Dimension-8 Operators in the Standard Model Effective Field Theory

TL;DR

This work provides a complete basis of dimension-8 operators in the Standard Model Effective Field Theory (SMEFT), including operators that vanish without flavor structure, totaling $N_{op}=44{,}807$ for $n_g=3$. It systematically classifies operators into 21 classes across bosonic, two-fermion, and four-fermion sectors, using tools such as BasisGen and Sym2Int to ensure independence under IBP and EOM. The authors connect the basis to phenomenology, notably light-by-light scattering and electroweak precision data via geoSMEFT, and they illustrate dim-8 effects through a scalar SU(2) quartet model, finding that such scenarios do not dramatically enhance double-Higgs production. They also discuss the expected structure of dimension-8 RGE, emphasizing the interplay with dimension-6 contributions and non-renormalization constraints. Overall, the paper provides a robust, non-redundant foundation for exploring high-dimension SMEFT effects in precision and collider contexts.

Abstract

We present a complete basis of dimension-8 operators in the Standard Model Effective Field Theory. Attention is paid to operators that vanish in the absence of flavor structure. There are dimension-8 SMEFT 44,807 operators. We also briefly discuss a few aspects of phenomenology involving dimension-8 operators, including light-by-light scattering and electroweak precision data.