Barut´s Lepton Mass Formula, Its Correction, and the Deduction of the Proton Mass.
Osvaldo F. Schilling · viXra · 2018
In a PRL published in 1979 A.O.Barut proposed a lepton mass formula of the form m(n)= 3/(2 alpha)n^4 Me , where Me is the electron mass, alpha is the fine-structure constant and n is an integer, with increasing leptons masses obtained from the values for m(n) added in sequence of n to Me . Such model assumes the leptons excess mass m(n) comes from kinetic-magnetic energies and arises from a coupling between the electron magnetic moment and the resulting magnetic field. The formula is good for the muon, with n=1. However, we show that the n-dependence in this formula should be n^2 rather than n^4( the proposed fourth power is incorrect !). Such correction makes Barut´s model formula consistent with the energies obtained for the physically analogous superconducting loop case, treated theoretically by Byers and Yang, which scales as n^2. We apply the corrected formula and reobtain the mass for the tau-lepton, now corresponding to n=4 and not 2, and for n=3 a “proton” with m ≈ 945 Mev/c^2 mass.