Small-instanton effects in an atlas of KSVZ axion models

Abstract

We investigate small-instanton contributions to the axion potential across a range of KSVZ models containing vector-like quarks~(VQs), using naive dimensional analysis. We consider scenarios containing a single VQ, multiple identical copies, and sets of distinct VQs, requiring in each case that the gauge couplings remain perturbative up to the Planck scale under the two-loop gauge running. The associated fermion zero-mode content varies between these cases, requiring different combinations of mass insertions and scalar--Yukawa contractions for its saturation. Increasing the copies of VQs can render the instanton-size integral dominated by instantons of the smallest size, corresponding to the scale near the ultraviolet~(UV) cut-off. The resulting contribution then becomes sensitive to the UV completion and the induced potential can compete with, or dominate over, the ordinary QCD contribution. Assuming that the QCD and small-instanton potentials are aligned, we determine the resulting axion-mass shift and its consequences for the axion--photon coupling. When the small-instanton induced susceptibility becomes comparable to or larger than the QCD susceptibility, the physical axion mass of $m_a$ is enhanced at fixed decay constant~$f_a$, while the axion-photon of $g_{a\gamma\gamma}$ coupling remains controlled by $f_a$ and the anomaly ratio of $E/N$. The standard QCD relation among $m_a$, $f_a$ and $g_{a\gamma\gamma}$ is consequently modified, opening new regions of the $(m_a,g_{a\gamma\gamma})$ plane for axion searches.