In models with anomalous U(1), the Stueckelberg field yields a physical axion after Higgs mixing that can produce dark matter relics only if the Stueckelberg scale is large enough.
Anomalous U(1)’s, Chern-Simons couplings and the Standard Model
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Gauging Axionic Symmetries and Dark Matter: In memory of George Lazarides
In models with anomalous U(1), the Stueckelberg field yields a physical axion after Higgs mixing that can produce dark matter relics only if the Stueckelberg scale is large enough.