Coherence of neutrino oscillations in the wave packet approach

C. Giunti; C.W. Kim

REVIEW

Coherence of neutrino oscillations in the wave packet approach

C. Giunti, C.W. Kim

High Energy Physics - Phenomenology · Submitted 18 Nov 1997 · 13 references

Pith's verdict: A useful, compact extension of the wave-packet formalism with a real algebra slip in Eq. (13) that shifts, but does not kill, the new coherence bound.

T0 · AI review

How this review was made: An AI referee (selfhosted/deepseek-v4.1-flash) read the paper on November 13, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

T0 AI review An AI read the paper and answered a fixed list of questions.
T1 Audit Automatic checks that the references and files the paper relies on exist and match.
T2 Compute The paper's code or calculations re-run with the same results.
T3 Formal statement The claims written out in a formal math language a computer can read.
T4 Proof Those claims proved, and the proof checked by computer.

How Pith checks papers →

· 2 major objections · 8 minor · Ask about this paper · The compiled record · Read the full review →

Challenge this review Comment (0) Read on arXiv ↗

Cite ▾

arXiv IDhep-ph/9711363 (version 2)

Pith IDMTEJWZZ7, Pith's permanent record of this paper and its review

CitationC. Giunti, C.W. Kim. "Coherence of neutrino oscillations in the wave packet approach." arXiv:hep-ph/9711363 (1997). https://pith.science/paper/MTEJWZZ7

Cite this reviewBibTeX for Pith's review of this paper

Claim paper

Why Pith says this

Highlight any text to comment on it.

Editor's note

read the letter

Short version: this is a sensible, compact paper that does the obvious next step — folding the detector's spatial and temporal coherence widths into the Giunti–Kim–Lee wave-packet formalism — and it lands a genuinely new claim, an upper bound on the coherence length. But Eq. (13) has an algebra error a referee should catch, and it matters for the quantitative statement, not the qualitative one. What's new and right: Eq. (8), σ_x² = σ_xP² + σ_xD², is a one-line convolution, but it's the right one, and it makes the Kiers–Nussinov–Weiss point transparent: a precise energy measurement in the detector means small σ_pD, large σ_xD, longer coherence length. The genuinely new piece is the ceiling, Eq. (14). The logic is clean: once σ_x exceeds the oscillation length, the unmeasured time average washes out the interference, so you cannot buy coherence indefinitely by measuring detector energies better. That is a real, quotable statement. Where it slips: the phase in Eq. (10) is exp{−iΔm²[ξT + (1−ξ)L]/2E}, so the T-dependent part is ξT. Integrating over T with the gaussian that localizes T near L gives exp{−2π²ξ²(σ_x/L_osc)²}, not the (1−ξ)² in Eq. (13). This is not cosmetic. The paper's own remark that ξ=0 (equal energy) removes the time dependence is consistent with ξ² and flatly contradicts Eq. (13), which gives maximal suppression at ξ=0 and none at ξ=1. For pion decay at rest, ξ≈0.2, so the bound moves by roughly a factor of four in σ_x — the ceiling survives, but the coefficient in Eq. (14) and the stated condition σ_x ≳ L_osc need fixing. Since Eq. (14) is already written as a loose '≲', the qualitative conclusion is safe; the quantitative statement is not. Footnote 3 is honest about the gaussian tail producing an unphysical early-time interaction, and defers the realistic treatment to [13], which is in preparation. That is an acknowledged limitation, not a hidden one, but it does mean the central calculation rests on an ansatz the authors know is imperfect. Who should read it: anyone working on wave-packet decoherence in long-baseline or astrophysical neutrino settings. It is a short, useful reference. Send it out; the referee should insist on Eq. (13) being redone.

