An underlying symmetry determines all elements of CKM and PMNS up to a universal constant?

TL;DR

This paper proposes a hidden symmetry underlying the CKM and PMNS matrices, suggesting their elements are determined by a universal parameter, potentially revealing fundamental aspects of particle physics.

Contribution

It introduces parametrization-independent relations that fix the CKM matrix elements up to a universal constant, implying a hidden symmetry in nature.

Findings

CKM matrix elements are fixed by a universal parameter.

Predicted CP phase for neutrinos is between 0° and 59°, centered at 39°.

Relations among matrix elements suggest an underlying symmetry.

Abstract

Observing the CKM matrix elements written in different parametrization schemes, one can notice obvious relations among the sine-values of the CP phases in those schemes. Using the relations, we establish a few parametrization-independent equations, by which the matrix elements of the CKM matrix can be completely fixed up to a universal parameter. If it is true, we expect that there should exist a hidden symmetry in the nature which determines the relations. Moreover, it requires a universal parameter, naturally it would be the famous Jarlskog invariant which is also parametrization independent. Thus the four parameters (three mixing angles and one CP phase) of the CKM matrix are not free, but determined by the symmetry and the universal parameter. As we generalize the rules to the PMNS matrix for neutrino mixing, the CP phase of the lepton sector is predicted to be within a range of $0\sim 59^\circ$ centered at $39^\circ$ (in the P$_a$ parametrization) which will be tested in the future experiments.