Flavor Bounds on The ALP–Fermion Couplings Under The “Invisible Axion” Assumption

The present manuscript is a brief, self--contained study of the ALP solution to the Strong CP problem of QCD. The Standard Model is embedded with an ALP via an Effective Field Theory truncated at the lowest non--renormalizable order in the Laurent expansion. The field content and the symmetry group are minimally extended adding a single pseudo--scalar light resonance to the Standard Model, that is the Goldstone boson of an anomalous global $U(1)_\mathrm{PQ}$ symmetry spontaneously broken at some high energy scale $f_a.$ The Effective Field Theory is then evolved along its Renormalization Group flow from this Ultra--Violet scale down to the perturbative limit of QCD. Some attention is dedicated to the non--perturbative regime of Strong Interactions with the QCD--Chiral Lagrangian. Weak annihilation-induced ALP emissions generated by flavor conserving couplings and weak mesonic decays induced by flavor violating ALP couplings are studied in the framework of a single experimental signature. This allows to extract important bounds and correlation information on the low--energy ALP--fermion couplings from flavor factories data. ALP--leptonic final state decays are also studied, a correction on the massless ALP limit and the full mass dependence of the decay width is recovered. This opens up the study for a plethora of signals able to project limits onto ALP--leptons and ALP--quarks parameters.