REVIEW
Neutrino production coherence and oscillation experiments
High Energy Physics - Phenomenology · Submitted 19 Jan 2012 · 25 references
Pith's verdict: The equivalence claim is correct and the §6 explanation is the real contribution; the finite-width correction is a smaller, more conditional result than the abstract implies.
T0 · AI review
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Referee report
The paper
The paper claims
The paper asks whether two ways of accounting for an extended neutrino source — summing production amplitudes versus averaging ordinary oscillation probabilities — give the same answer, and shows they do exactly for pointlike parent pions,
The reading
What carries the argument
The load-bearing object is the interference kernel $G_(x_1-x_2)$, a convolution of two pion shape factors with a decay exponential, evaluated at shifted arguments. Its width is $[v_g/(v_g-v_)]_{x}$ — the pion width stretched by the velocity mismatch between neutrino and pion — and this stretched width is what sets both the size of the correction and, in the large-width limit, the scale of production decoherence. Two dimensionless parameters organize the phenomenology: $_p = 2l_p/l_{osc}$ for a short tunnel (few pions decay before the wall) and $= 2l_{decay}/l_{osc}$ for a long tunnel (most pions decay in flight), with the identity $_p = _p$ tying them together. A further result is that detecting the muon accompanying the neutrino, or letting the pion collide with neighbours in a way that records its position, localizes the emission point to a width $_{x}$ and thereby restores production coherence rather than destroying it.
Extended reading notes
Core claim
The central claim is a sharp equivalence statement plus a sharp boundary on it. Coherent amplitude summation over the pion trajectory and incoherent averaging of the standard oscillation probability over the production coordinate coincide exactly when the parent pion is pointlike and detection is perfectly localized in space and time; in that case the usual practice of averaging over source and detector sizes correctly captures whatever decoherence is present. The equivalence is not an accident of the calculation but follows from the structure of the general result, in which the oscillation probability is written as an integral over a kernel $K_{jk}(z)$ weighted by the decay exponential. For pointlike pions $K_{jk}(z)$ is independent of the mass indices $j,k$, so the mass sum reproduces the standard probability inside the integral. For finite-width pion wave packets $K_{jk}(z)$ retains its $j,k$ dependence and the reduction fails. In that case the leading correction is an added phase $A_$ proportional to $[v_g/(v_g-v_)](_{}^2/2P)_{x}$, whose coefficient is $2x$ for a Gaussian pion wave packet and $1/3$ for a box-shaped one — the same structure, differing only by a number of order one, which the authors also reproduce from a purely geometric argument about where along the pion wave packet the emission can occur.
Load-bearing premise
The finite-width results assume the pion wave function can be written as a shape factor moving at one definite group velocity multiplied by a decay exponential attached in one definite way; the authors note in footnote 6 that this attachment is ambiguous once the pion has finite width, and they remove the ambiguity only by requiring the pion to decay slowly compared with its own width, $_{x}/v_$ small.
Editorial extensions
If this is right
- For present accelerator experiments the correction from finite pion width is negligible: making $A_$ of order one would need pion energies around $10^3$ TeV at $_{x} \sim 10^{-4}$ cm and $^2 \sim 1$ eV$^2$, so standard source-averaging is safe there.
- Production decoherence for a long decay tunnel is governed by $$, and for a short tunnel by $_p$; large values of either suppress the oscillating terms and leave a flat, energy-independent survival probability with no baseline dependence.
- Because detecting the charged lepton from the decay tags the production point, muon tagging narrows the effective production region and reduces the averaging, which can partially restore oscillations that source averaging would wash out.
- The same reasoning applies to any parent decay — kaon, muon, beta decay — provided the accompanying particles go undetected, so the conclusions are not specific to pions.
- In the limit of a pointlike parent at rest the decoherence parameters vanish, which explains why decay-at-rest sources such as LSND and KARMEN are essentially free of production-decoherence effects.
