On the Geometric Phase and Majorana Neutrinos

TL;DR

This paper investigates how geometric phases in neutrino flavor transitions differ for Majorana neutrinos and could serve as tools to distinguish them from Dirac neutrinos, highlighting the role of the Majorana phase.

Contribution

It demonstrates that geometric invariants depend on the Majorana phase and are sensitive to the neutrino's nature, providing a potential method to differentiate Majorana from Dirac neutrinos.

Findings

Geometric invariants depend on the Majorana phase.

Dependence on the Majorana phase cannot be removed by rephasing.

Geometric invariants could distinguish neutrino types.

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, can depend on the representation of the mixing matrix and then 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 in principle be used as tools to distinguish between Dirac and Majorana neutrinos.