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Neutrino Magnetic Moment and Mass: an Update

In 1977 an expression for the magnetic moment of a massive Dirac neutrino was deduced in the context of electroweak interactions at the one-loop level. A linear dependence on the neutrino mass was found. Alternatively, a magnetic moment for a massive neutrino arising from gravitational origin is predicted by the so-called Wilson-Blackett law. The latter relation may also be deduced from a gravitomagnetic interpretation of the Einstein equations. Both formulas for the magnetic moment can be combined, yielding a value for the smallest neutrino mass m1. 
 
The gravitomagnetic moment, i.e., the magnetic moment from gravitational origin, may contain different g-factors for the massive neutrino eigenstates m1, m2 and m3, respectively. Starting from the Dirac equation, a g-factor g = 2 has been deduced for a neutrino in first order, related to the derivation of the g-factor of charged leptons. When a value g = 2 is inserted, a value of 1.530 meV is obtained for the lightest neutrino mass m1, the main result of this work. The remaining neutrino masses can then be calculated from observed neutrino oscillations. The so-called geometric mean mass relation between the three neutrino masses appears to be in fair agreement with our results. A possible dependence of the neutrino mass on the electroweak coupling constant is discussed. 
 
The neutrino with the smallest mass m1 may also possess the smallest magnetic moment of all known elementary particles. Its gravitomagnetic formula is a combination of three Planck units.