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.
Highlights
The absence of evidence for beyond-the-Standard Model (BSM) physics in high-energy proton-proton collisions at the LHC, and in large classes of low-energy precision measurements, all indicate that the scale of BSM physics (Λ) is significantly higher than the electroweak scale (v): Λ ≫ v ≃ 246 GeV
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
The Levi-Civita tensor appearing in the Weinberg operator is not strictly defined in D dimensions and one must fix a scheme when encountering it within dimensional regularization
Summary
The absence of evidence for beyond-the-Standard Model (BSM) physics in high-energy proton-proton collisions at the LHC, and in large classes of low-energy precision measurements, all indicate that the scale of BSM physics (Λ) is significantly higher than the electroweak scale (v): Λ ≫ v ≃ 246 GeV. In such a scenario, the effects of BSM physics at low energies E ≪ Λ can be described in terms of effective operators consisting of SM fields that obey the SM gauge and Lorentz symmetries [1,2,3]. The RGEs depend on anomalous dimensions that can be calculated in perturbation theory
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