Deviations of exact neutrino textures using radiative neutrino masses

The Weinberg operator allows for the construction of radiative Majorana neutrino masses. In this letter, it will be shown that it is possible to construct a one-loop diagram that will be the principal component of the neutrino mass matrix and that will have an exact mixing matrix with $\theta_{13} =0$. The addition of a two-loop diagram, which is naturally suppressed, allows the creation of the correct perturbations that will give a neutrino mixing matrix with entries inside experimental constrains, including the possibility of large CP Dirac phases.