  The Standard Model Effective Field Theory (SMEFT) offers a powerful
theoretical framework for parameterizing the low-energy effects of heavy new
particles with masses far above the scale of electroweak symmetry breaking.
Additional light degrees of freedom extend the effective theory. We show that
light new particles that are weakly coupled to the SM via non-renormalizable
interactions induce non-zero Wilson coefficients in the SMEFT Lagrangian via
renormalization-group evolution. For the well-motivated example of axions and
axion-like particles (ALPs) interacting with the SM via classically
shift-invariant dimension-5 interactions, we calculate how these interactions
contribute to the one-loop renormalization of the dimension-6 SMEFT operators,
and how this running sources additional contributions to the Wilson
coefficients on top of those expected from heavy new states. As an application,
we study the ALP contributions to the magnetic dipole moment of the top quark
and comment on implications of electroweak precision constraints on ALP
couplings.
