Perturbed Yukawa textures in the minimal seesaw model

\noindent We revisit the \textit{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, $\delta$ and $\sigma$, 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 $\delta$ and $\sigma$ 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 $\mathcal{O}\left(\textrm{10}\,\%\right)$. % 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.