Fitting flavour symmetries: the case of two-zero neutrino mass textures

Abstract

We present a numeric method for the analysis of the fermion mass matrices predicted in flavour models. The method does not require any previous algebraic work, it offers a $\chi^{2}$ comparison test and an easy estimate of confidence intervals. It can also be used to study the stability of the results when the predictions are disturbed by small perturbations. We have applied the method to the case of two-zero neutrino mass textures using the latest available fits on neutrino oscillations, derived the available parameter space for each texture and compared them. Textures $A_{1}$ and $A_{2}$ seem favoured because they give a small $\chi^{2}$, allow for large regions in parameter space and give neutrino masses compatible with Cosmology limits. The other "allowed" textures remain allowed although with a very constrained parameter space, which, in some cases, could be in conflict with Cosmology. We have also revisited the "forbidden" textures and studied the stability of the results when the texture zeroes are not exact. Most of the forbidden textures remain forbidden, but textures $F_{1}$ and $F_{3}$ are particularly sensitive to small perturbations and could become allowed.