Perturbative running of the topological angles

Abstract

We argue that in general renormalizable field theories the topological angles may develop an additive beta function starting no earlier than 2-loop order. The leading expression is uniquely determined by a single model-independent coefficient. The associated divergent diagrams are identified and a few independent methods for extracting the beta function in dimensional regularization are discussed. We show that the peculiar nature of the topological angles implies non-trivial constraints on the anomalous dimension of the CP-violating operators and discuss how a non-vanishing beta function affects the Weyl consistency conditions. Some phenomenological considerations are presented.

19 pages plus appendix, 1 figure. v2: version published in JHEP

References in corpus (3)

• The CKM Phase and $\bar{\theta }$ in Nelson-Barr Models
• The local RG equation and chiral anomalies
• Renormalization of the topological charge density in QCD with dimensional regularization

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• Two-loop corrections to QCD $\theta$ angle from evanescent operator in the BMHV scheme
• Effective description of Nelson-Barr models and the theta parameter
• Nelson-Barr Models with Vector-Like Quark Doublets
• Weak Scale Triggers in the SMEFT