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

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Sumino, Y.

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Koide's mass formula is an empirical relation among the charged lepton masses
which holds with a striking precision. We present a model of charged lepton
sector within an effective field theory with U(3) \times SU(2) family gauge
symmetry, which predicts Koide's formula within the present experimental
accuracy. Radiative corrections as well as other corrections to Koide's mass
formula have been taken into account. We adopt a known mechanism, through which
the charged lepton spectrum is determined by the vacuum expectation value of a
9-component scalar field \Phi. On the basis of this mechanism, we implement the
following mechanisms into our model: (1) The radiative correction induced by
family gauge interaction cancels the QED radiative correction to Koide's mass
formula, assuming a scenario in which the U(3) family gauge symmetry and
SU(2)_L weak gauge symmetry are unified at 10^2-10^3 TeV scale; (2) A simple
potential of \Phi invariant under U(3) \times SU(2) leads to a realistic
charged lepton spectrum, consistent with the experimental values, assuming that
Koide's formula is protected; (3) Koide's formula is stabilized by embedding
U(3) \times SU(2) symmetry in a larger symmetry group. Formally fine tuning of
parameters in the model is circumvented (apart from two exceptions) by
appropriately connecting the charged lepton spectrum to the boundary (initial)
conditions of the model at the cut-off scale.

Comment: 37 pages, 9 figures; Sec.2 added; arguments added in Secs.5 and 7; Version to appear in JHEP

Comment: 37 pages, 9 figures; Sec.2 added; arguments added in Secs.5 and 7; Version to appear in JHEP

##### Keywords

High Energy Physics - Phenomenology