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arXiv:1610.08679 · Physics Letters B

Geometric phase of neutrinos: Differences between Dirac and Majorana neutrinos

Antonio Capolupo, S. M. Giampaolo, Beatrix C. Hiesmayr, Giuseppe Vitiello

Published Mar 8, 2018• 27 citations
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Abstract

We analyze the non-cyclic geometric phase for neutrinos. We find that the geometric phase and the total phase associated to the mixing phenomenon provide a theoretical tool to distinguish between Dirac and Majorana neutrinos. Our results hold for neutrinos propagating in vacuum and through the matter. We feed the values of the experimental parameters in our formulas in order to make contact with experiments. Although it remains an open question how the geometric phase of neutrinos could be detected, our theoretical results may open new scenarios in the investigation of the neutrino nature.

DOI
10.1016/j.physletb.2018.03.016

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We analyze the non-cyclic geometric phase for neutrinos. We find that the geometric phase and the total phase associated to the mixing phenomenon provide a theoretical tool to distinguish between Dirac and Majorana neutrinos. Our results hold for neutrinos propagating in vacuum and through the matter. We feed the values of the experimental parameters in our formulas in order to make contact with experiments. Although it remains an open question how the geometric phase of neutrinos could be detected, our theoretical results may open new scenarios in the investigation of the neutrino nature.
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The Pancharatnam - Berry phase (PBP) of purely geometric origin appears as a reparametrization invariant quantity of ray Space. In this article, we investigate the properties exhibited by PBP in neutrino mixing. We map the neutrino flavour modes to independent flavour vacuum states and compute PBP using Bargmann invariant. We derive the exact formula for PBP in two flavour approximation using the kinematic approach. Our result reproduces previous results of Blasone et al. under cyclic condition. Inspired by the work of Mukunda and Simon, we investigate the total and dynamical phases separately. This method leads us to identify the existence of nodal points in the mixing parameter space. At nodal points, PBP changes by a value πππ, and it originates from the total phase. We report the direct relation between nodal points and MSW resonance, giving physical meaning to nodal points. Our analysis shows the ability of PBP to differentiate between different mass hierarchies and set numerical bounds to Δm2Δm^2Δm2 by changing total energy. We extend our studies to three flavour model and found that PBP is sensitive to the Dirac CPCPCP phase (δCPδ_{CP}δCP​). Using our NNN-qubit architecture of the NNN-flavour neutrino model, one can immediately study the dynamical characteristics like mode entanglement between neutrino flavour modes.
We show that the phase appearing in neutrino flavor oscillation formulae has a geometric and topological contribution. We identify a topological phase appearing in the two flavor neutrino oscillation formula using Pancharatnam's prescription of quantum collapses between nonorthogonal states. Such quantum collapses appear naturally in the expression for appearance and survival probabilities of neutrinos. Our analysis applies to neutrinos propagating in vacuum or through matter. For the minimal case of two flavors with CPCPCP conservation, our study shows for the first time that there is a geometric interpretation of the neutrino oscillation formulae for the detection probability of neutrino species.
We investigate the geometric structure of a Hermitian two-level mixing Hamiltonian motivated by neutral meson oscillations and its connections with qubit, fermionic, and topological descriptions. Mapping the Hamiltonian to an effective qubit representation, we analyze the geometric phase associated with cyclic parameter evolution on the Bloch sphere. Without identifying the complex mixing phase with a physical CP-violation observable, we interpret it as a CP-like geometric parameter controlling the azimuthal orientation of the Hamiltonian vector and its reversal under phase conjugation. Third-order Bargmann invariants constructed from the eigenstates yield an associated discrete phase whose dependence on the mixing parameters is examined alongside the continuous geometric construction. The cyclic evolution is also represented as a single-qubit RzR_zRz​ phase operation and expressed through Majorana bilinears. Extending the construction to the momentum-dependent Bogoliubov-de Gennes Hamiltonian of the Kitaev chain, we relate momentum-space winding to the topological regimes and the quantized Berry (Zak) phase in the real-parameter model, while the corresponding Bargmann construction approaches the global phase in the continuum limit. Together, these results provide a geometric perspective connecting phase structure, qubit operations, fermionic representations, and momentum-space topology within related two-level Hamiltonians.