  We study a "heavy" QCD axion whose coupling to the standard model is
dominated by $a G \widetilde{G}$ but with $m_a \gg m_\pi f_\pi / f_a$. This is
well motivated theoretically as it can evade the infamous axion quality
problem. It also poses interesting challenges for its experimental search due
to its suppressed couplings to photons and leptons. Such axion with mass around
a GeV is kinematically inaccessible or poorly constrained by most experimental
probes except B-factories. We study $B \to K a$ transitions as a powerful probe
of the heavy QCD axion by performing necessary 2-loop calculations for the
first time. We find some of the existing limits are enhanced. For forthcoming
data sets of the Belle II experiment, we provide a projection that $f_a$ of a
few TeV is within its future reach, which is relevant to the quality problem.
