Axions and anomalous $U(1)$'s

TL;DR

This paper explores the existence and properties of axions in string-inspired models with anomalous U(1) gauge groups, focusing on their potential to solve the strong CP problem and their phenomenological implications.

Contribution

It clarifies how light axions naturally emerge in such models and analyzes their masses and couplings, especially in relation to nonperturbative effects and supersymmetry breaking.

Findings

Light axions can arise from anomalous U(1) models with charged scalars.

In minimal models, axion mass is linked to supersymmetry breaking scale.

Extended models can produce intermediate-scale axion decay constants.

Abstract

Inspired by recent studies of high-scale decay constant or flavorful QCD axions, we review and clarify their existence in effective string models with anomalous $U(1)$ gauge groups. We find that such models, when coupled to charged scalars getting vacuum expectation values, always have one light axion, whose mass can only come from nonperturbative effects. If the main nonperturbative effect is from QCD, then it becomes a Peccei-Quinn axion candidate for solving the strong CP problem. We then study simple models with universal Green-Schwarz mechanism and only one charged scalar field: in the minimal gaugino condensation case the axion mass is tied to the supersymmetry breaking scale and cannot be light enough, but slightly refined models maintain a massless axion all the way down to the QCD scale. Both kinds of models can be extended to yield intermediate scale axion decay constants. Finally, we gauge flavorful axion models under an anomalous $U(1)$ and discuss the axion couplings which arise.