On the geometric phase for Majorana and Dirac neutrinos

Abstract

We analyze the geometric phase for neutrinos and we demonstrate that the geometric invariants associated to transitions between different neutrino flavors, for Majorana neutrinos, is not left unchanghed by rephasing transformations and are sensitive to the nature of neutrinos. The dependence of geometric invariants on the Majorana phase cannot be eliminated by a charged lepton rephasing transformation. By considering kinematic and geometric approach we also demonstrate that the Majorana phase is relevant in the projective Hilbert space. Geometric invariants can therefore be used as tools to distinguish between Dirac and Majorana neutrinos.

Fermion mixing in curved spacetime

“…We have used the sample values sin 2 (θ) = 0.3, k = 5, m 1 = 1, m 2 = 20 and t 0 = 0.1. with those of eq. (20). Both show amplitude and phase variations with respect to the (flat) Pontecorvo oscillation formulae.…”

“…In particular the amplitude variations present in eqs. (23) and (20) are a distinctive feature of quantum field theory in curved spacetime. The latter cannot be obtained in the quantum mechanical limit, which in curved space modifies the Pontecorvo formulae only in the phase of the oscillations [42].…”

“…These peculiarities place neutrinos beyond the standard model of particles. Many of the issues related to neutrino physics, including the origin of their mass [15], their fundamental nature [16,17,18,19,20] and the overall number of flavors [21] are still open. It is nevertheless clear that neutrinos play a fundamental role in the universe at all the scales.…”

Quantum Field Theory of Neutrino Mixing in Spacetimes with Torsion

“…They are possibly linked to the original baryon asimmetry [64], to dark matter [65,66], and dark energy [67]. Neutrinos also pose several challenges to the standard model of particles, and many aspects of neutrino physics, including the basic mechanism behind flavor oscillations , the origin of their mass and their fundamental nature [89][90][91][92][93][94][95][96], are yet to be clarified.…”

Axion like particles, fifth force and neutron interferometry

“…Phenomena, ranging from neutrino mixing [1,2,3,4,5,6,7] to the dark matter and energy [8,9], to the muon g-2 anomaly [10,11], together with the strong CP problem (i.e. the absence of CP symmetry violation in strong interaction, solved by Peccei and Quinn [12,13] by introducing pseudo-scalar particles known as axions [12,13,14,15,16]) show the necessity of physics beyond the standard model of particles [17].…”