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

Abstract

The residual ${\mathbb{Z}}_2^{23}$ (${\mathbb{Z}}_2^{\hat{I}¼\ddot{I}„}$) and ${\mathbb{Z}}_2^{12}$ (${\mathbb{Z}}_2^s$ or ${\overline{\mathbb{Z}}}_2^s$) 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 ${\mathbb{Z}}_2^{23}$ 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 ${\mathbb{Z}}_2^{12}$ symmetries. It turns out that the quark-lepton complementarity conditions are natural consequences of unifying residual ${\mathbb{Z}}_2^{23}\otimes {\mathbb{Z}}_2^{12}$ symmetries in both lepton and quark sectors.

4 pages