There are three generations of charged leptons - the electron, muon, and tau. Masses of elementary particles are considered as fundamental constants. Modern physics believes these masses could be calculated from more fundamental mass scale, e.g., the Planck mass. Scientists seek for such relationship for many years. However, a relation between mass-spectrum of charged leptons and the Planck mass is still unknown. Here we show a way to derive the mass-spectrum of charged leptons from the Planck mass.

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Lepton-quark symmetry and Barut's lepton mass formula

Mass-spectrum of Charged Leptons from the Planck Mass

An extension of Barut's (1979) lepton mass formula to quark masses, using lepton-quark symmetry is applied to obtain the masses of the third and fourth generation quarks. The t-quark mass is found to be quite a bit smaller than present estimates.

Quark masses using Barut-like mass formula

Using the wave functions and the expressions for the magnetic moments of top hadrons, given in tables I–IV, as well as the estimates of the quark magnetic moments, the numerical values of the magnetic moments of top hadrons can be calculated.

Magnetic moments of top hadrons

https://link.aps.org/pdf/10.1103/PhysRevLett.19.1264

A Model of Leptons

A recently proposed mass formula for the muon is extended to $\ensuremath{\tau}$ and other heavy leptons. It is postulated that a quantized magnetic self-energy of magnitude $\frac{3}{2}{\ensuremath{\alpha}}^{\ensuremath{-}1}{n}^{4}{M}_{e}$, where $n$ is a new quantum number, be added to the rest mass of a lepton to get the next heavy lepton in the chain $e$, $\ensuremath{\mu}$, $\ensuremath{\tau},\ensuremath{\cdots}$, with $n=1$ for $\ensuremath{\mu}$, $n=2$ for $\ensuremath{\tau}$, etc. I predict ${M}_{\ensuremath{\tau}}=1786.08$ MeV, and for the next lepton ${M}_{\ensuremath{\delta}}=10293.7$ MeV.

Lepton-quark symmetry and Barut's lepton mass formula

Citations

Mass-spectrum of Charged Leptons from the Planck Mass

Quark masses using Barut-like mass formula

Magnetic moments of top hadrons

References

A Model of Leptons

Lepton mass formula

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