Referee report

Significance

If the derivation holds, the paper gives a compact and physically transparent clarification of the wave-packet formalism: the identification in Eq. (8) that the coherence width is the quadrature sum of production and detection widths is a genuine and useful statement, and the resulting bound Eq. (14) is a falsifiable scaling relation obtained without free parameters or fits. The paper is appropriately explicit in crediting Ref. [6] for the original observation that detection-energy resolution can increase the coherence length, and it frames its own contribution as the ceiling on that increase rather than as a competing claim. The scope is modest (a short letter-length derivation within an existing gaussian ansatz), but the result would be of practical use to anyone estimating whether a given source-detector configuration can retain oscillation coherence.

Major objections (2)

[Eqs. (10), (13), (14)] The suppression factor F_ab in Eq. (13) does not follow from the time integral of Eq. (10). In Eq. (10) the T-dependent part of the phase is exp[−i Δm²_ab ξT/(2E)], since the phase is ξT + (1−ξ)L; the gaussian overlap localizes T within a window of width σ_x around L, so the T-integral yields exp[−ξ²(Δm²_ab)²σ_x²/(8E²)] = exp[−2π²ξ²(σ_x/L_osc_ab)²], not the (1−ξ)² of Eq. (13). This is load-bearing, not cosmetic, because it reverses the two limits the paper itself discusses. At ξ = 0 the text after Eq. (13) correctly states that the time dependence of the oscillatory term is eliminated, so the time average should give F_ab = 1; Eq. (13) instead gives maximal suppression. At ξ = 1 Eq. (13) gives F_ab = 1, i.e. no bound at all, which directly contradicts the abstract's claim of a universal bound determined by E and Δm². With the correct ξ², the coherence-loss condition becomes σ_x ≳ L_osc/(2πξ) rather than σ_x ≳ L_osc, and Eq. (14) becomes L_coh ≲ 16E³/(ξΔm⁴) up to the same O(1) convention already used there. For ξ ≈ 0.2 the numerical coefficient changes only by an O(1) factor, so the parametric scaling E³/(Δm²)² survives, but the ξ-dependence and the stated condition on σ_x must be corrected, and the abstract's phrasing that the bound is 'determined by the neutrino energy and the mass-squared difference' must be amended to include ξ.
[Eq. (5) and footnote 3] The headline bound Eq. (14) is derived precisely in the regime where the authors themselves flag the gaussian detection packet of Eq. (5) as unphysical. Footnote 3 acknowledges that when σ_xD is dominated by the temporal coherence width, Eq. (5) introduces an interaction for times earlier than the neutrino's arrival, and that a realistic treatment requires inserting a θ(x − L + σ̃_xD) and solving Eq. (6) numerically, deferred to Ref. [13], which is listed as 'in preparation'. Since the bound of Eq. (14) concerns large σ_x, i.e. exactly the large-temporal-width regime, the paper should either provide even a rough estimate showing that the bound survives the θ-function cutoff, or explicitly soften the claim to a statement valid within the gaussian model. As it stands the central quantitative result rests on an approximation the manuscript itself identifies as unreliable in the relevant limit, and the supporting treatment is unpublished.

Minor objections (8)

