  In an attempt to uncover any underlying physics in the standard model (SM),
we suggest a $\mu$--$\tau$ power law in the lepton sector, such that relatively
large 13 mixing angle with bi-large 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 CP problem, in a way that no
domain wall problem occurs, based on $A_{4}\times U(1)_{X}$ 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 each other. So,
the scale of Peccei-Quinn symmetry breaking is shown to be roughly located
around $10^{12}$ 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 axion. We examine the model predictions, arisen from the
$\mu$--$\tau$ 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 $m_a\simeq2.53\times10^{-5}$ eV and the
axion coupling to photon $g_{a\gamma\gamma}\simeq1.33\times10^{-15}~{\rm
GeV}^{-1}$. And subsequently the square of the ratio between them is shown to
be 1 or 2 orders of magnitude lower than that of the conventional axion model.

High Energy Physics - Phenomenology