Reading between the lines
- The equivalence argument is really a statement about when a kernel loses its dependence on the neutrino mass label; this suggests a general diagnostic — write the probability as an integral over a production kernel and check whether it factorizes — that would apply to any proposed source, not just pion decay tunnels.
- The stretched width $[v_g/(v_g-v_)]_{x}$ is the same velocity-mismatch factor that appears in the coherence energy uncertainty, which hints that the finite-width correction and the standard production-coherence condition are two faces of one kinematic quantity rather than independent effects.
- Because the correction is a phase shift rather than a suppression at leading order, a finite pion width would be nearly invisible in a total-rate measurement but could in principle show up as a distortion of the oscillation pattern at high energy — a harder but cleaner signature than decoherence.
- The paper's own remark that the correction could become large for parent pions of extremely high energy suggests that any future ultra-high-energy neutrino source with an extended parent wave packet would need the amplitude treatment rather than the standard averaging.
Original abstract
Neutrino oscillations are only observable when the neutrino production, propagation and detection coherence conditions are satisfied. In this paper we consider in detail neutrino production coherence, taking \pi\to \mu \nu \ decay as an example. We compare the oscillation probabilities obtained in two different ways: (1) coherent summation of the amplitudes of neutrino production at different points along the trajectory of the parent pion; (2) averaging of the standard oscillation probability over the neutrino production coordinate in the source. We demonstrate that the results of these two different approaches exactly coincide, provided that the parent pion is considered as pointlike and the detection process is perfectly localized. In this case the standard averaging of the oscillation probability over the finite spatial extensions of the neutrino source (and detector) properly takes possible decoherence effects into account. We analyze the reason for this equivalence of the two approaches and demonstrate that for pion wave packets of finite width \sigma_{x\pi} the equivalence is broken. The leading order correction to the oscillation probability due to \sigma_{x\pi}\ne 0 is shown to be \sim [v_g/(v_g-v_\pi)]\sigma_{x\pi}/l_{osc}, where v_g and v_\pi \ are the group velocities of the neutrino and pion wave packets, and l_{osc} is the neutrino oscillation length.
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.
The abstract, sentence by sentence
Neutrino oscillations are only observable when the neutrino production, propagation and detection coherence conditions are satisfied. In this paper we consider in detail neutrino production coherence, taking \pi\to \mu \nu \ decay as an example. We compare the oscillation probabilities obtained in two different ways: (1) coherent summation of the amplitudes of neutrino production at different points along the trajectory of the parent pion; (2) averaging of the standard oscillation probability over the neutrino production coordinate in the source. We demonstrate that the results of these two different approaches exactly coincide, provided that the parent pion is considered as pointlike and the detection process is perfectly localized. In this case the standard averaging of the oscillation probability over the finite spatial extensions of the neutrino source (and detector) properly takes possible decoherence effects into account. We analyze the reason for this equivalence of the two approaches and demonstrate that for pion wave packets of finite width \sigma_{x\pi} the equivalence is broken. The leading order correction to the oscillation probability due to \sigma_{x\pi}\ne 0 is shown to be \sim [v_g/(v_g-v_\pi)]\sigma_{x\pi}/l_{osc}, where v_g and v_\pi \ are the group velocities of the neutrino and pion wave packets, and l_{osc} is the neutrino oscillation length.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Neutrino oscillations are only observable when the neutrino production, propagation and detection coherence conditions are satisfied. | background 1.00 | 0.07 | 0.05 | asserted 1.00 |
| s1 | In this paper we consider in detail neutrino production coherence, taking \pi\to \mu \nu \ decay as an example. | contribution 0.98 | 0.85 | 0.03 | asserted 0.71 |
| s2 | We compare the oscillation probabilities obtained in two different ways: (1) coherent summation of the amplitudes of neutrino production at different points along the trajectory of the parent pion; (2) averaging of the standard oscillation probability over the neutrino production coordinate in the source. | method 0.86 | 0.92 | 0.05 | asserted 0.68 |