[Eq. (11)] The argument of the first exponential, written as '2πi x Loscab', appears to be a typesetting error; it should presumably read 2πi L/L_osc_ab. Please check the whole equation for similar corruption.
[Eq. (9)] The parameter ξ is introduced as 'determined by energy-momentum conservation in the production process to first order in m_a²/E²' without a derivation, and the value ξ ≈ 0.2 for pion decay at rest is quoted without support. A one-line derivation or an explicit reference would make the subsequent ξ-dependence checkable by the reader.
[Eq. (14)] The numerical coefficient of Eq. (14) does not follow from setting σ_x = L_osc in Eq. (12): that substitution gives 16√2π E³/Δm⁴, whereas E(L_osc)² = 16π²E³/Δm⁴ corresponds to σ_x ≈ 2.2 L_osc. Since the text states the condition as σ_x ≳ L_osc, the convention used to pass from Eq. (12) to Eq. (14) should be stated explicitly.
[Eq. (12) and discussion] The paper gives no numerical illustration of the bound. A short table of L_coh,max for representative values of E and Δm² (e.g. solar, atmospheric, and reactor scales) would make the practical content of Eq. (14) concrete and would let the reader judge whether the bound is ever approached in existing experiments.
[Eq. (5)] The detected-neutrino state is taken to be time-independent, so the temporal coherence width of the detection process enters only through the single gaussian width σ_xD. The text asserts that σ_xD is 'the maximum between the spatial and temporal coherence widths of the detection process', which is only justified when the two are comparable; a sentence on the regime of validity would help.
[Normalization after Eq. (11)] The normalization Σ_β P_αβ(L) = 1 is imposed by hand after the time integration rather than shown to follow from it. Since the prefactor of Eq. (10) is left as a proportionality, a brief demonstration that the L → 0 limit reproduces the normalization would close this gap.
[References] Reference [13] is listed as 'in preparation' and carries the numerical check on which the robustness of the main result depends; a published or preprint version should be supplied if at all possible. Reference [9] is also a preprint and should be updated to its published form if one exists.
[Throughout] The manuscript text contains numerous broken words from typesetting (e.g. 'appro ach', 'conﬁrming', 'neutr ino', 'propag ating', 'detectio n'). These should be cleaned up before publication.

How Pith checks papers → · Full audit of this paper →

The paper

The paper claims

Precise measurement of the particles that detect a neutrino can stretch the distance over which its mass states still interfere, but a wave-packet calculation puts a ceiling on that stretch, set by the neutrino energy and the mass-squared差距

The reading

Neutrino oscillations only happen if the different mass eigenstates in a neutrino beam stay coherent long enough to interfere at the detector. Earlier wave-packet treatments of this effect accounted for the production process but dropped the corresponding coherence widths of the detection process. This paper adds them back: the detected neutrino is described by its own gaussian wave packet, and the transition amplitude becomes an overlap integral between the propagating packet and that detection packet. The result confirms that sharply measuring the energies of the particles involved in detection widens the effective packet and lengthens the coherence length, but it also shows the gain cannot run away: past a bound set by the neutrino energy and the mass-squared difference, the interference is washed out no matter how good the energy measurement is.

What carries the argument

The load-bearing device is the overlap integral between two gaussian wave packets: the propagating state produced at the source and a separate gaussian state representing the neutrino the detector is able to absorb. Their widths add in quadrature, $1sigma_x^2 = 1sigma_{xP}^2 + 1sigma_{xD}^2$, which is what lets the detection process enter the coherence length at all. The second device is the average of the probability over the detection time $T$, which is not measured in real experiments. That average converts the packet-separation gaussian into the damping factor $1exp[-(L/L_{1mathrm{coh}}^{ab})^2]$ multiplied by $F_{ab} = 1exp[-2pi^2(1-1xi)^2 (1sigma_x/L_{1mathrm{osc}}^{ab})^2]$, where $1xi$ parametrizes how the mass eigenstate energies are fixed by production kinematics. The interplay of these two exponentials is what produces both the claimed gain and the claimed ceiling.

Extended reading notes

Core claim

The paper's central claim is that the coherence length of neutrino oscillations has an upper bound. Working in the wave-packet formalism, the authors write the flavor-changing amplitude as the overlap $A_{1D0}(L,T) = 1int dx 1langle1 u_1beta(x-L)|1 u_1alpha(x,T)1rangle$ of the propagating neutrino state with a detection state that carries its own momentum width $1sigma_{pD}$, so that the width controlling coherence is $1sigma_x^2 = 1sigma_{xP}^2 + 1sigma_{xD}^2$ rather than the production width alone. Averaging the resulting probability over the unmeasured detection time $T$ gives the standard oscillation phase together with a damping factor $1exp[-(L/L_{1mathrm{coh}}^{ab})^2]$ and an extra factor $F_{ab}$, with $L_{1mathrm{coh}}^{ab} = 4sqrt{2}1sigma_x E^2/|1Delta m_{ab}^2|$. Because a precise energy measurement in the detector means a small $1sigma_{pD}$ and hence a large $1sigma_{xD}$, the coherence length can indeed be increased, as Kiers, Nussinov and Weiss had observed. But once $1sigma_x$ exceeds the oscillation length, the phase of the interference term depends sensitively on the unmeasured $T$, and the time average erases the interference. That yields the ceiling $L_{1mathrm{coh}}^{ab} 1lesssim E,(L_{1mathrm{osc}}^{ab})^2 = 16pi^2 E^3/(1Delta m_{ab}^2)^2$, beyond which the coherence length stops being a meaningful quantity because coherence is lost at every distance.

