  We perform a model-independent analysis of the magnetic and electric dipole
moments of the muon and electron. We give expressions for the dipole moments in
terms of operator coefficients of the low-energy effective field theory (LEFT)
and the Standard Model effective field theory (SMEFT). We use one-loop
renormalization group improved perturbation theory, including the one-loop
matching from SMEFT onto LEFT, and one-loop lepton matrix elements of the
effective-theory operators. Semileptonic four-fermion operators involving light
quarks give sizable non-perturbative contributions to the dipole moments, which
are included in our analysis. We find that only a very limited set of the SMEFT
operators is able to generate the current deviation of the magnetic moment of
the muon from its Standard Model expectation.
