor physics, and
electric dipole moments. We find that indirect probes are competitive or
dominant for both CP-even and CP-odd observables, even after accounting for
uncertainties associated with hadronic and nuclear matrix elements,
illustrating the importance of including operator mixing in constraining the
Standard Model Effective Field Theory. We also study scenarios where multiple
anomalous top couplings are generated at the high scale, showing that while the
bounds on individual couplings relax, strong correlations among couplings
survive. Finally, we find that enforcing minimal flavor violation does not
significantly affect the bounds on the top couplings.
