Aspects of particle mixing in Quantum Field Theory

TL;DR

This paper reviews particle mixing in Quantum Field Theory, presenting new oscillation formulas, analyzing the structure of mixed fields, and exploring implications for neutrino physics and cosmology.

Contribution

It introduces corrected oscillation formulas, analyzes the unitary inequivalence of mixed field states, and studies non-perturbative vacuum effects related to neutrino mixing.

Findings

New oscillation formulas with corrections to quantum mechanical ones

Non-zero contribution to the cosmological constant from neutrino mixing vacuum

Potential detection of effects in meson systems like η-η' and φ-ω

Abstract

The results obtained on the particle mixing in Quantum Field Theory are reviewed. The Quantum Field Theoretical formulation of fermion and boson mixed fields is analyzed in detail and new oscillation formulas exhibiting corrections with respect to the usual quantum mechanical ones are presented. It is proved that the space for the mixed field states is unitary inequivalent to the state space where the unmixed field operators are defined. The structure of the currents and charges for the charged mixed fields is studied. Oscillation formulas for neutral fields are also derived. Moreover the study some aspects of three flavor neutrino mixing is presented, particular emphasis is given to the related algebraic structures and their deformation in the presence of CP violation. The non-perturbative vacuum structure associated with neutrino mixing is shown to lead to a non-zero contribution to the value of the cosmological constant. Finally, phenomenological aspects of the non-perturbative effects are analyzed. The systems where this phenomena could be detected are the $\eta-\eta'$ and $\phi-\omega$ mesons.