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arXiv:hep-ph/0006204 · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Noncyclic phase for neutrino oscillation

Xiang‐Bin Wang, L. C. Kwek, Yong Liu, C. H. Oh

Published Feb 5, 2001• 23 citations
arXivHTMLPDF

Abstract

We provide explicit formulas for the noncyclic phases or Pancharatnam phases of neutrino oscillations. Since the Pancharatnam phase is a generalization of the Berry phase, our results generalize the previous findings for the Berry phase in a recent paper [M. Blasone, P. A. Henning, and G. Vitiello, Phys. Lett. B 466 262 (1999)]. Unlike the Berry phase, the noncyclic phase offers a distinctive advantage in terms of measurement and prediction. In particular, for three-flavor mixing, our explicit formula offers an alternative means of determining the CP-violating phase. Our results can also be extended easily to explore the noncyclic phase associated with neutron-antineutron oscillations.

DOI
10.1103/physrevd.63.053003

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We provide explicit formulas for the noncyclic phases or Pancharatnam phases of neutrino oscillations. Since the Pancharatnam phase is a generalization of the Berry phase, our results generalize the previous findings for the Berry phase in a recent paper [M. Blasone, P. A. Henning, and G. Vitiello, Phys. Lett. B 466 262 (1999)]. Unlike the Berry phase, the noncyclic phase offers a distinctive advantage in terms of measurement and prediction. In particular, for three-flavor mixing, our explicit formula offers an alternative means of determining the CP-violating phase. Our results can also be extended easily to explore the noncyclic phase associated with neutron-antineutron oscillations.
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.
A critique of a recent experiment [Wagh et.al., Phys.Rev.Lett.81, 1992 (7 Sep 1998)] to measure the noncyclic phase associated with a precessing neutron spin in a neutron interferometer, as given by the Pancharatnam criterion, is presented. It is pointed out that since the experiment measures, not the noncyclic phase itself, but a quantity derived from it, it misses the most interesting feature of such a phase, namely the different sign associated with states lying in the upper and the lower hemispheres, a feature originating in the existence of a phase singularity. Such effects have earlier been predicted and seen in optical interference experiments using polarization of light as the spinor [Bhandari, Phys.Rep.281, 1 (Mar 1997)].
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.
The geometric picture of neutrino oscillations offers a unique way to study the quantum mechanics of this phenomenon. In this picture, the propagation of a neutrino beam is described by a density matrix evolving in a state space with non-trivial geometry. We derive explicit expressions of the mixed state geometric phase which arise during such an evolution for both two and three flavor neutrino oscillations. We show that, in the case of two flavor neutrino oscillations, the geometric phase is independent of the Majorana phase and it can be used as a measure of coherence of the neutrino beam.
Neutrino flavor oscillations, a fundamental process in particle physics, involve the transition between different neutrino flavors, governed by a complex relationship between mass and flavor eigenstates. Traditionally, probabilistic measures are used to study neutrino oscillations, but recent research suggests that quantum complexity, specifically quantum spread complexity, offers deeper insights, especially regarding charge-parity (CP) violation. Our work shows that quantum complexity can predict CP-violating phases that align with experimental observations from T2K and NOvA. This approach provides a new connection between quantum information theory and particle physics, revealing the potential of complexity in neutrino studies.