Load-bearing premise

The derivation treats the detected neutrino as a gaussian wave packet sharing the propagating states' average momenta and averages the probability over all detection times from minus to plus infinity, an approximation the authors themselves note gives the detector an unphysical response before the neutrino arrives.

Editorial extensions

If this is right

Coherence lengths quoted for oscillation experiments should be computed from the larger of the production and detection coherence widths, not from the production width alone.
An experiment that measures the recoil particles' energies very precisely gains coherence length only up to $16pi^2 E^3/(1Delta m^2)^2$; beyond that the gain does not translate into visible oscillations.
In the opposite regime, where the effective packet width exceeds the oscillation length, the observable transition probability flattens to the averaged value $1sum_a |U_{1alpha a}|^2|U_{1beta a}|^2$ with no oscillatory term.
The same washout logic applies when the source distance $L$ rather than the time $T$ is unknown, which the authors note is the situation relevant to neutrino oscillations in the early universe.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The ceiling is a statement about the unmeasured time, not about the neutrino itself: if a detection scheme could time-stamp the interaction to within the oscillation period, the interference the paper says is washed out would in principle be recoverable.
Because the bound scales as $E^3/(1Delta m^2)^2$, the loss of coherence is most severe for low-energy neutrinos with large mass splittings, which is the regime of solar and reactor neutrinos rather than accelerator beams.
The authors' own footnote concedes that the gaussian detection packet lets the detector respond before the neutrino arrives; a retarded, causal packet would likely soften rather than remove the ceiling, and checking whether the bound survives that replacement is a concrete calculational target.

Original abstract

The temporal and spatial coherence widths of the microscopic process by which a neutrino is detected are incorporated in the quantum mechanical wave packet treatment of neutrino oscillations, confirming the observation of Kiers, Nussinov and Weiss that an accurate measurement of the energies of the particles participating in the detection process can increase the coherence length. However, the wave packet treatment presented here shows that the coherence length has an upper bound, determined by the neutrino energy and the mass-squared difference, beyond which the coherence of the oscillation process is lost.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,408 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.89 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.61 · compares with prior results 0.91 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

The temporal and spatial coherence widths of the microscopic process by which a neutrino is detected are incorporated in the quantum mechanical wave packet treatment of neutrino oscillations, confirming the observation of Kiers, Nussinov and Weiss that an accurate measurement of the energies of the particles participating in the detection process can increase the coherence length. However, the wave packet treatment presented here shows that the coherence length has an upper bound, determined by the neutrino energy and the mass-squared difference, beyond which the coherence of the oscillation process is lost.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The temporal and spatial coherence widths of the microscopic process by which a neutrino is detected are incorporated in the quantum mechanical wave packet treatment of neutrino oscillations, confirming the observation of Kiers, Nussinov and Weiss that an accurate measurement of the energies of the particles participating in the detection process can increase the coherence length.	contribution 0.50	0.27	0.11	asserted 0.98
s1	However, the wave packet treatment presented here shows that the coherence length has an upper bound, determined by the neutrino energy and the mass-squared difference, beyond which the coherence of the oscillation process is lost.	result 0.98	0.90	0.79	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.98.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References

Works cited (13)

[13]

