Quantum Field Theory of three flavor neutrino mixing and oscillations with CP violation

TL;DR

This paper develops a quantum field theory framework for three-flavor neutrino mixing, deriving exact oscillation formulas and exploring the algebraic structure and CP violation effects, advancing understanding of neutrino oscillations.

Contribution

It constructs the Hilbert space for three-flavor neutrinos, derives new mixing parameterizations, and reveals a deformed su(3) algebra due to CP violation.

Findings

Exact neutrino oscillation formulas with new features

Identification of a deformed su(3) algebra in mixing currents

Discussion of CP and T violation effects

Abstract

We study in detail the Quantum Field Theory of mixing among three generations of Dirac fermions (neutrinos). We construct the Hilbert space for the flavor fields and determine the generators of the mixing transformations. By use of these generators, we recover all the known parameterizations of the three-flavor mixing matrix and we find a number of new ones. The algebra of the currents associated with the mixing transformations is shown to be a deformed $su(3)$ algebra, when CP violating phases are present. We then derive the exact oscillation formulas, exhibiting new features with respect to the usual ones. CP and T violation are also discussed.