Assign the two non-Weinberg SU(2) mixing angles to PMNS or CKM

Determine whether the two additional mixing angles derived from the SU(2) gauge action on the 1-dimensional quaternionic representation of the binary tetrahedral group Q8 × Z3 correspond to lepton-mixing angles in the PMNS matrix or quark-mixing angles in the CKM matrix of the Standard Model.

Background

The paper reviews how U(1) and SU(2) gauge actions on complex and quaternionic representations can yield mixing angles relevant to the Standard Model. One of the angles is expected to be the electroweak (Weinberg) angle, but the identification of the other two angles with either lepton- or quark-mixing is not fixed by the discrete symmetry alone.

The author notes a tentative identification proposed elsewhere, but emphasizes that, from the perspective of the discrete model developed here, the assignment of these angles to PMNS or CKM remains unsettled in the absence of additional criteria or calculations.