C. Giunti, C.W. Kim and U.W. Lee, in preparation. 7

View on Pith
[4]

C. Giunti, C.W. Kim and U.W. Lee, Phys. Rev. D 44, 3635 (1991)

View on Pith 1991
[6]

K. Kiers, S. Nussinov and N. Weiss, Phys. Rev. D 53, 537 (1996)

View on Pith 1996
[1]

S. Nussinov, Phys. Lett. B 63, 201 (1976)

View on Pith 1976
[2]

S.M. Bilenky and B. Pontecorvo, Phys. Rep. 41, 225 (1978)

View on Pith 1978
[3]

B. Kayser, Phys. Rev. D 24, 110 (1981)

View on Pith 1981
[5]

C. Giunti, C.W. Kim, J.A. Lee and U.W. Lee, Phys. Rev. D 48, 4310 (1993)

View on Pith 1993
[7]

J.E. Campagne, Phys. Lett. B 400, 135 (1997)

View on Pith 1997
[8]

C. Giunti, C.W. Kim and U.W. Lee, hep-ph/9709494

View on Pith Pith review arXiv
[9]

K. Kiers and N. Weiss, hep-ph/9710289

View on Pith Pith review arXiv
[10]

J. Rich, Phys. Rev. D 48, 4318 (1993)

View on Pith 1993
[11]

W. Grimus and P. Stockinger, Phys. Rev. D 54, 3414 (1996)

View on Pith 1996
[12]

R.G. Winter, Lett. Nuovo Cimento 30, 101 (1981)

View on Pith 1981

Forward citations

Cited by 18 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Beyond $\Delta m^2$: Absolute Mass Sensitivity in Neutrino Oscillations
hep-ph 2026-08 conditional novelty 6.0 of 10

The NLO oscillation phase includes a term proportional to (m_i^4 - m_j^4)/E^3, making oscillation experiments sensitive in principle to the absolute neutrino mass scale, with JUNO projected to bound the lightest mass ...
Real and Virtual Propagation in Neutrino Oscillations
hep-ph 2026-06 unverdicted novelty 6.0 of 10

In Gaussian wave-packet QFT, flavor oscillations switch on only after a propagation-time threshold set by the wave-packet energy uncertainty and the intermediate particle's decay width; below it the neutrino is purely...
Damping of neutrino oscillations, decoherence and the lengths of neutrino wave packets
hep-ph 2022-08 accept novelty 6.0 of 10

Reactor and chromium-source neutrino wave packets are estimated to be 10^-5 to 10^-4 cm long, making wave-packet decoherence unobservable in those experiments.
Neutrino production coherence and oscillation experiments
hep-ph 2012-01 conditional novelty 6.0 of 10

Coherent amplitude summation and incoherent probability averaging over a neutrino source agree exactly for pointlike pions and localized detection, and differ at order [v_g/(v_g - v_pi)] sigma_xpi / l_osc for finite p...
Superluminal neutrinos in long baseline experiments and SN1987a
hep-ph 2011-09 conditional novelty 6.0 of 10

The MINOS and OPERA superluminal neutrino hints are in tension with SN1987a bounds unless the Lorentz-violating velocity shift is a step function that switches on between supernova and long-baseline energies.

Show 13 more citing papers

Oscillations of neutrinos and mesons in quantum field theory
hep-ph 2001-09 accept novelty 6.0 of 10

A single external wave packet framework in quantum field theory reproduces stationary oscillation models as a limit and yields a unified oscillation formula for stable and unstable neutrinos and mesons, including deco...
Neutrino oscillations inside ultrarelativistic matter: on the role of the Tolman VI spacetime
gr-qc 2026-10 conditional novelty 5.0 of 10

Neutrino flavor oscillations and resonances are derived analytically in the Tolman VI spacetime, with spinoptics corrections becoming dominant near the central naked singularity, leading to flavor equilibrium.
CP asymmetry and visible decay in $3+1$ neutrino oscillations on a quantum computer
hep-ph 2026-09 conditional novelty 5.0 of 10

