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

TL;DR

This paper derives the corrected equations of motion for the Standard Model Effective Field Theory, highlighting how contact operators influence matching procedures and basis dependence, with applications to recent B-meson decay anomalies.

Contribution

It provides the SMEFT equations of motion including corrections from dimension-5 and dimension-6 operators, clarifying their impact on matching and basis dependence.

Findings

Corrected equations of motion for SMEFT with contact operator effects

Demonstrated basis dependence in matching coefficients

Applied results to interpret B-meson decay anomalies

Abstract

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.