Unifying Residual $\mathbb Z^{23}_2 \otimes \mathbb Z^{12}_2$ Symmetries and Quark-Lepton Complementarity

TL;DR

This paper proposes a unified framework using residual $ ext{Z}_2$ symmetries to explain quark and lepton mixing patterns, naturally deriving quark-lepton complementarity through symmetry unification.

Contribution

It introduces a model unifying residual $ ext{Z}_2$ symmetries in quark and lepton sectors to explain mixing angles and quark-lepton complementarity.

Findings

Residual symmetries explain mixing angle hierarchies.

Unified symmetry predicts vanishing 2-3 and 1-3 CKM angles.

Quark-lepton complementarity emerges naturally from the model.

Abstract

The residual $\mathbb Z^{23}_2$ ($\mathbb Z^{\mu\tau}_2$) and $\mathbb Z^{12}_2$ ($\mathbb Z^s_2$ or $\overline{\mathbb Z}^s_2$) symmetries can not only apply to the lepton sector, but also explain the mainly $1$--$2$ mixing in the quark sector. With both up and down quarks subject to the same $\mathbb Z^{23}_2$ symmetry, which interchanges the second and third generations, the $1$--$3$ and $2$--$3$ mixing angles in CKM vanish while the Cabibbo angle is dictated by two residual $\mathbb Z^{12}_2$ symmetries. It turns out that the quark-lepton complementarity conditions are natural consequences of unifying residual $\mathbb Z^{23}_2 \otimes \mathbb Z^{12}_2$ symmetries in both lepton and quark sectors.