Visible decay of an unstable sterile neutrino shifts the vacuum muon-to-electron CP asymmetry almost equally through parent attenuation and regenerated daughter interference, a decomposition validated analytically and...
Fundamental physics with the diffuse supernova background neutrinos
hep-ph 2020-07 conditional novelty 5.0 of 10

Ten years of Hyper-Kamiokande or Theia DSNB data would measure the Hubble constant to roughly 40%, constrain star formation parameters, and probe neutrino lifetimes near 10^9 s/eV and pseudo-Dirac mass splittings near...
Decoherence in neutrino propagation through matter, and bounds from IceCube/DeepCore
hep-ph 2018-03 conditional novelty 5.0 of 10

IceCube and DeepCore atmospheric neutrino data push the allowed neutrino decoherence parameters down to a few times 10^-24 GeV, improving earlier limits by up to nine orders of magnitude for some energy dependences.
A framework for testing leptonic unitarity by neutrino oscillation experiments
hep-ph 2016-09 accept novelty 5.0 of 10

A (3+N) sterile-neutrino framework shows that for sterile mass-squared differences above about 0.1 eV², oscillation probabilities reduce to a non-unitary 3x3 mixing matrix plus a constant leaking term, giving a model-...
Neutrino oscillations: Quantum mechanics vs. quantum field theory
hep-ph 2010-01 accept novelty 5.0 of 10

The QM neutrino wave packet parameters are derived from QFT, and the correctly normalized oscillation probability is shown to follow from QFT without an ad hoc unitarity imposition.
Paradoxes of neutrino oscillations
hep-ph 2009-05 accept novelty 5.0 of 10

The standard neutrino oscillation formula follows without the 'same energy' or 'same momentum' assumptions whenever production/detection and propagation coherence hold, and a reordered summation convention explains wh...
How astrophysical neutrino sources could be used for early measurements of neutrino mass hierarchy and leptonic CP phase
hep-ph 2006-04 accept novelty 5.0 of 10

Astrophysical neutrino flavor ratios could enhance early measurements of the neutrino mass hierarchy and CP phase when combined with reactor and beam experiments.
Residual Entanglement vs. Residual Coherence: A Wave Packet Approach in Neutrino Oscillation with Matter
hep-ph 2026-11 conditional novelty 4.0 of 10

The paper derives expressions for residual entanglement and coherence in three-flavor neutrino oscillations using a wave-packet approach in matter and analyzes their behavior for DUNE and extended baselines.
White Paper on Light Sterile Neutrino Searches and Related Phenomenology
hep-ex 2022-03 accept novelty 3.0 of 10

A comprehensive review of the four short-baseline neutrino anomalies, the beyond-Standard-Model interpretations proposed for them, and the experimental portfolio needed to resolve them.
keV Neutrino Model Building
hep-ph 2013-02 accept novelty 2.0 of 10

The review organizes the model-building literature for keV sterile neutrino dark matter, showing which mechanisms can produce the keV scale and which models survive the X-ray, seesaw, and neutrino-oscillation constraints.
Status and Perspectives of Neutrino Physics
hep-ph 2021-11 accept novelty 1.0 of 10

A panel-authored review of neutrino physics that consolidates the three-neutrino oscillation picture, the open questions of mass ordering, CP phase, absolute mass scale and sterile states, and the experimental and inf...

How the literature uses it

36 arXiv papers cite this in 59 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 35 sentences without a confident label

Contests it 1 paper

This differs from statements frequently found in the literature, e.g., Refs. [ref] , where it is said that all neutrino mass eigenstates are produced at the moment the source decays, and the different mass eigenstates propagate with different velocities in the lab frame.

Neutrino Oscillation Measurements Computed in Quantum Field Theory · Discussion and Conclusions · contest 0.79

Uses its method or tool 5 papers

Localization is implemented by assigning Gaussian wave packets to all external lines and performing the calculation accordingly [ref] .

