ALP interactions with mesons and baryons at $\mathcal{O}(1/f_a)$: a general field redefinition invariant approach

Abstract: We develop a field-redefinition-invariant description of hadronic amplitudes outside the WZW sector at $\mathcal{O}(1/f_a)$, including general flavour-conserving and flavour-changing quark couplings. Starting from the most general CP-conserving Lagrangian for ALP interactions with the QCD sector, we identify invariant Wilson coefficient combinations and match them onto the $U(3)$ chiral theory. Using LSZ reduction, we choose fields for which ALP--meson mixing vanishes at this order; amplitudes then depend only on direct invariant couplings, while the anomalous gluonic interaction remains encoded in the $U(1)_A$ sector. For the baryon octet, we derive the general vector and axial couplings and identify, to our knowledge for the first time, an independent invariant ALP--baryon interaction from a second topological singlet structure in the $U(3)$ baryon Lagrangian. We constrain flavour-changing couplings with rare hyperon decays and show in an explicit ultraviolet model that running and matching can generate them from flavour-diagonal high-scale couplings. Finally, we estimate baryon--antibaryon widths and find that, in a gluophilic benchmark, their sum can exceed individual exclusive mesonic widths for $2~\text{GeV} \le m_a \le 3~\text{GeV}$.