In a simple extension of the standard electroweak theory where the phenomenon of lepton flavor mixing is described by a 3x3 unitary matrix V, the electric and magnetic dipole moments of three active neutrinos are suppressed not only by their tiny masses but also by the Glashow-Iliopoulos-Maiani (GIM) mechanism. We show that it is possible to lift the GIM suppression if the canonical seesaw mechanism of neutrino mass generation, which allows V to be slightly non-unitary, is taken into account. In view of current experimental constraints on the non-unitarity of V, we find that the effective electromagnetic transition dipole moments of three light Majorana neutrinos and the rates of their radiative decays can be maximally enhanced by a factor of O(10^2) and a factor of O(10^4), respectively. This important observation reveals an intrinsic and presumably significant correlation between the electromagnetic properties of massive neutrinos and the origin of their small masses.
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