# Flavon VEV Scales in U(3)$\times$U(3)$'$ Model

## TL;DR

This paper estimates the energy scales of flavon VEVs in a U(3)×U(3)' family symmetry model, maintaining its successful predictions for quark and lepton masses and mixings.

## Contribution

It reconstructs the flavon VEV scale estimates within a previously successful model without altering its phenomenological results.

## Key findings

- VEV scale for ({f 8+1}, {f 1}) flavons is about 10 TeV.
- VEV scale for ({f 3}, {f 3}^*) flavons is about 10^4 TeV.
- VEV scale for ({f 1}, {f 8+1}) flavons is about 10^7 TeV.

## Abstract

We have already proposed a quark and lepton mass matrix model based on U(3)$\times$U(3)$'$ family symmetry as the so-called Yukawaon model, in which the U(3) symmetry is broken by VEVs of flavons $(\Phi_f)_i^{\ \alpha}$ which are $({\bf 3}, {\bf 3}^*)$ of U(3)$\times$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. 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 $({\bf 8+1}, {\bf 1})$, $({\bf 3}, {\bf 3}^*)$, and $({\bf 1}, {\bf 8+1})$ are of 25the orders of $10$ TeV, $10^4$ TeV, and $10^7$ TeV, respectively.