Perturbed Yukawa textures in the minimal seesaw model

We revisit the minimal seesaw model, i.e., the type-I seesaw mechanism involving only two right-handed neutrinos. This model represents an important minimal benchmark scenario for future experimental updates on neutrino oscillations. It features four real parameters that cannot be fixed by the current data: two CP -violating phases, δ and σ, as well as one complex parameter, z, that is experimentally inaccessible at low energies. The parameter z controls the structure of the neutrino Yukawa matrix at high energies, which is why it may be regarded as a label or index for all UV completions of the minimal seesaw model. The fact that z encompasses only two real degrees of freedom allows us to systematically scan the minimal seesaw model over all of its possible UV completions. In doing so, we address the following question: suppose δ and σ should be measured at particular values in the future — to what extent is one then still able to realize approximate textures in the neutrino Yukawa matrix? Our analysis, thus, generalizes previous studies of the minimal seesaw model based on the assumption of exact texture zeros. In particular, our study allows us to assess the theoretical uncertainty inherent to the common texture ansatz. One of our main results is that a normal light-neutrino mass hierarchy is, in fact, still consistent with a two-zero Yukawa texture, provided that the two texture zeros receive corrections at the level of O\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{O} $$\end{document} (10%). While our numerical results pertain to the minimal seesaw model only, our general procedure appears to be applicable to other neutrino mass models as well.