Flavored Peccei-Quinn symmetry

In an attempt to uncover any underlying physics in the standard model (SM), we suggest a μ--τ power law in the lepton sector, such that relatively large 13 mixing angle with bilarge ones can be derived. On the basis of this, we propose a neat and economical model for both the fermion mass hierarchy problem of the SM and a solution to the strong charge parity ($CP$) problem, in a way that no domain wall problem occurs, based on A₄×U(1)X symmetry in a supersymmetric framework. Here we refer to the global U(1)X symmetry that can explain the above problems as ``flavored Peccei-Quinn symmetry.'' In the model, a direct coupling of the SM gauge singlet flavon fields responsible for spontaneous symmetry breaking to ordinary quarks and leptons, both of which are charged under U(1)X, comes to pass through Yukawa interactions, and all vacuum expectation values breaking the symmetries are connected to each other. So the scale of Peccei-Quinn symmetry breaking is shown to be roughly located around the 10¹² GeV section through its connection to the fermion masses. The model predictions are shown to lie on the testable regions in the very near future through on-going experiments for neutrino oscillation, neutrinoless double beta decay, and the axion. We examine the model predictions, arisen from the μ--τ power law, on leptonic $CP$ violation, neutrinoless double beta decay, and atmospheric mixing angle, and show that the fermion mass and mixing hierarchies are in good agreement with the present data. Interestingly, we show the model predictions on the axion mass mₐ2.53×10^-5 eV and the axion coupling to photon g_aγγ1.33×10^-15 GeV^-1. And subsequently the square of the ratio between them is shown to be one or two orders of magnitude lower than that of the conventional axion model.