Gauging Axionic Symmetries and Dark Matter: In memory of George Lazarides

TL;DR

This paper explores the cosmological role of gauged axions in models with anomalous U(1) symmetries, highlighting their potential as dark matter candidates and their unique formation history.

Contribution

It connects the cosmology of gauged axions with anomalous gauge symmetries, Stueckelberg fields, and dark matter, emphasizing the impact of electroweak and QCD misalignments.

Findings

Gauged axions can contribute to dark matter relic abundance with a sufficiently large Stueckelberg scale.

The physical axion-like state emerges after Higgs-Stueckelberg mixing and electroweak symmetry breaking.

The cosmological history of gauged axions differs from that of Peccei-Quinn axions due to their unique formation mechanisms.

Abstract

These notes are written for a memorial Session dedicated to George Lazarides. They revisit a joint work on the cosmology of a gauged axion and place it in a broader line of ideas connecting anomalous gauge symmetries, orientifold effective actions, Stueckelberg fields and dark matter. In models with an anomalous extra $U(1)$ symmetry, the Stueckelberg pseudoscalar participates in the restoration of gauge invariance through Wess-Zumino counterterms and, after electroweak symmetry breaking, may leave a physical axion-like state. Its cosmological history differs from that of an ordinary Peccei-Quinn axion: the physical field appears only after Higgs-Stueckelberg mixing, is subject to sequential electroweak and QCD misalignment, and can give an appreciable dark-matter relic abundance only when the Stueckelberg scale is sufficiently large. This perspective connects naturally with George's earlier insight that the vacuum structure of axion models must be understood together with the gauge structure in which it is embedded. I dedicate these notes to his memory, with gratitude for the collaboration and for the clarity with which he connected particle physics to the early universe.