Exact accidental U(1) symmetries for the axion

Luc Darmé,Enrico Nardi

doi:10.1103/physrevd.104.055013

Luc Darmé, Enrico Nardi

Open Access

https://doi.org/10.1103/physrevd.104.055013

Copy DOI

Abstract

We study a class of gauge groups that can automatically yield a perturbatively exact Peccei-Quinn symmetry, and we outline a model in which the axion quality problem is solved at all operator dimensions. Gauge groups belonging to this class can also enforce and protect accidental symmetries of the clockwork type, and we present a toy model where an ``invisible'' axion arises from a single low scale breaking of the gauge and global symmetries.

Highlights

The nontrivial structure of the vacuum of Yang-Mills theories [1] implies that CP violation is a built-in feature in QCD [2,3]
Among the deepest new questions stand the very origin of the axion or, more precisely, “which is the origin of the PQ symmetry”? There are good reasons to believe that global symmetries cannot be fundamental, and this is especially true for anomalous symmetries that do not survive at the quantum level
We show that so far an uncharted class of flavor1 gauge symmetries of the form SUðMÞ × SUðNÞ with M ≠ N, that we denote as “rectangular” symmetries, allows us to solve at the root the origin and quality problems by enforcing automatically Uð1Þ symmetries that are either perturbatively exact at the Lagrangian level or that become exact on the vacuum

Summary

INTRODUCTION

The nontrivial structure of the vacuum of Yang-Mills theories [1] implies that CP violation is a built-in feature in QCD [2,3]. A convincing rationale for θ ≈ 0 is provided by the Peccei-Quinn (PQ) mechanism [7,8], which postulates a global Abelian symmetry endowed with a mixed Uð1ÞPQ-SUð3ÞC anomaly and broken spontaneously. A second issue, known as “the PQ symmetry quality problem,” arises because to comply with the bound jθj < 10−10, Uð1ÞPQ must be respected by all effective operators acquiring a vacuum expectation value (VEV) up to dimension D ≳ 11. We point out that rectangular symmetries can prove useful to solve the axion scale problem We illustrate this by constructing a toy model in which a clockwork Uð1ÞPQ arises automatically and is spontaneously broken together with the gauge symmetries by vPQ ≪ va

RECTANGULAR GAUGE GROUPS AND ACCIDENTAL Uð1ÞPQ

Uð1Þ-breaking operators

Vacuum structure of the operators

M arg det

A GAUGE SYMMETRY FOR A CLOCKWORK AXION

CONCLUSIONS