Flavon VEV scales in U(3)×U(3)‧ model

We have recently proposed a quark and lepton mass matrix model based on U(3)×U(3)‧ family symmetry as the so-called Yukawaon model, in which the U(3) symmetry is broken by VEVs of flavons (Φf)iα which are (3,3∗) of U(3)×U(3)‧. 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. However, our final goal is not only to give well-satisfied fitting of quark and lepton masses and mixings, but also to investigate physics behind such a successful parameter fitting. Therefore, our next concern is scales of VEVs of the flavons because we have not paid attention to scales of flavons in the previous study. In order to give consistency among the scales, the previous flavon model is drastically changed together with economizing number of the flavons, but with keeping previous phenomenological success. We estimate that VEVs of flavons with (8 + 1,1), (3,3∗) and (1,8 + 1) are of the orders of 10 TeV, 10⁴ TeV and 10⁷ TeV, respectively.