Extending the Standard Model Effective Field Theory with the Complete Set of Dimension-7 Operators

TL;DR

This work provides a complete, gauge-invariant basis for dimension-$7$ SMEFT operators built from Standard Model fields. It shows that all dimension-$7$ operators are fermionic and violate lepton number, with a subset also violating baryon number, and it organizes them into six distinct classes guided by hypercharge constraints and SM equations of motion. The resulting set contains $20$ independent operators, enabling detailed studies of baryogenesis, leptogenesis, and other beyond-SM probes within an EFT framework. The analysis also highlights potential model extensions and outlines future theoretical directions, such as computing the one-loop anomalous dimension matrix and exploring holomorphy in the SMEFT at dimension $7$.

Abstract

We present a complete list of the independent dimension-7 operators that are constructed using the Standard Model degrees of freedom and are invariant under the Standard Model gauge group. This list contains only 20 independent operators; far fewer than the 63 operators available at dimension 6. All of these dimension-7 operators contain fermions and violate lepton number, and 7 of the 20 violate baryon number as well. This result extends the Standard Model Effective Field Theory (SMEFT) and allows a more detailed exploration of the structure and properties of possible deformations from the Standard Model Lagrangian.