Renormalization Group Equations for the Dimension-7 SMEFT Operators

TL;DR

This paper develops bases and renormalization group equations for dimension-7 operators in the SMEFT, enabling detailed analysis of their effects on lepton- and baryon-number-violating processes.

Contribution

It introduces new bases for dim-7 SMEFT operators and derives complete one-loop RGEs including mixing among different operator dimensions.

Findings

Complete one-loop RGEs for dim-5 and dim-7 operators are obtained.

Relations between Green's basis and physical basis are established.

Results facilitate studies of lepton- and baryon-number-violating processes.

Abstract

In this talk, a Green's basis and a new physical basis for dimension-seven (dim-7) operators in the Standard Model effective field theory (SMEFT) are proposed. The reduction relations between those two bases are also presented, where some redundant dim-6 operators in the Green's basis are involved if the dim-5 operator exists. Taking advantage of these two bases for dim-7 operators and the associated reduction relations, we work out the complete one-loop renormalization group equations (RGEs) for dim-5 and dim-7 operators up to $\mathcal{O} \left( \Lambda^{-3} \right)$ in the SMEFT, including not only the mixing among the same dimensional operators but also that among different dimensional ones. These results can be exploited to study full one-loop RG effects on some lepton- or baryon-number-violating processes up to $\mathcal{O} \left( \Lambda^{-3} \right)$ in the SMEFT, such as neutrino masses, neutrinoless double beta decay, meson and nucleon decays.