We discuss the construction of the most general CP-violating chiral Lagrangian for an axion-like particle (ALP). Starting with an effective Lagrangian containing light quarks and gluons, we provide its matching onto a chiral effective Lagrangian at \( \mathcal{O} \) (p2) described in terms of mesons and baryons, identifying the correspondence between the Jarlskog invariants of the two theories. After deriving the ALP interactions with mesons and baryons, we analyse a few relevant phenomenological implications such as the permanent electric dipole moments of nucleons and the CP-violating ALP and kaon decays. This work provides the necessary tools for further phenomenological analyses connecting low-energy observables with the couplings of the underlying ultraviolet complete theory.
