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Constraint on super-luminal neutrinos from vacuum Cerenkov processes
High Energy Physics - Phenomenology · Submitted 11 Nov 2011
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We conclude that if the muon-neutrino velocity has a quadratic energy dependence, then OPERA result is consistent with non-observation of forbidden neutrino decays and large deviations from the standard pion decay lifetime.
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The abstract, sentence by sentence
We examine the Cerenkov-like emission of $e^+ e^-$ from muon super-luminal muon neutrinos assuming a quadratic energy dependence of the neutrino velocity arising from Lorentz violating interactions. We find that with the OPERA result for the neutrino-photon velocity difference, the decay length for the process $\nu_\mu\rightarrow \nu_\mu e^+ e^-$ is 17,039 km which is much larger than the OPERA neutrinos path length of 730 km. We also calculate the pion rate for super-luminal outgoing neutrinos, and we find that the deviation of the pion decay length from the standard Lorentz conserving case at the OPERA neutrino energy is 2%. We conclude that if the muon-neutrino velocity has a quadratic energy dependence, then OPERA result is consistent with non-observation of forbidden neutrino decays and large deviations from the standard pion decay lifetime.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We examine the Cerenkov-like emission of $e^+ e^-$ from muon super-luminal muon neutrinos assuming a quadratic energy dependence of the neutrino velocity arising from Lorentz violating interactions. | contribution 0.92 | 0.75 | 0.03 | asserted 0.57 |
| s1 | We find that with the OPERA result for the neutrino-photon velocity difference, the decay length for the process $\nu_\mu\rightarrow \nu_\mu e^+ e^-$ is 17,039 km which is much larger than the OPERA neutrinos path length of 730 km. | result 1.00 | 0.94 | 0.10 | asserted 1.00 |
| s2 | We also calculate the pion rate for super-luminal outgoing neutrinos, and we find that the deviation of the pion decay length from the standard Lorentz conserving case at the OPERA neutrino energy is 2%. | result 1.00 | 0.95 | 0.05 | asserted 1.00 |
| s3 | We conclude that if the muon-neutrino velocity has a quadratic energy dependence, then OPERA result is consistent with non-observation of forbidden neutrino decays and large deviations from the standard pion decay lifetime. | interpretation 0.99 | 0.72 | 0.95 | hedged possibility 0.92 |
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The paper
Original abstract
We examine the Cerenkov-like emission of $e^+ e^-$ from muon super-luminal muon neutrinos assuming a quadratic energy dependence of the neutrino velocity arising from Lorentz violating interactions. We find that with the OPERA result for the neutrino-photon velocity difference, the decay length for the process $\nu_\mu\rightarrow \nu_\mu e^+ e^-$ is 17,039 km which is much larger than the OPERA neutrinos path length of 730 km. We also calculate the pion rate for super-luminal outgoing neutrinos, and we find that the deviation of the pion decay length from the standard Lorentz conserving case at the OPERA neutrino energy is 2%. We conclude that if the muon-neutrino velocity has a quadratic energy dependence, then OPERA result is consistent with non-observation of forbidden neutrino decays and large deviations from the standard pion decay lifetime.
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References
How the literature uses it
14 arXiv papers cite this in 28 sentences
Papers citing it · 15 sentences without a confident label
Contests it 1 paper
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The authors in Ref. [ref] then approximate the energy loss using a constant value of $δ$ so that they give in their eq.(21) a mean decay time that scales as the 5th power of the $ν$ energy when in fact the dependence of $δ$ on energy shows that the decay time has to scale with the 11th power of this energy, as we have shown here.
Estimates of Radiation by Superluminal Neutrinos · Introduction · contest 0.91
Builds on it 2 papers
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It also incorporates as limiting cases studies of nonrenormalizable neutrino operators [ref] , including discussions of modified dispersion relations in the context of superluminal neutrinos [ref] .
Neutrinos with Lorentz-violating operators of arbitrary dimension · Introduction · 0.92
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This generalises our earlier calculation of the $n=2$ and $n=4$ cases [ref] .
