  Two categories of four-fermion SMEFT operators are semileptonic (two quarks
and two leptons) and hadronic (four quarks). At tree level, an operator of a
given category contributes only to processes of the same category. However,
when the SMEFT Hamiltonian is evolved down from the new-physics scale to low
energies using the renormalization-group equations (RGEs), due to operator
mixing this same SMEFT operator can generate operators of the other category at
one loop. Thus, to search for a SMEFT explanation of a low-energy anomaly, or
combination of anomalies, one must: (i) identify the candidate semileptonic and
hadronic SMEFT operators, (ii) run them down to low energy with the RGEs, (iii)
generate the required low-energy operators with the correct Wilson
coefficients, and (iv) check that all other constraints are satisfied. In this
paper, we illustrate this method by finding all SMEFT operators that, by
themselves, provide a combined explanation of the (semileptonic) $\bar b \to
\bar s \ell^+ \ell^-$ anomalies and the (hadronic) $B \to K \pi$ puzzle.
