Robustness of Neutrino Mass Matrix Predictions

We investigate the stability of neutrino mass matrix predictions on important and currently unknown observables. Those are the octant of $\theta_{23}$, the sign of $\sin\delta$ and the neutrino mass ordering. Determining those unknowns is expected to be useful in order to distinguish neutrino mass models. Therefore it may be interesting to know how robust the predictions of a mass matrix for the octant of $\theta_{23}$ or the neutrino mass ordering are. By applying general multiplicative perturbations we explicitly quantify how probable it is that a perturbed mass matrix predicts an octant of $\theta_{23}$ different from the original mass matrix, or even a neutrino mass ordering different from the original one. Both the general case and an explicit flavor symmetry model are studied. We give the probabilities as a function of the smallest neutrino mass, showing that for values exceeding 0.1 eV the chance to switch the prediction quickly approaches $50\,\%$.