Mixing Angles and Non-Degenerate Systems of Particles

Abstract

Defining, in the framework of quantum field theory, their mass eigenstates through their matricial propagator, we show why the mixing matrices of non-degenerate coupled systems should not be parametrized as unitary. This is how, for leptonic binary systems, two-angles solutions with discrete values pi/4 [pi/2] and pi/2 [pi] (in addition to the trivial case 0 [pi]) arise when weak leptonic currents of mass eigenstates approximately satisfy the two properties of universality and vanishing of their non-diagonal neutral components. Charged weak currents are also discussed, which leads to a few remarks concerning oscillations. We argue that quarks, which cannot be defined on shell because of the confinement property, are instead more naturally endowed with unitary Cabibbo-like mixing matrices, involving a single unconstrained mixing angle. The similarity between neutrinos and neutral kaons is outlined, together with the role of the symmetry by exchange of families.

arXiv comment1 sentence added in the abstract

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Cited by in corpus (5)

• Fermion flavor mixing in models with dynamical mass generation
• Mixing angles of quarks and leptons in Quantum Field Theory
• Charged lepton mixing via heavy sterile neutrinos
• The emergence of the Cabibbo angle in non-degenerate coupled systems of fermions
• Mixing angles of quarks and leptons as an outcome of SU(2) horizontal symmetries