A universal shape of empirical mass formula for all leptons and quarks

الأصل · EN

A specific universal shape of empirical mass formula is proposed for all leptons ν₁, ν₂, ν₃ and e-, μ-, τ- as well as all quarks u, c, t and d, s, b of three generations, parametrized by three free constants μ, ε, ξ assuming four different triplets of values. Four such triplets of parameter values are determined or estimated from the present data. Mass spectra in the four cases are related to each other by shifting the triplet of parameters μ, ε, ξ. For charged leptons ξ≃ 0 (but probably ξ≠ 0). If for them ξ is put to be exactly 0, then mτ= 1776.80 MeV is predicted after the input of experimental mₑ and mμ (the central value of experimental mτ= 1776.99⁺⁰.²⁹₋₀.₂₆ MeV corresponds to ξ=1.8× 10⁻³≠ 0). For neutrinos 1/ξ≃ 0 (but 1/ξ≠ 0 in the case of normal hierarchy m²ν₁ ≪ m²ν₂ ≪ m²ν₃). If for neutrinos 1/ξ is conjectured to be exactly 0, then (mν₁, mν₂, mν₃) (1.5, 1.2, 5.1)× 10⁻² eV are predicted after the input of experimental estimates |m²ν₂ - m²ν₁| 8.0× 10⁻⁵ eV² and |m²ν₃ - m²ν₂| 2.4× 10⁻³ eV². Thus, the mass ordering of neutrino states 1 and 2 is then inverted, while the position of state 3 is normal.