Neutrino oscillations: quantum mechanics vs. quantum field theory

Akhmedov, Evgeny Kh.; Kopp, Joachim

doi:10.1007/jhep04(2010)008

Cited by 101 publications

(116 citation statements)

References 25 publications

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“…It is beams' finite sizes that provide natural regularization of the divergence. The next illustration is neutrino oscillations -a phenomenon that is intrinsically spatially and temporarily localized [4][5][6].…”

Section: Non-plane-wave Statesmentioning

confidence: 99%

“…A consistent relativistic scattering theory beyond the plane-wave approximation is absent by now, even though a number of non-plane-wave solutions for relativistic wave equations have long been known [34] and specific calculations were made [1][2][3][4][5][6]. For vortex beams, a corresponding ad hoc formalism has been recently developed by Ivanov and Serbo [27,28].…”

Section: Non-plane-wave Statesmentioning

confidence: 99%

“…The answer is that this formalism turns out to be the most convenient and elegant tool in the paraxial regime when σ p p , complementary and alternative to the wave-function approach (cf. [5,6,36]). …”

Section: Why Wigner Functions?mentioning

confidence: 99%

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Scattering of wave packets with phases

Karlovets

2017

J. High Energ. Phys.

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A general problem of 2 → N f scattering is addressed with all the states being wave packets with arbitrary phases. Depending on these phases, one deals with coherent states in (3 + 1) D, vortex particles with orbital angular momentum, the Airy beams, and their generalizations. A method is developed in which a number of events represents a functional of the Wigner functions of such states. Using width of a packet σ p / p as a small parameter, the Wigner functions, the number of events, and a cross section are represented as power series in this parameter, the first non-vanishing corrections to their plane-wave expressions are derived, and generalizations for beams are made. Although in this regime the Wigner functions turn out to be everywhere positive, the cross section develops new specifically quantum features, inaccessible in the plane-wave approximation. Among them is dependence on an impact parameter between the beams, on phases of the incoming states, and on a phase of the scattering amplitude. A model-independent analysis of these effects is made. Two ways of measuring how a Coulomb phase and a hadronic one change with a transferred momentum t are discussed.

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Section: Non-plane-wave Statesmentioning

confidence: 99%

Section: Non-plane-wave Statesmentioning

confidence: 99%

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Scattering of wave packets with phases

Karlovets

2017

J. High Energ. Phys.

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“…In the perturbative regime (2), an expansion analogous to (4) single packet, the negative regions become noticeable only when it is focused to a spot comparable to λ c . From this one may deduce that it is practically impossible to get out of the WKB regime.…”

Section: Going Beyond the Wkb Regimementioning

confidence: 99%

“…On the other hand, a proper discussion of its limits of applicability in the scattering problems seems to be absent in literature, which is a bit disturbing, especially when striving for higher-order radiative corrections. There are also important examples from the collider physics, atomic physics, neutrino physics, etc., in which the plane-wave model becomes inapplicable -see, for instance, [1,2,3,4,5,6] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Quantum scattering beyond the plane-wave approximation

Karlovets

2017

J. Phys.: Conf. Ser.

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Abstract. While a plane-wave approximation in high-energy physics works well in a majority of practical cases, it becomes inapplicable for scattering of the vortex particles carrying orbital angular momentum, of Airy beams, of the so-called Schrödinger cat states, and their generalizations. Such quantum states of photons, electrons and neutrons have been generated experimentally in recent years, opening up new perspectives in quantum optics, electron microscopy, particle physics, and so forth. Here we discuss the non-plane-wave effects in scattering brought about by the novel quantum numbers of these wave packets. For the well-focused electrons of intermediate energies, already available at electron microscopes, the corresponding contribution can surpass that of the radiative corrections. Moreover, collisions of the cat-like superpositions of such focused beams with atoms allow one to probe effects of the quantum interference, which have never played any role in particle scattering.

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Quantum flavor oscillations extended to the Dirac theory

Bernardini

Guzzo²,

Nishi

2011

Fortschritte der Physik

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This report deals with the quantum theory of flavor oscillations in vacuum, extended to fermionic particles in the several subtle aspects of the first and second quantization theories. In this scenario, the use of the Dirac equation is required for a satisfactory evolution of fermionic mass-eigenstates since in the standard treatment of oscillations the mass-eigenstates are implicitly assumed to be scalars and, consequently, the spinorial form of neutrino wave functions is not included in the calculations. Within first quantized theories, besides flavor oscillations, chiral oscillations automatically appear when we set the dynamic equations for a fermionic Dirac-type particle. The left-handed chiral nature of created and detected neutrinos can be implemented in the first quantized Dirac theory in presence of mixing; the probability loss due to the changing of initially left-handed neutrinos to the undetected right-handed neutrinos can be obtained in analytic form. In the context of a causal relativistic theory of a free particle, one of the two effects should be present in flavor oscillations: (a) rapid oscillations or (b) initial flavor violation. Concerning second quantized approaches, a simple second quantized treatment exhibits a tiny but inevitable initial flavor violation without the possibility of rapid oscillations. Such effect is a consequence of an intrinsically indefinite but approximately well defined neutrino flavor. The violation effects are shown to be much larger than loop induced lepton flavor violation processes, already present in the standard model in the presence of massive neutrinos with mixing. The conclusions of this report lead to lessons concerning flavor mixing, chiral oscillations, interference between positive and negative frequency components of Dirac equation solutions, and the field formulation of quantum oscillations.Comment: 116 pages, 10 figures (The abstract was suppressed due to online title limitations of the abstract field. See the manuscript for obtaining the complete abstract

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Neutrino oscillations: quantum mechanics vs. quantum field theory

Cited by 101 publications

References 25 publications

Scattering of wave packets with phases

Scattering of wave packets with phases

Quantum scattering beyond the plane-wave approximation

Quantum flavor oscillations extended to the Dirac theory

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