Real and Virtual Propagation in Neutrino Oscillations · External Wave Packet Model · 0.85
In this section we present a simple one-dimensional quantum-mechanical wave-packet model [ref] in which the momentum uncertainties of the states which describe the produced and detected massive neutrinos are approximated by Gaussian distributions.

Neutrino Flavor States and the Quantum Theory of Neutrino Oscillations · Quantum-Mechanical Wave-Packet Model · 0.82
We do this using the wave-packet formalism for neutrino propagation [ref] and by properly investigating the kinematical constraints imposed by the neutrino production process.

Beyond $\Delta m^2$: Absolute Mass Sensitivity in Neutrino Oscillations · Neutrino Oscillations Beyond Leading Order · 0.98

Compares with it 2 papers

We can also use the fact that $Δv=Δm^2/2E_ν^2$ to find: [equation] It is notable that the wavepacket separation term obtained in this limit corresponds precisely to the one obtained through a treatment that ignores the entangled recoil altogether, for example Ref. [ref] .

The Width of a Beta-decay-induced Antineutrino Wavepacket · From parent localization scale to neutrino coherence distance · 0.99
While intriguing, results consistent with ours have been found in the literature [ref] .

Beyond $\Delta m^2$: Absolute Mass Sensitivity in Neutrino Oscillations · Production kinematics and the next-to-leading-order phase · 0.81

Cites it as background 13 papers

From a theoretical perspective, the wave-packet formulation in quantum field theory (WPQFT) provides one of the most fundamental frameworks for describing neutrino oscillations, and the basics of the formalism were established in [ref] .

Real and Virtual Propagation in Neutrino Oscillations · Introduction · 0.91
That the finite width of the wavepacket has implications for neutrino oscillation phenomenology has been long recognized and widely studied theoretically [ref] .

The Width of a Beta-decay-induced Antineutrino Wavepacket · Introduction · 0.99
The microscopic layer relates to the theories in the literature [ref] , which can be represented by either the Fock-PS or the Wigner-PS on which Fock states and the Wigner quasi-probability distribution are represented, respectively.

Microscopic and Macroscopic Effects in the Decoherence of Neutrino Oscillations · Introduction · 0.85

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [13]

C. Giunti, C.W. Kim and U.W. Lee, in preparation. 7

View on Pith

[2] [4]

C. Giunti, C.W. Kim and U.W. Lee, Phys. Rev. D 44, 3635 (1991)

View on Pith 1991

[3] [6]

K. Kiers, S. Nussinov and N. Weiss, Phys. Rev. D 53, 537 (1996)

View on Pith 1996

[4] [1]

S. Nussinov, Phys. Lett. B 63, 201 (1976)

View on Pith 1976

[5] [2]

S.M. Bilenky and B. Pontecorvo, Phys. Rep. 41, 225 (1978)

View on Pith 1978

[6] [3]

B. Kayser, Phys. Rev. D 24, 110 (1981)

View on Pith 1981

[7] [5]

C. Giunti, C.W. Kim, J.A. Lee and U.W. Lee, Phys. Rev. D 48, 4310 (1993)

View on Pith 1993

[8] [7]

J.E. Campagne, Phys. Lett. B 400, 135 (1997)

View on Pith 1997

[9] [8]

C. Giunti, C.W. Kim and U.W. Lee, hep-ph/9709494

View on Pith Pith review arXiv

[10] [9]

K. Kiers and N. Weiss, hep-ph/9710289

View on Pith Pith review arXiv

[11] [10]

J. Rich, Phys. Rev. D 48, 4318 (1993)

View on Pith 1993

[12] [11]

W. Grimus and P. Stockinger, Phys. Rev. D 54, 3414 (1996)

View on Pith 1996

[13] [12]

R.G. Winter, Lett. Nuovo Cimento 30, 101 (1981)

View on Pith 1981