Probing axion in the DFSZ model

We show that with the introduction of new right-handed neutrinos $N_R$, the Peccei--Quinn ($PQ$) transformation in the DFSZ (Dine--Fischler--Srednicki--Zhitnitsky) model depends only on the $PQ$ charge of the scalar singlet $\phi$, namely $PQ_\phi$, and is independent of the sine and cosine of $\arctan(v_u/v_d)$. The model consists of four new scalars: a charged Higgs boson $H^\pm$, a CP-odd scalar $A$, and two CP-even scalars with masses at the EW scale (of a few hundred GeV), and a superheavy inflaton $\Phi$. The scalar fields have been presented in the form of unitary matrices, in which there is no mixing between the axion and the Goldstone boson $G_Z$. As a result, there are two kinds of couplings between the axion and fermions, namely Yukawa-like interactions and anomaly-induced ones associated with derivative axion couplings. {The model belongs to the DFSZ I kind since the axion - photon coupling with $\fr E N = \fr 8 3$.} The trilinear Higgs self-coupling is investigated. We have shown that, in the parameter region where new scalar fields such as the singly charged Higgs boson $H^\pm$ and the CP-odd scalar $A$ have masses around 150 GeV and the vacuum expectation value of one Higgs doublet ($v_u$) is of the order of a few GeV, the coupling modifier $\kappa_\lambda$-a probe of new physics-is consistent with the current experimental constraints.