Geometric and Majorana phases in neutrino oscillations

TL;DR

This paper demonstrates that gauge-invariant geometric phases in neutrino oscillations do not depend on Majorana phases, confirming that such phases cannot reveal the neutrino's Majorana or Dirac nature.

Contribution

The study proves that all gauge-invariant Aharonov--Anandan phases in neutrino oscillations are independent of Majorana phases, extending the understanding of neutrino phase invariance.

Findings

Gauge-invariant phases are independent of Majorana phases

Oscillation experiments cannot distinguish Majorana from Dirac neutrinos

Geometric phases are not sensitive to neutrino nature

Abstract

Geometric (Aharonov--Anandan) phases in neutrino oscillations have been claimed [Phys. Lett. B 780 (2018) 216] to be sensitive to the Majorana phases in neutrino mixing. More recently, however, it has been pointed out [Phys. Lett. B 818 (2021) 136376] that the proposed phases are not gauge invariant. Using both kinematic and geometric approaches, we show that all gauge-invariant Aharonov--Anandan phases (including the off-diagonal geometric phases associated with flavor transitions) are independent of the Majorana phases. This finding, which generalizes the well-known fact that conventional oscillation experiments cannot discern the Dirac or Majorana nature of the neutrino, implies that a hypothetical interference experiment cannot distinguish between the two either.