Entangled maximal mixings in U_PMNS=U_l^dagger U_nu, and a connection to complex mass textures

TL;DR

This paper explores configurations of the PMNS matrix with maximal mixings, analyzing their implications for CP violation, and connects these to complex mass textures influenced by phase patterns like Froggatt-Nielsen models.

Contribution

It introduces new configurations of the PMNS matrix with maximal mixings, examines their CP violation implications, and links them to complex mass textures and phase patterns.

Findings

Large theta_13 can naturally arise in one configuration.

Certain configurations allow for significant CP violation.

Sum rules for phases are systematically classified.

Abstract

We discuss two different configurations of U_PMNS=U_l^dagger U_nu with maximal mixings in both U_l and U_nu. The non-maximal 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 theta_13 and strong deviations from maximal mixings. The other possibility is generically close to tri-bimaximal mixing, and allows for large CP violation. We demonstrate how the determination of the theta_23 octant and the precision measurement of delta_CP could discriminate among different qualitative sub-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 eta=theta_C exp(i 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 Phi to leading order. In the entire study, we encounter three different classes of sum rules, which we systematically classify.