Hidden Symmetry of the CKM and Neutrino Mapping Matrices

Understand

We propose that the smallness of the light quark masses is related to the smallness of the T violation in hadronic weak interactions.

• Accordingly, for each of the two quark sectors ("upper" and "lower") we construct a 3\times 3 mass matrix in a bases of unobserved quark states, such that the "upper"and "lower" basis states correspond exactly via the $W^\pm$ transitions in the weak interaction.
• In the zeroth approximation of our formulation, we assume T conservation by making all matrix elements real.
• In addition, we impose a "hidden symmetry" (invariance under simultaneous translations of all three basis quark states in each sector), which ensures a zero mass eigenstate in each sector.