Galactic dynamo and nucleosynthesis limit on the Dirac neutrino masses

The dynamo mechanism for generating the magnetic fields of galaxies requires the existence of a primordial seed field, which induces oscillations between the left- and right-handed Dirac neutrinos. We consider the excitation of the right-handed neutrinos in the early Universe due to these oscillations and show that nucleosynthesis sets stringent upper limit on the size of the neutrino magnetic moments: ${\mathrm{\mu }}_{\nu }$≲6.5×${10}^{\mathrm{-}34}$ ${\mathrm{\mu }}_{\mathit{B}}$ [1 G/${\mathit{B}}_{\mathrm{seed}}$(${\mathit{T}}_{\mathrm{now}}$)]. In the standard model these limits can be translated to a constraint on the neutrino masses, given by ${\mathit{tsumm}}_{\nu \mathit{i}}$(2.1×${10}^{\mathrm{-}15}$ eV) [1 G/${\mathit{B}}_{\mathrm{seed}}$(${\mathit{T}}_{\mathrm{now}}$)]. We also set upper limits on the transition magnetic moments.