Heavy meson chiral perturbation theory constraints on a charm-coupled GeV-scale QCD axion

The QCD axion with charm-only Peccei-Quinn coupling evades the isospin-violation problem of light-quark models in $\chi$PT. Since $m_c>{\mathrm{\Lambda }}_{\mathrm{Q}\mathrm{C}\mathrm{D}}$, we employ heavy meson chiral perturbation theory (HMChPT) to constrain this GeV-scale axion, including its CP-even radial partner $\sigma$ and the axion $a$. In HMChPT, $\sigma$ enters at leading order with $O(1)$ coupling, while $a$ couples only at $O(1\mathrm{/}{m}_c)$ and manifests via axion-pion mixing with ${\theta }_{a\pi }\simeq f_{\pi }\mathrm{/}{f}_a\sim 0.04$. We analyze $D$-meson masses, $D$-$D^{\ast }$ splitting, charmonium, $D$-$D$ scattering, $B_s$ mixing, rare $D$ decays, and the channels $K^{+}\to {\pi }^{+}a$, $B\to Ka$. No fatal HMChPT constraint emerges, unlike the $\chi$PT isospin issue. The strongest bound is from $\sigma$-mediated $B_s$-${\bar{B}}_s$ mixing; axion-pion mixing opens testable rare decays, though rates are slightly below current sensitivity.