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We apply a fully automated extension of the $R^*$-operation capable ofcalculating higher-loop anomalous dimensions of n-point Green's functions ofarbitrary, possibly non-renormalisable, local Quantum Field Theories. We focuson the case of the CP-violating Weinberg operator of the Standard ModelEffective Field Theory whose anomalous dimension is so far known only at oneloop. We calculate the two-loop anomalous dimension in full QCD and thethree-loop anomalous dimensions in the limit of pure Yang-Mills theory. We findsizeable two-loop and large three-loop corrections, due to the appearance of anew quartic group invariant. We discuss phenomenological implications forelectric dipole moments and future applications of the method.

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