Mixing angles of quarks and leptons in Quantum Field Theory

Understand

Arguments coming from Quantum Field Theory are supplemented with a 1-loop perturbative calculation to settle the non-unitarity of mixing matrices linking renormalized mass eigenstates to bare flavor states for non-degenerate coupled fermions.

• We simultaneously diagonalize the kinetic and mass terms and counterterms in the renormalized Lagrangian.
• SU(2)_L gauge invariance constrains the mixing matrix in charged currents of renormalized mass states, for example the Cabibbo matrix, to stay unitary.
• Leaving aside CP violation, we observe that the mixing angles exhibit, within experimental uncertainty, a very simple breaking pattern of SU(2)_f horizontal symmetry linked to the algebra of weak neutral currents, the origin of which presumably lies beyond the Standard Model.