Theoretical prediction of neutrino and electron mass in the theory of scale relativity
Résumé
We have long ago, in the framework of the scale relativity theory, derived a theoretical relation between the mass of the electron and the fine structure constant [1], which writes to lowest order 8 3 α ln(m P /m e) = 1 (where m P is the Planck mass). This relation is improved by taking account of threshold effects on the running charge and mass at the electron Compton scale, leading to an agreement with the experimental values at the 10 −5 level. Then we suggest the existence of a similar relation valid for neutrinos, which writes 2α ln(m P /m ν) = 1. From this relation, we theoretically predict a lightest neutrino mass m ν = m P exp(−α −1 /2) = 0.0214 eV. The masses of the two heavier neutrinos, 0.0231 eV and 0.0552 eV, can then be obtained from experimental results of neutrino oscillations.
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