1. On the neutrino and electron masses in the theory of scale relativity
- Author
-
Nottale, Laurent, HEP, INSPIRE, Laboratoire Univers et Théories (LUTH (UMR_8102)), Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de Paris, and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7)
- Subjects
fundamental constant: fine structure ,General Physics (physics.gen-ph) ,Physics - General Physics ,relativity theory ,[PHYS.PHYS.PHYS-GEN-PH] Physics [physics]/Physics [physics]/General Physics [physics.gen-ph] ,electron: mass ,High Energy Physics::Phenomenology ,scale: Planck ,FOS: Physical sciences ,neutrino: mass ,neutrino: oscillation ,[PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph] ,experimental results - Abstract
We have long ago derived a theoretical relation between the mass of the electron and the fine structure constant \cite{Nottale1994}, which writes to lowest order $\alpha \ln (m_{\mathbb{P}}/m_e) = 3/8$ (where $m_{\mathbb{P}}$ is the Planck mass). We suggest the existence of a similar relation valid for neutrinos, $\alpha \ln ({m_{\mathbb{P}}}/{m_\nu} ) =1/2$. From this relation, we theoretically predict a lightest neutrino mass $m_{\nu} = m_{\mathbb{P}}\exp (-\alpha^{-1}/2 )=0.0214$ 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., Comment: 12 pages, 2 figures
- Published
- 2021