Equations of Motion for the Standard Model Effective Field Theory: Theory and Applications

The equations of motion for the Standard Model Effective Field Theory (SMEFT) differ from those in the Standard Model. Corrections due to local contact operators modify the equations of motion and impact matching results at sub-leading order in the operator expansion. As a consequence, a matching coefficient in $\mathcal{L}^{(n)}$ (for operators of dimension $n$) can be dependent on the basis choice for $\mathcal{L}^{(m<n)}$. We report the SMEFT equations of motion with corrections due to $\mathcal{L}^{(5,6)}$. We demonstrate the effect of these corrections when matching to sub-leading order by considering the interpretation of recently reported $B \to K^{(*)} \ell^+ \ell^-$ lepton universality anomalies in the SMEFT.