The Too Visible QCD Axion

TL;DR

This paper investigates the challenges of a GeV-scale QCD axion model, highlighting structural issues that prevent resolving pion mass splitting and constraints from fifth-force experiments, thus questioning its viability.

Contribution

The study analyzes extensions to Murayama's axion model, revealing fundamental obstructions due to symmetry breaking that hinder solving key phenomenological problems.

Findings

The model predicts an unacceptably large pion mass splitting.

Structural obstructions prevent resolving the pion splitting issue.

Light axion scenarios are excluded by fifth-force constraints.

Abstract

Murayama proposed a GeV-scale axion theory where the up-quark mass term is generated dynamically by the QCD chiral condensate, spontaneously breaking a Peccei-Quinn symmetry. It predicts a too large mass splitting between neutral and charged pions. Trying to solve this problem we explore extensions. Despite some partial improvements, we identify a structural obstruction: the new Peccei-Quinn spurion breaks the accidental isospin symmetry of the chiral Lagrangian, leading to an enhanced higher-order operator. As a consequence, pion scatterings too are distorted. We also examine the limit in which the axion becomes light, finding that it is excluded by fifth-force constraints.