Entangled maximal mixings inUPMNS=Ul†Uν, and a connection to complex mass textures

Abstract

Listen

Translate article

We discuss two different configurations of ${U}_{\mathrm{PMNS}}={U}_{\ensuremath{\ell}}^{\ifmmode\dagger\else\textdagger\fi{}}{U}_{\ensuremath{\nu}}$ with maximal mixings in both ${U}_{\ensuremath{\ell}}$ and ${U}_{\ensuremath{\nu}}$. The nonmaximal mixing angles are assumed to be small, which means that they can be expanded in. Since we are particularly interested in the implications for $CP$ violation, we fully take into account complex phases. We demonstrate that one possibility leads to intrinsically large ${sin}^{2}2{\ensuremath{\theta}}_{13}$ and strong deviations from maximal mixings. The other possibility is generically close to tribimaximal mixing, and allows for large $CP$ violation. We demonstrate how the determination of the ${\ensuremath{\theta}}_{23}$ octant and the precision measurement of ${\ensuremath{\delta}}_{CP}$ could discriminate among different qualitative cases. In order to constrain the unphysical and observable phases even further, we relate our configurations to complex mass matrix textures. In particular, we focus on phase patterns which could be generated by powers of a single complex quantity $\ensuremath{\eta}\ensuremath{\simeq}{\ensuremath{\theta}}_{C}\mathrm{exp}(i\ensuremath{\Phi})$, which can be motivated by Froggatt-Nielsen-like models. For example, it turns out that in all of the discussed cases, one of the Majorana phases is proportional to $\ensuremath{\Phi}$ to leading order. In the entire study, we encounter three different classes of sum rules, which we systematically classify.