How Magnetic is the Dirac Neutrino?

We derive model-independent, “naturalness” upper bounds on the magnetic moments \mu_\nu of Dirac neutrinos generated by physics above the scale of electroweak symmetry breaking. In the absence of fine-tuning of effective operator coefficients, we find that current information on neutrino mass implies that |\mu_\nu | < 10^(-14) Bohr magnetons. This bound is several orders of magnitude stronger than those obtained from analyses of solar and reactor neutrino data and astrophysical observations.