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arXiv:2308.14574 · Physica Scripta

Chiral and flavor oscillations in a hyperentangled neutrino state

Victor A. S. V. Bittencourt, Massimo Blasone A, Gennaro Zanfardino

Published Nov 8, 2024• 6 citations
arXivHTMLPDF

Abstract

Abstract In addition to flavor oscillations, Dirac neutrinos also undergo the so-called chiral oscillations, a consequence of the free-particle dynamics under the Dirac equation. Such a transition between different chiralities affect the flavor transitions, but also can generate non-trivial correlations between the internal degrees of freedom of the particle. In this paper, we show that the state of a massive oscillating neutrino produced by weak interaction process, is an hyperentangled state, in which flavor, chirality, and spin exhibit non-trivial correlations. Using complete complementarity relations, we show that both chiral and flavor oscillations redistribute correlations and coherence in time among different partitions of the system. In a similar way, we consider a spin entangled lepton-antineutrino pair and show that there is a dynamical redistribution of spin-spin entanglement into correlations and coherence between the other degrees-of-freedom. Our analysis provides a complete characterization of the quantum correlations involved in lepton-antineutrino pairs and in single particle neutrino evolution, and provides a further insight on possible routes to interpret and measure chiral oscillations.

DOI
10.1088/1402-4896/ad9097

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Abstract In addition to flavor oscillations, Dirac neutrinos also undergo the so-called chiral oscillations, a consequence of the free-particle dynamics under the Dirac equation. Such a transition between different chiralities affect the flavor transitions, but also can generate non-trivial correlations between the internal degrees of freedom of the particle. In this paper, we show that the state of a massive oscillating neutrino produced by weak interaction process, is an hyperentangled state, in which flavor, chirality, and spin exhibit non-trivial correlations. Using complete complementarity relations, we show that both chiral and flavor oscillations redistribute correlations and coherence in time among different partitions of the system. In a similar way, we consider a spin entangled lepton-antineutrino pair and show that there is a dynamical redistribution of spin-spin entanglement into correlations and coherence between the other degrees-of-freedom. Our analysis provides a complete characterization of the quantum correlations involved in lepton-antineutrino pairs and in single particle neutrino evolution, and provides a further insight on possible routes to interpret and measure chiral oscillations.
Abstract We study the evolution of quantum correlations in a lepton-antineutrino pair, as produced in weak interactions (e.g. pion decay). Assuming an inital state entangled in the spins of the two particles, we show that both chiral and flavor (neutrino) oscillations affect spin correlations. Such corrections are relevant in the non-relativistic regime. In the second part we focused our attention on the weak process n + νe → p + e in which the results found in the previous sections could be observed.
Dirac bispinors belong to an irreducible representation of the complete Lorentz group, which includes parity as a symmetry yielding two intrinsic discrete degrees of freedom: chirality and spin. For massive particles, chirality is not dynamically conserved, which leads to chiral oscillations. In this contribution, we describe the effects of this intrinsic structure of Dirac bispinors on the quantum entanglement encoded in a lepton-antineutrino pair. We consider that the pair is generated through weak interactions, which are intrinsically chiral, such that in the initial state the lepton and the antineutrino have definite chirality but their spins are entangled. We show that chiral oscillations induce spin entanglement oscillations and redistribute the spin entanglement to chirality-spin correlations. Such a phenomenon is prominent if the momentum of the lepton is comparable with or smaller than its mass. We further show that a Bell-like spin observable exhibits the same behavior of the spin entanglement. Such correlations do not require the knowledge of the full density matrix. Our results show novel effects of the intrinsic bispinor structure and can be used as a basis for designing experiments to probe chiral oscillations via spin correlation measurements.
The phenomena of particle mixing and flavor oscillations in elementary-particle physics can be addressed from the point of view of quantum information theory, and described in terms of multi-mode entanglement of single-particle states. In this paper we show that such a description can be extended to the domain of quantum field theory, where we uncover a fine structure of quantum correlations associated with multi-mode, multi-particle entanglement. By means of an entanglement measure based on the linear entropies associated with all the possible bipartitions, we analyze the entanglement in the states of flavor neutrinos and antineutrinos. Remarkably, we show that the entanglement is connected with experimentally measurable quantities, i.e. the variances of the lepton numbers and charges.
The phenomena of particle mixing and flavor oscillations in elementary-particle physics can be addressed from the point of view of quantum information theory, and described in terms of multi-mode entanglement of single-particle states. In this paper we show that such a description can be extended to the domain of quantum field theory, where we uncover a fine structure of quantum correlations associated with multi-mode, multi-particle entanglement. By means of an entanglement measure based on the linear entropies associated with all the possible bipartitions, we analyze the entanglement in the states of flavor neutrinos and antineutrinos. Remarkably, we show that the entanglement is connected with experimentally measurable quantities, i.e. the variances of the lepton numbers and charges.
Flavor oscillations in elementary particle physics are related to multimode entanglement of single-particle states. We show that mode entanglement can be expressed in terms of flavor transition probabilities, and therefore that single-particle entangled states acquire a precise operational characterization in the context of particle mixing. We treat in detail the physically relevant cases of two- and three-flavor neutrino oscillations, including the effective measure of CP violation. We discuss experimental schemes for the transfer of the quantum information encoded in single-neutrino states to spatially delocalized two-flavor charged-lepton states, thus showing, at least in principle, that single-particle entangled states of neutrino mixing are legitimate physical resources for quantum information tasks.
In charged current weak interaction processes, neutrinos are produced in an entangled state with the charged lepton. This correlated state is disentangled by the measurement of the charged lepton in a detector at the production site. We study the dynamical aspects of disentanglement, propagation, and detection, in particular, the conditions under which the disentangled state is a coherent superposition of mass eigenstates. The appearance and disappearance far-detection processes are described from the time evolution of this disentangled ``collapsed'' state. The familiar quantum mechanical interpretation and factorization of the detection rate emerges when the quantum state is disentangled on time scales much shorter than the inverse oscillation frequency, in which case the final detection rate factorizes in terms of the usual quantum mechanical transition probability provided the final density of states is insensitive to the neutrino energy difference. We suggest possible corrections for short-baseline experiments. If the charged lepton is unobserved, neutrino oscillations and coherence are described in terms of a reduced density matrix obtained by tracing out an unobserved charged lepton. The diagonal elements in the mass basis describe the production of mass eigenstates whereas the off-diagonal ones provide a measure of coherence. It is shown that coherences are of the same order of the diagonal terms on time scales up to the inverse oscillation frequency, beyond which the coherences oscillate as a result of the interference between mass eigenstates.