Renormalization-group equations of the LEFT at two loops: dimension-six operators

TL;DR

This paper calculates two-loop anomalous dimensions for dimension-six operators in the low-energy effective field theory below the electroweak scale, aiding precision tests of physics beyond the Standard Model.

Contribution

It provides the third part of a systematic two-loop calculation of anomalous dimensions for baryon-number conserving dimension-six operators in the LEFT, including corrections for evanescent and chiral-symmetry-breaking effects.

Findings

Computed renormalization of four-fermion and three-gluon operators

Analyzed power corrections to lower-dimension operators

Results support precision low-energy BSM searches

Abstract

We present the third part of a systematic calculation of the two-loop anomalous dimensions for the low-energy effective field theory below the electroweak scale (LEFT): insertions of dimension-six operators that conserve baryon number. In line with our previous publications, we obtain the results in the algebraically consistent 't Hooft-Veltman scheme for $\gamma_5$, corrected for evanescent as well as chiral-symmetry-breaking effects through finite renormalizations. We compute the renormalization of the dimension-six four-fermion and three-gluon operators, as well as the power corrections to lower-dimension operators in the presence of masses, i.e., the down-mixing into dimension-five dipole operators, masses, gauge couplings, and theta terms. Our results are of interest for a broad range of low-energy precision searches for physics beyond the Standard Model.