A Geometric Picture For Fermion Masses

Abstract

We describe a geometric picture for the pattern of fermion masses of the three generations which is invariant with respect to the renormalization group below the electroweak scale. Moreover, we predict the upper limit for the ratio between the Dirac masses of the $\mu$ and $\tau$ neutrinos, $m_{{\nu }_{\mu }}/m_{{\nu }_{\tau }}<(9.6\pm 0.6)10^{-3}$.

7 pages LATEX + 1 figure

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• The strange formula of Dr. Koide
• Lorentz group and mass spectrum of elementary particles
• Determining quark and lepton mass matrices by a geometrical interpretation
• A modified version of the Koide formula from flavor nonets in a scalar potential model and in a Yukawaon model