The Too Visible QCD Axion

TL;DR

The paper scrutinizes Murayama's GeV-scale QCD axion model in which the up-quark mass is generated dynamically by the QCD condensate via a PQ scalar. It shows that the associated PQ spurion inevitably breaks isospin in the chiral Lagrangian, introducing a dominant higher-order operator that yields order-one corrections to both pion masses and pion-pion scattering, conflicting with precise low-energy meson data. While various PQ-charge generalizations can mildly mitigate the tension, none sufficiently resolves the pion-mass problem, and the Kaplan–Manohar ambiguity or loop corrections fail to fully restore agreement. In the heavy-PQ-scalar regime the effective chiral theory inherits new PQ-invariant operators that continue to distort meson observables, and in the light-invisible axion limit the accompanying light scalar mediates a fifth force tightly constrained by experiments, effectively ruling out this class of models. The authors conclude that realizing a QCD-scale axion in this framework is strongly constrained or excluded, and the remaining viable path would be a DFSZ-like scenario with a larger spontaneous PQ breaking scale.

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.