Fermion flavor mixing in models with dynamical mass generation

TL;DR

This paper introduces a model-independent method to analyze fermion flavor mixing with momentum-dependent self-energies, revealing non-unitary CKM matrices and non-trivial flavor-changing currents in strongly coupled dynamical mass generation models.

Contribution

It develops a novel approach for fermion mixing with momentum-dependent self-energies, extending beyond constant mass matrices, and explores its implications on flavor physics and gauge interactions.

Findings

Effective CKM matrix is generally non-unitary.

Momentum dependence leads to non-trivial flavor-changing currents.

Interaction and mass bases are not related by a unitary transformation.

Abstract

We present a model-independent method of dealing with fermion flavor mixing in the case when instead of constant, momentum-independent mass matrices one has rather momentum-dependent self-energies. This situation is typical for strongly coupled models of dynamical fermion mass generation. We demonstrate our approach on the example of quark mixing. We show that quark self-energies with a generic momentum dependence lead to an effective Cabibbo-Kobayashi-Maskawa (CKM) matrix, which turns out to be in general non-unitary, in accordance with previous claims of other authors, and to non-trivial flavor changing electromagnetic and neutral currents. We also discuss some conceptual consequences of the momentum-dependent self-energies and show that in such a case the interaction basis and the mass basis are not related by a unitary transformation. In fact, we argue that the latter is merely an effective concept, in a specified sense. While focusing mainly on the fermionic self-energies, we also study the effects of momentum-dependent radiative corrections to the gauge bosons and to the proper vertices. Our approach is based on an application of the Lehmann-Symanzik-Zimmermann (LSZ) reduction formula and for the special case of constant self-energies it gives the same results as the standard approach based on the diagonalization of mass matrices.