| s3 | We demonstrate that the results of these two different approaches exactly coincide, provided that the parent pion is considered as pointlike and the detection process is perfectly localized. | result 1.00 | 0.90 | 0.28 | asserted 1.00 |
| s4 | In this case the standard averaging of the oscillation probability over the finite spatial extensions of the neutrino source (and detector) properly takes possible decoherence effects into account. | interpretation 0.72 | 0.65 | 0.23 | asserted 0.98 |
| s5 | We analyze the reason for this equivalence of the two approaches and demonstrate that for pion wave packets of finite width \sigma_{x\pi} the equivalence is broken. | contribution 0.74 | 0.94 | 0.23 | asserted 1.00 |
| s6 | The leading order correction to the oscillation probability due to \sigma_{x\pi}\ne 0 is shown to be \sim [v_g/(v_g-v_\pi)]\sigma_{x\pi}/l_{osc}, where v_g and v_\pi \ are the group velocities of the neutrino and pion wave packets, and l_{osc} is the neutrino oscillation length. | result 1.00 | 0.93 | 0.28 | asserted 1.00 |
What was examined, and what was not
- arXiv listing abstract v2
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
Figures
Figures reproduced from arXiv:1201.4128 by the authors.
References
How the literature uses it
33 arXiv papers cite this in 49 sentences
Papers citing it · 30 sentences without a confident label
Contests it 1 paper
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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 1 paper
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We first estimate the coherence length of PeV neutrinos as follows [ref] .
Coherent Propagation of PeV Neutrinos and the Dip in the Neutrino Spectrum at IceCube · Neutrino Propagation · 0.83
Compares with it 1 paper
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[ref] in the limit of an infinitely long pion-decay tunnel ($l_p →∞$).
Neutrino oscillations and scattering theory · Derivation · 0.99
Cites it as background 14 papers
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In particular, possible manifestations of neutrino WP separation in reactor experiments [ref] and experiments with radioactive neutrino sources [ref] have been investigated (for earlier and related discussions, including those for other neutrino experiments, see e.g. [ref] ).
Damping of neutrino oscillations, decoherence and the lengths of neutrino wave packets · Introduction · 0.99
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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
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[ref] for a discussion.
Neutrino oscillations and scattering theory · Discussion · 0.95
What it cites · 20 sentences without a confident label
Uses data or values from 4 papers
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In table 1 we give the parameters $Γl_p/v_π$, $ϕ_p$ and $ξ$, along with some other relevant physical characteristics, for a number of experiments [ref] .
Active to sterile neutrino mixing limits from neutral-current interactions in MINOS · Implications for neutrino oscillation experiments · 0.95
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In table 1 we give the parameters $Γl_p/v_π$, $ϕ_p$ and $ξ$, along with some other relevant physical characteristics, for a number of experiments [ref] .
NOvA: Present and Future · Implications for neutrino oscillation experiments · 0.95
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In table 1 we give the parameters $Γl_p/v_π$, $ϕ_p$ and $ξ$, along with some other relevant physical characteristics, for a number of experiments [ref] .
T2K Results and Future Plans · Implications for neutrino oscillation experiments · 0.95
Cites as support 1 paper
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[ref] where, along with the probability summation, a simplified treatment of the quantum mechanical coherent amplitude summation was given.
Active to sterile neutrino oscillations: Coherence and MINOS results · Discussion · 0.96
Cites as background 2 papers
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The oscillation probability $P_αβ(L)$ is given, up to a normalization factor, by (see, e.g., [ref] ) P_αβ(L)=∑_j,kU^*_αj U_βj^ U_αk^ U_βk^* I_jk(L) ,
Paradoxes of neutrino oscillations · Neutrino wave packet in the coordinate space · 0.82
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[ref] , where it was considered in the framework of incoherent summation of probabilities of neutrino production at different points inside the neutrino source.
Active to sterile neutrino oscillations: Coherence and MINOS results · Introduction · 0.88
Discussion
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