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Recently we have proposed mechanisms to explain origins of the charged leptonspectrum as well as Koide's mass formula, on the basis of U(3)\times O(3)family gauge symmetry. In this note, we review the basic ideas of thesemechanisms. Without technical details, and adding some speculations, we give asketch of the mechanisms, what the important points are and what assumptionsare involved.  We adopt a known scenario, in which the charged lepton spectrum is determinedby the vacuum expectation value of a scalar field that takes values on 3-by-3matrix. Within this scenario, we propose a mechanism, in which the radiativecorrection induced by U(3) family gauge interaction cancels the QED radiativecorrection to Koide's mass formula. We consider SU(9)\times U(1) symmetrybroken down to U(3)\times O(3) symmetry. This leads to a potential model whichpredicts Koide's mass formula and the charged lepton spectrum consistent withthe experimental values, by largely avoiding fine tuning of parameters. Theseare discussed within an effective theory, and we argue for its validity andusefulness.

Family Gauge Symmetry as an Origin of Koide's Mass Formula and Charged Lepton Spectrum