Implications of equalities among the elements of CKM and PMNS matrices

TL;DR

This paper explores equalities among CKM and PMNS matrix elements, revealing potential hidden symmetries and deriving mixing textures that suggest a broken underlying symmetry in particle physics.

Contribution

It introduces approximate equalities among CKM matrix elements based on parametrization schemes and extends these ideas to the PMNS matrix, proposing a possible hidden symmetry.

Findings

Derived new mixing textures consistent with some known forms.

Identified approximate equalities hinting at a broken underlying symmetry.

Suggested a potential universal pattern in quark and lepton mixing matrices.

Abstract

Investigating the CKM matrix in different parametrization schemes, it is noticed that those schemes can be divided into a few groups where the sine values of the CP phase for each group are approximately equal. Using those relations, several approximate equalities among the elements of CKM matrix are established. Assuming them to be exact, there are infinite numbers of solutions and by choosing special values for the free parameters in those solutions, several textures presented in literature are obtained. The case can also be generalized to the PMNS matrix for the lepton sector. In parallel, several mixing textures are also derived by using presumed symmetries, amazingly, some of their forms are the same as what we obtained, but not all. It hints existence of a hidden symmetry which is broken in the practical world. The nature makes its own selection on the underlying symmetry and the way to break it, while we just guess what it is.