From transition magnetic moments to majorana neutrino masses
  It is well known that a majorana mass induces a (small) transition magnetic moment. The converse is also true; in this paper we estimate the loop contribution of transition magnetic moments $[\mu]_{\alpha \beta}$ to the neutrino mass matrix $[m]_{\alpha \beta}$. We show that for hierarchical neutrino masses, the contribution of $[\mu]_{e \tau}$ to $[m]_{e \tau}$ can exceed the experimental value of $[m]_{e \tau}$. 
Sacha Davidson, Martin Gorbahn, Arcadi Santamaria