From CP Phases to Yukawa Textures: Maximal Yukawa Hierarchies in Minimal Seesaw Models

The type-I seesaw mechanism involving only two right-handed neutrinos represents a minimal model to account for the observed masses and mixings in the Standard Model neutrino sector. This model features four real parameters that cannot be fully fixed by the current data: two CP-violating phases, delta and sigma, as well as one complex parameter, z, that is experimentally inaccessible at low energies. We perform a systematic scan of this model over the complex z plane, addressing the following question: Suppose delta and sigma should be measured at particular values in the future---what are then the conceivable maximal hierarchies in the neutrino Yukawa matrix that are still consistent with all observations? In this sense, our analysis generalizes previous studies of the type-I seesaw mechanism with two right-handed neutrinos that assume exact texture zeros in the neutrino Yukawa matrix. As we are able to demonstrate, relaxing the assumption of exact texture zeros, significantly enlarges the range of possible Yukawa matrices. For instance, allowing for corrections of up to O(10%), it turns out that models with an approximate two-zero texture can be realized even in the case of a normally ordered light-neutrino mass spectrum. This represents an important caveat to the conventional wisdom that two-zero textures and a normal mass hierarchy are actually inconsistent with each other in seesaw models with only two right-handed neutrinos. Similarly, we show that, also in the case of an inverted hierarchy, small perturbations can resurrect Yukawa textures that are conventionally believed to be ruled out by the data.