Repressing Anarchy in Neutrino Mass Textures

The recent results that $\theta_{13}$ is relatively large, of the order of the previous upper bound, and the indications of a sizable deviation of $\theta_{23}$ from the maximal value are in agreement with the predictions of Anarchy in the lepton sector. The quark and charged lepton hierarchies can then be reproduced in a SU(5) GUT context by attributing non-vanishing $U(1)_{FN}$ charges, different for each family, only to the SU(5) tenplet states. The fact that the observed mass hierarchies are stronger for up quarks than for down quarks and charged leptons supports this idea. As discussed in the past, in the flexible context of $SU(5)\otimes U(1)_{FN}$, different patterns of charges can be adopted going from Anarchy to various types of hierarchy. We revisit this approach by also considering new models and we compare all versions to the present data. As a result we confirm that, by relaxing the extreme ansatz of equal $U(1)_{FN}$ charges for all SU(5) pentaplets and singlets, better agreement with the data than for Anarchy is obtained without increasing the model complexity. We also present the distributions obtained in the different models for the Dirac CP-violating phase. Finally we discuss the relative merits of these simple models.