A Geometric Picture for Fermion Masses

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 μ and τ neutrinos, ( mνμ/mντ ) ≤ (9.6 ± 0.6) × 10. The Standard Model [1, 2] of strong and electroweak interactions describes accurately all the observed phenomena of elementary particles. In this framework, the fermion masses are essentially free parameters that must be fixed by experiment. Many efforts have been devoted to find relations among fermion masses, empirically and/or theoretically. For example, a composite model for “fundamental” fermions proposed in [3] predicts the following relation among the masses of the three generations of quarks and leptons mf(3) ∼ √