Charged lepton mass sum rule from U(3) family Higgs potential model

It is pointed out that if we assume U(3)-family nonet Higgs scalars which couple to charged leptons bilinearly, a simple Higgs potential with a term which breaks the U(3)-family into SU(3)-family will lead to a mass sum rule,

m_e +m_\mu +m_\tau =(2/3) (\sqrt{m_e} +\sqrt{m_\mu} +\sqrt{m_\tau})^2

. This sum rule is in excellent agreement with experiment. The sum rule is also in good agreement with experiment when applied to the masses of down-quarks, d, s, and b.

lepton: mass
mass: lepton
lepton: mass formula
mass formula: lepton
lepton: charged particle
sum rule
symmetry breaking: U(3)
potential: Higgs
quark: mass
mass: quark

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