Two- and three-loop anomalous dimensions of Weinberg's dimension-six CP-odd gluonic operator

TL;DR

This paper extends the calculation of anomalous dimensions of Weinberg's CP-odd gluonic operator to two and three loops, revealing significant higher-order corrections with implications for electric dipole moments.

Contribution

It introduces an automated method to compute higher-loop anomalous dimensions of non-renormalisable operators, applied here to the Weinberg operator in QCD and Yang-Mills theory.

Findings

Two-loop anomalous dimension in full QCD calculated.

Three-loop anomalous dimensions in pure Yang-Mills obtained.

Large corrections due to new group invariants observed.

Abstract

We apply a fully automated extension of the $R^*$-operation capable of calculating higher-loop anomalous dimensions of n-point Green's functions of arbitrary, possibly non-renormalisable, local Quantum Field Theories. We focus on the case of the CP-violating Weinberg operator of the Standard Model Effective Field Theory whose anomalous dimension is so far known only at one loop. We calculate the two-loop anomalous dimension in full QCD and the three-loop anomalous dimensions in the limit of pure Yang-Mills theory. We find sizeable two-loop and large three-loop corrections, due to the appearance of a new quartic group invariant. We discuss phenomenological implications for electric dipole moments and future applications of the method.