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arXiv:1810.01648 · Physical review. D/Physical review. D.

Flavor-energy uncertainty relations for neutrino oscillations in quantum field theory

Massimo Blasone A, Petr Jizba B, L. A. Smaldone

Published Jan 24, 2019• 30 citations
arXivHTMLPDF

Abstract

In the context of quantum field theory, we derive flavor-energy uncertainty relations for neutrino oscillations. By identifying the nonconserved flavor charges with the ``clock observables,'' we arrive at the Mandelstam-Tamm version of time-energy uncertainty relations. In the ultrarelativistic limit, these relations yield the well-known condition for neutrino oscillations. Ensuing nonrelativistic corrections to the latter are explicitly evaluated. The analogy among flavor states and unstable particles and a novel interpretation of our uncertainty relations, based on the unitary inequivalence of Fock spaces for flavor and massive neutrinos, are also discussed.

DOI
10.1103/physrevd.99.016014

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We discuss the role of finite time and energy uncertainty in the quantum field theory description of neutrino oscillations. In order to to achieve this goal, we review the flavor Fock-space approach and the time-energy uncertainty relation in the Mandelstam--Tamm form, expressed as a flavor-energy uncertainty relation. Such relation, together with the inequivalence of mass and flavor neutrinos Fock spaces, puts a lower bound on neutrino energy uncertainty. Similar considerations can be derived by a perturbative computation of flavor transitions, which employs the Dirac picture to compute flavor transition probability. Remarkably, both flavor Fock space and interaction picture approach lead to the same oscillation probability, within the approximation adopted in the perturbative calculation.
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Neutrino oscillations is a phenomenon which is characterized by a finite oscillation time (length). For such phenomena time-energy uncertainty relation is valid. This means that energy uncertainty is needed for oscillations to occur. We consider neutrino oscillations from this point of view. We demonstrate that for mixed neutrino states, which describe flavor neutrinos nue\\nu_{e}nue​, numu\\nu_{\\mu}numu​ and nutau\\nu_{\\tau}nutau​, translational invariance does not take place.
Abstract Neutrino oscillation is deemed as an interesting physical phenomenon and shows the nonclassical features made apparently by the Leggett–Garg inequality. The uncertainty principle is one of the fundamental features that distinguishes the quantum world to its classical counterpart. And the principle can be depicted in terms of entropy, which forms the so-called entropic uncertainty relations (EUR). In this work, the entropic uncertainty relations that are relevant to the neutrino-flavor states are investigated by comparing the experimental observation of neutrino oscillations to predictions. From two different neutrino sources, we analyze ensembles of reactor and accelerator neutrinos for different energies, including measurements performed by the Daya Bay collaboration using detectors at 0.5 and 1.6 km from their source, and by the MINOS collaboration using a detector with a 735km distance to the neutrino source. It is found that the entropy-based uncertainty conditions strengths exhibits non-monotonic evolutions as the energy increases. We also quantify the systemic quantumness measured by quantum correlation, and derive the intrinsic relationship between quantum correlation and EUR. Furthermore, we utilize EUR as a criterion to detect entanglement of neutrino-flavor state. Our results could illustrate the potential applications of neutrino oscillations on quantum information processing in the weak-interaction processes.