How light the lepton flavor changing gauge bosons can be

Spontaneous breaking of inter-family (horizontal) gauge symmetries can be at the origin of the mass hierarchy between the fermion families. The corresponding gauge bosons have flavor-nondiagonal couplings which generically induce the flavor changing phenomena, and this puts strong lower limits on the flavor symmetry breaking scales. However, for special choices of chiral horizontal symmetries the flavor changing effects can be naturally suppressed. For the sake of demonstration, we consider the case of leptonic gauge symmetry SU(3)e\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$SU(3)_e$$\end{document} acting between the right-handed leptons and show that the respective gauge bosons can have mass in the TeV range, without contradicting the existing experimental limits.