Geometric phases in neutrino mixing

Abstract

Neutrinos can acquire both dynamic and geometric phases due to the non-trivial mixing between mass and flavour eigenstates. In this article, we derive the general expressions for all plausible gauge invariant diagonal and off-diagonal geometric phases in the three flavour neutrino model using the kinematic approach. We find that diagonal and higher order off-diagonal geometric phases are sensitive to the mass ordering and the Dirac CP violating phase $\delta$. We show that, third order off-diagonal geometric phase (${\Phi }_{\mu e\tau }$) is invariant under any cyclic or non-cyclic permutations of flavour indices when the Dirac CP phase is zero. For non-zero $\delta$, we find that ${\Phi }_{\mu e\tau }(\delta )={\Phi }_{e\mu \tau }(-\delta )$. Further, we explore the effects of matter background using a two flavour neutrino model and show that the diagonal geometric phase is either 0 or $\pi$ in the MSW resonance region and takes non-trivial values elsewhere. The transition between zero and $\pi$ occurs at the point of complete oscillation inversion called the nodal point, where the diagonal geometric phase is not defined. Also, in two flavour approximations, two distinct diagonal geometric phases are co-functions with respect to the mixing angle. Finally, in the two flavour model, we show that the only second order off-diagonal geometric phase is a topological invariant quantity and is always $\pi$.

arXiv comment12 pages, accepted for publication in Modern Physics Letters A, similar to the accepted version, different from arXiv:2104.12632

References in corpus (38)

• Discrete Flavor Symmetries and Models of Neutrino Mixing
• Geometric phases for mixed states in interferometry
• Observation of Berry's Phase in a Solid State Qubit
• Constraint on the Matter-Antimatter Symmetry-Violating Phase in Neutrino Oscillations
• Kinematic approach to the mixed state geometric phase in nonunitary evolution
• First measurement of neutrino oscillation parameters using neutrinos and antineutrinos by NOvA
• Geometric phase in open systems
• Geometric phase from Aharonov-Bohm to Pancharatnam-Berry and beyond
• Another possible way to determine the Neutrino Mass Hierarchy
• Present status and future challenges of non-interferometric tests of collapse models
• Off-Diagonal Geometric Phases
• Statistical Evaluation of Experimental Determinations of Neutrino Mass Hierarchy
• Off-diagonal geometric phase for mixed states
• Berry phase in a composite system
• Vacuum induced Spin-1/2 Berry phase
• Geometric phase with nonunitary evolution in presence of a quantum critical bath
• Absence of Vacuum Induced Berry Phases without the Rotating Wave Approximation in Cavity QED
• Combined sensitivity to the neutrino mass ordering with JUNO, the IceCube Upgrade, and PINGU
• Demonstration of Communication using Neutrinos
• Bargmann Invariants and Geometric Phases - a Generalised Connection
• Eigenvalues: the Rosetta Stone for Neutrino Oscillations in Matter
• Topological phase in two flavor neutrino oscillations
• Bargmann invariants and off-diagonal geometric phases for multi-level quantum systems -- a unitary group approach
• Three-Body Decays of Heavy Dirac and Majorana Fermions
• Measurement of a Vacuum-Induced Geometric Phase
• Berry phase for oscillating neutrinos
• Noncyclic geometric phase for neutrino oscillation
• The Quantum Geometric Phase between Orthogonal States
• Geometric phase of neutrino propagating through dissipative matter
• Berry Phase in Neutrino Oscillations
• Geometric phases in neutrino oscillations with nonlinear refraction
• Geometric phase for neutrino propagation in magnetic field
• Geometric phase and neutrino mass hierarchy problem
• Determination of the neutrino mass hierarchy with a new statistical method
• Geometric and Majorana phases in neutrino oscillations
• Noncyclic geometric phases and helicity transitions for neutrino oscillations in a magnetic field
• Interference phenomenon and geometric phase for Dirac neutrino in pion+ decay
• Comment on: "Geometric phase of neutrinos: differences between Dirac and Majorana neutrinos" [Phys. Lett. B 780, 216 (2018)]