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

Abstract

The QCD axion with charm-only Peccei-Quinn coupling evades the isospin-violation problem of light-quark models in $\chi$PT. Since $m_c>\Lambda_{\rm QCD}$, 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 $O(1/m_c)$ and manifests via axion-pion mixing with $\theta_{a\pi}\simeq f_\pi/f_a\sim0.04$. We analyze $D$-meson masses, $D$-$D^*$ splitting, charmonium, $D$-$D$ scattering, $B_s$ mixing, rare $D$ decays, and the channels $K^+\to\pi^+a$, $B\to K a$. 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.