CKM matrix and flavor symmetries

Understand

Following the way proposed recently by Hernandez and Smirnov, we seek possible residual symmetries in the quark sector with a focus on the von Dyck groups.

• We begin with two extreme cases in which both $\theta_{13}$ and $\theta_{23}$ or only $\theta_{13}$ are set to zero.
• Then, cases where all the Cabibbo-Kobayashi-Maskawa parameters are allowed to take nonzero values are explored.
• The $Z_7$ symmetry is favorable to realize only the Cabibbo angle.