Mixing Angles and Non-Degenerate Systems of Particles

Quentin Duret, Bruno Machet

Published 2006-06-29, updated 2006-09-11Version 2

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.