Flavon VEV Scales in U(3)$\times$U(3)${}^{\mathrm{\prime }}$ Model

We have already proposed a quark and lepton mass matrix model based on U(3)$\times$U(3)${}^{\mathrm{\prime }}$ family symmetry as the so-called Yukawaon model, in which the U(3) symmetry is broken by VEVs of flavons $({\mathrm{\Phi }}_f{)}_i^{\alpha }$ which are $(\mathbf{3},{\mathbf{3}}^{\ast })$ of U(3)$\times$U(3)${}^{\mathrm{\prime }}$. The model has successfully provided the unified description of quark and lepton masses and mixings by using the observed charged lepton masses as only family-number dependent input parameters. Our next concern is scales of VEVs of the flavons. In the present paper, we estimate the magnitudes of the VEV scales of flavons of the model which is newly reconstructed without changing the previous phenomenological success of parameter fitting for masses and mixings of quarks and leptons. We estimate that VEVs of flavons with $(\mathbf{8}+\mathbf{1},\mathbf{1})$, $({\bf 3}, {\bf 3}^*)$,and$({\bf 1}, {\bf 8+1})$areof25theordersof$10$TeV,$10^4$ TeV, and ${10}^7$ TeV, respectively.