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arXiv · 1907.04923

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

Jordy de Vries·Giulio Falcioni·Franz Herzog·Ben Ruijl
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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.

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Jordy de Vries, Giulio Falcioni, Franz Herzog, Ben Ruijl. 2019-07-10. Two- and three-loop anomalous dimensions of Weinberg's dimension-six CP-odd gluonic operator. https://doi.org/10.1103/physrevd.102.016010

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