Small Instanton Effects on Composite Axion Mass

TL;DR

This paper examines how small instanton effects influence the axion mass in composite axion models, finding these effects are negligible due to global symmetries, which has implications for axion physics and model building.

Contribution

It demonstrates that in Composite Accidental Axion models, small instanton effects are suppressed by global chiral U(1) symmetries, clarifying their role in axion mass generation.

Findings

Small instanton effects are negligible compared to QCD effects.

Global chiral U(1) symmetries suppress instanton contributions.

Insights into dynamics of composite axion models and instanton effects.

Abstract

This paper investigates the impact of small instanton effects on the axion mass in composite axion models. In particular, we focus on the Composite Accidental Axion (CAA) models, which are designed to address the axion quality problem, and where the Peccei-Quinn (PQ) symmetry emerges accidentally. In the CAA models, the QCD gauge symmetry is embedded in a larger gauge group at high energy. These models contain small instantons not included in low-energy QCD, which could enhance the axion mass significantly. However, in the CAA models, our analysis reveals that these effects on the axion mass are non-vanishing but are negligible compared to the QCD effects. The suppression of the small instanton effects originates from the global chiral U(1) symmetries which are not broken spontaneously and play a crucial role in eliminating $\theta$-terms in the hidden sectors through anomalies. We find these U(1) symmetries restrict the impact of small instantons in hidden sectors on the axion mass. Our study provides crucial insights into the dynamics within the CAA models and suggests broader implications for understanding small instanton effects in other composite axion models.