Naturally quality-safe GeV axion with charm coupling

Abstract

The GeV-scale QCD axion -- where Peccei-Quinn (PQ) symmetry is broken by the QCD condensate at $f_a\sim\mathcal{O}(1)$~GeV -- faces a structural isospin problem: the PQ spurion coupling to light quarks ($u,d,s$) breaks $\mathrm{SU}(2)$ isospin, generating an unacceptable $\sim 15\%$ $\pi^0$--$\pi^\pm$ mass splitting. We show that coupling the PQ scalar to the charm quark instead eliminates this violation entirely, and lowering $m_\phi\sim 3$--$4$~MeV makes the charm Yukawa $\kappa_c\propto m_\phi$ perturbative ($\kappa_c<1$). The resulting $f_a\sim\text{GeV}\ll M_{\rm Pl}$ solves the axion quality problem: even the lowest-dimension $d=6$ Planck-suppressed operator gives $m_{\rm PQ}/m_a\sim 10^{-14}$, without any additional symmetry. The model predicts a distinctive {\it negative} $\Delta N_{\rm eff}\sim -0.1$ for $m_\phi\sim 3$~MeV, testable by CMB-S4. The $B\to K\sigma$ penguin predicts $\mathrm{BR}\sim 2\times 10^{-5}$, consistent with the Belle~II evidence for $B^+\to K^+\nu\bar{\nu}$ at $(2.3\pm0.7)\times 10^{-5}$~\cite{BelleII:2024knv}. All ten classes of experimental, astrophysical, and cosmological constraints are satisfied in the viable window $m_\phi\sim 3$--$4$~MeV, with the $B_s$ mixing constraint pending a dedicated lattice calculation.