Form of axion in DFSZ models with $$U(1)_{PQ}$$ symmetry

Abstract The physical state of the axion in the DFSZ model is determined by exact diagonalization of the mass mixing matrix in the CP-odd sector, where the Peccei–Quinn (PQ) mechanism is applied to determine the PQ charges of the model’s particles. The PQ charges of all fields are parametrized solely by the PQ charge of the singlet scalar and the mixing angle between the two neutral components of the doublet scalars. The physical forms of the axion are defined using the PQ charges of the scalars alongside the general axion parametrization. Both approaches yield consistent and physically reasonable axion states. The constraint on the PQ charge in the DFSZ- I model is also discussed. Furthermore, using an approximated axion state that retains only the imaginary component of the singlet scalar, the anomalous axion–photon–photon coupling is re-examined by utilizing the defined PQ charges of the model’s fermions. Finally, using the exact physical state, the triple couplings of the axion with two Standard Model (SM) fermions are studied, and the axion decay into a pair of photons is evaluated via the renormalizable interactions arising from the kinetic terms of the scalar fields.