A UNIVERSAL SHAPE OF EMPIRICAL MASS FORMULA FOR ALL LEPTONS AND QUARKS

摘要

A specific universal shape of empirical mass formula is proposed for all leptons ν_1, ν_2, ν_3, 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 approx = 0 (but probably ξ ≠ 0). If for them ξ is put to be exactly 0, then m_τ = 1776.80 MeV is predicted after the input of experimental m_e and m_μ (the central value of experimental m_τ = 1776.99_(-0.26)~(+0.29) MeV corresponds to ξ = 1.8 x 10~(-3) ≠ 0). For neutrinos 1/ξ approx = 0 (but 1/ξ ≠ 0 in the case of normal hierarchy m_(υ_1)~2 < < m_(υ_2)~2 < < m_(υ_3)~2). If for neutrinos 1/ξ is conjectured to be exactly 0, then (m_(υ_1),m_(υ_2),m_(υ3))～ (1.5,1.2,5.1) x 10~(-2) eV are predicted after the input of experimental estimates |m_(υ_2)~2 - m_(υ_1)~2 | ～ 8.0 x 10~(-5) eV~2 and |m_(υ_3)~2 - m_(υ_2)~2| ～ 2.4 x 10~(-3) eV~2. Thus, the mass ordering of neutrino states 1 and 2 is then inverted, while the position of state 3 is normal.