Revisiting Renormalization Group Equations of the SMEFT Dimension-Seven Operators

TL;DR

This paper provides the first explicit renormalization group equations for all non-redundant dimension-seven operators in the Standard Model effective field theory, enabling detailed studies of their effects on lepton- and baryon-number-violating processes.

Contribution

It derives the complete one-loop RGEs for dim-7 operators in SMEFT using a physical basis, including mixing effects, which was not previously available.

Findings

Complete RGEs for all non-redundant dim-7 operators obtained.

Analysis confirms consistency with non-renormalization theorem.

Partial validation performed using different tools and gauges.

Abstract

In this work, we revisit the renormalization group equations (RGEs) of dimension-seven (dim-7) operators in the Standard Model effective field theory (SMEFT) resulting from mixing among dim-7 operators themselves by means of the background field method. Adopting a recently proposed physical basis for dim-7 operators, we achieve the explicit RGEs of all non-redundant dim-7 operators in the SMEFT for the first time. Together with those originating from the dim-5 and dim-6 operators, these results constitute the complete RGEs of dim-7 operators, and hence can be exploited to study full RG-running effects on some lepton- or baryon-number-violating processes involving dim-7 operators in the SMEFT, such as neutrino masses, neutrinoless double beta decay, meson and nucleon decays. We perform an analysis of the structure and perturbative power counting of the obtained one-loop anomalous dimension matrix, which is consistent with a non-renormalization theorem and the naive dimension analysis. Additionally, a partial check on some results is carried out by means of different tools and quantum field gauges.