Is Heavy Quark Axion Necessarily Hadronic Axion?

Abstract

We show that heavy quark axion is not necessarily a hadronic axion, which manifests in the quark and lepton seesaw mechanism. We introduce a heavy $SU(2)$ singlet fermion for each known fermion in order to unify the axion scale and the seesaw scale. The light quarks and leptons gain their masses by the seesaw mechanism. Even though our axion model gives a kind of heavy quark axion, the axion has tree level lepton--axion coupling suppressed by $F_a$, contrary to a widely known belief that heavy quark axions are hadronic.