Perturbative running of the topological angles

TL;DR

This paper investigates the renormalization group flow of topological angles in quantum field theories, revealing they can acquire an additive beta function starting at two-loop order, with implications for CP violation and consistency conditions.

Contribution

It demonstrates that topological angles can develop a two-loop order additive beta function, uniquely determined by a model-independent coefficient, and explores its implications.

Findings

Topological angles can have a non-zero beta function starting at two-loop order.

The beta function is determined by a single model-independent coefficient.

Non-zero beta functions impose constraints on CP-violating operators.

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.