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

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Original languageEnglish
Article number016010
JournalPhysical Review D
Publication statusPublished - 15 Jul 2020


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 nonrenormalizable, 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 sizable 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.

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  • hep-ph

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