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: μ_ν{}6.5×{}10^-34{{{μ}}}B$ [1 G/${B}seed$(${T}now$)]. In the standard model these limits can be translated to a constraint on the neutrino masses, given by ${tsumm}_{{ν}i}(2.1×{10}^{{{-}}15}$ eV) [1 G/${B}seed$(${T}now$)]. We also set upper limits on the transition magnetic moments.