Quantum field theory of three flavor neutrino mixing and oscillations withCPviolation

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.

Entanglement of Dirac bi-spinor states driven by Poincaré classes of SU(2)⊗SU(2) coupling potentials

“…To summarize, given that the Dirac equation is the equation of motion for fermionic fields [23], the entanglement content of Dirac particles [36][37][38] may also have a formulation extended to the context of Dirac fields, as in the description of fermion mixing [39] and neutrino oscillations [40]. …”

Neutrino oscillations from relativistic flavor currents

“…In this framework, there has been recently a remarkable progress in the study of the problem of field mixing in Quantum Field Theory (QFT) [8,9,10,11,12,13,14,15,16,17,18,19,20]. It is important to remark that, in spite of the fact of being usually treated in Quantum Mechanics (QM), the mixing between states of different masses is not even allowed in a non-relativistic theory due to the Bargmann superselection rules [21].…”

“…An analysis of the currents associated to mixing for the case of three flavor neutrino mixing with CP violation and for boson mixing can be found in Refs. [10,11].…”

Lorentz invariance for mixed neutrinos

“…[18]: one has a total conserved charge Q associated with the global U (1) symmetry and time-dependent charges associated to the (broken) SU (2) symmetry. Such charges are the relevant physical quantities for the study of flavor oscillations [10,14]. They are also essential in the definition of (physical) flavor neutrino states, as the one produced in a beta decay, for example.…”

“…This naturally pointed to QFT where the problem found its resolution [9][10][11][12]. Subsequently an even more consistent picture emerged with the discovery of an associated geometric phase [13], the extension to the case of threeflavours [14] and bosons [15,16] and to the case of neutral fields [17]. The study of relativistic flavor currents [18,19] was recently used to solve the phenomenologically very relevant problem of finding a space-oscillation formula [20].…”