Neutrino processes with power law dispersion relations · $ν_μ→ν_μe^+e^-$ · 0.99
Uses its method or tool 1 paper
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Using the above definitions in eq.([ref]) and substituting in eq.([ref]) gives the rate of electron-positron pair emission as [equation] where $f$ is complicated function of $x$, $θ̃$ and $θ̃_̃1̃$ [ref] .
Neutrino processes with power law dispersion relations · $ν_μ→ν_μe^+e^-$ · 0.82
Compares with it 2 papers
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Concerning the detailed relationship between our calculation and that in Ref. [ref] , we note that the authors in Ref. [ref] make a numerical estimate for the $ν→ν+e^++e^-$ process with the quadratic dispersion for the $ν$ superluminality and with the usual special relativity dispersion for the $e^-, e^+$ with the result that the coefficient of $G_F^2E^5δ^3(1-4sin^2θ_w+8sin^4θ_w)$ in the Cohen-Glashow process is 1/45197.8 vs the exact result [ref] 1/41672.4, neglecting the lepton rest masses.
Estimates of Radiation by Superluminal Neutrinos · Introduction · 0.97
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The results are consistent with [ref] quantitatively and [ref] qualitatively.
Replaying neutrino bremsstrahlung with general dispersion relations · Introduction · 1.00
Cites it as support 1 paper
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The vacuum-Cherenkov-type process of point (iv) is not forbidden but has a significantly reduced rate [ref] .
Spontaneously broken Lorentz invariance from the dynamics of a heavy sterile neutrino · Discussion · 0.96
Cites it as background 4 papers
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Recently, the OPERA experiment of superluminal neutrinos has been widely discussed [ref] .
Superluminal Neutrinos from Special Relativity with de Sitter Space-time Symmetry · Conclusions and Discussions · 1.00
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Several solutions to these challenges have been proposed as well [ref] .
The Superluminal Neutrinos from Deformed Lorentz Invariance · Introduction · 0.85
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From the theoretical point of view, many groups have already studied the possible solutions or pointed out the challenges to the OPERA anomaly [ref] .
Constraints on Neutrino Velocities Revisited · Introduction · 1.00
What it cites · 18 sentences without a confident label
Compares with 1 paper
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The OPERA result find that muon neutrinos of average energy 17.5 GeV traverse a distance of 730 km from CERN to Gran Sasso with a velocity $c_ν$ which exceeds the photon velocity, δ(E=17.5GeV)= (v_ν-c)/c= (2.48 ±0.28 (stat) ±0.30 (syst) ) ×10^-5 This is comparable with an earlier measurement of muon neutrino velocity by MINOS [ref] who found that muon neutrinos of average energy 3 GeV traversing a distance 730 km exceed c by an amount, $δ(E=3 GeV)= (5.1 ±2.9) ×10^-5$.
Measurement of neutrino velocity with the MINOS detectors and NuMI neutrino beam · Introduction · 0.83
Cites as support 4 papers
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This implies that the dispersion relation $E^2=p^2(1+η^')$ to describe energy independent super-luminal neutrino velocities can be ruled out as pointed out in [ref] .
New Constraints on Neutrino Velocities · Energy independent neutrino velocity · 0.96
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This implies that the to be consistent with all observations, the neutrino velocity is energy dependent [ref] .
Probes of Lorentz Violation in Neutrino Propagation · Introduction · 0.97
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This implies that the to be consistent with all observations, the neutrino velocity is energy dependent [ref] .
Interpreting OPERA results on superluminal neutrino · Introduction · 0.97
Cites as background 5 papers
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Models of Lorentz violation which can give an energy dependent neutrino velocity are discussed in [ref] .
Possible cosmogenic neutrino constraints on Planck-scale Lorentz violation · Introduction · 0.88
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Models of Lorentz violation which can give an energy dependent neutrino velocity are discussed in [ref] .
On the Possibility of Superluminal Neutrino Propagation · Introduction · 0.88
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Horava-Lifshitz theories [ref] provide a framework where theories are made renormalizable by the introduction of Lorentz violating higher derivative terms in the Lagrangian.
Quantum Gravity at a Lifshitz Point · Introduction · 0.99
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