Superluminal Neutrinos Research Articles

Lorentz and CPT breaking in gamma-ray burst neutrinos from string theory

Previous studies on high-energy gamma-ray burst neutrinos from IceCube suggest a neutrino speed variation at the Lorentz violation (LV) scale of ~6.4 × 1017 GeV, with opposite velocity variances between neutrinos and antineutrinos. Within a spacetime foam model, inspired by string theory, we develop an approach to describe the suggested neutrino/antineutrino propagation properties with both Lorentz invariance and CPT symmetry breaking. A threshold analysis on the bremsstrahlung of electron-positron pair (ν → νee+) for the superluminal (anti)neutrino is performed. We find that, due to the energy violation caused by the quantum foam, such reaction may be restricted to occur at sufficient high energies and could even be kinematically forbidden. Constraints on neutrino LV from vacuum ee+ pair emission are naturally avoided. Future experiments are appealed to test further the CPT violation of cosmic neutrinos and/or neutrino superluminality.

Decay of superluminal neutrinos in the collinear approximation

The kinematics of the three-body decay, with a modified energy-momentum relation of the particles due to a violation of Lorentz invariance, is presented in detail in the collinear approximation. The results are applied to the decay of superluminal neutrinos producing an electron-positron or a neutrino-antineutrino pair. Explicit expressions for the energy distributions, required for a study of the cascade of neutrinos produced in the propagation of superluminal neutrinos, are derived.

Lorentz- and CPT-violating neutrinos from string/D-brane model

We show that the space-time foam model from string/D-brane theory predicts a scenario in which neutrinos can possess linearly energy dependent speed variation, together with an asymmetry between neutrinos and antineutrinos, indicating the possibility of Lorentz and CPT symmetry violation for neutrinos. Such a scenario is supported by a phenomenological conjecture from the possible associations of IceCube ultrahigh-energy neutrino events with the gamma-ray bursts. It is also consistent with the constraints set by the energy-losing decay channels (e.g., e+e− pair emission, or neutrino splitting) upon superluminal neutrino velocities. We argue that the plausible violations of energy-momentum conservation during decay may be responsible for the stable propagation of these neutrinos, and hence for the evasion of relevant constraints.

Limiting superluminal neutrino velocity and Lorentz invariance violation by neutrino emission from the blazar TXS 0506+056

The detection of high-energy neutrino coincident with the blazar TXS 0506+056 provides a unique opportunity to test Lorentz invariance violation (LIV) in the neutrino sector. Thanks to the precisely measured redshift, i.e., $z=0.3365$, the comoving distance of the neutrino source is determined. In this work, we obtain and discuss the constraints on the superluminal neutrino velocity $\delta_\nu$ and the LIV by considering the energy loss of superluminal neutrino during propagation. Given superluminal electron velocity ($\delta_e \ge 0$), a very stringent constraint on superluminal neutrino velocity can be reached, i.e., $\delta_\nu \lesssim 1.3\times 10^{-18}$, corresponding to the quantum gravity (QG) scale $M_{\rm QG,1} \gtrsim 5.7 \times 10^{3} M_{\rm Pl}$ and $M_{\rm QG,2} \gtrsim 9.3 \times 10^{-6} M_{\rm Pl}$ for linear (quadratic) LIV, which are $\sim 12$ orders of magnitude tighter for linear LIV and $\sim 9$ orders tighter for quadratic LIV compared to the time-of-flight constraint from MeV neutrinos of SN 1987A. While given the subluminal electron velocity, a weaker constraint on the superluminal neutrino velocity is obtained, i.e., $\delta_\nu \lesssim 8 \times 10^{-17}$, which is consistent with the conclusions of previous works. We also study the neutrino detection probability due to the distortion of neutrino spectral shape during propagation, which gives slightly weaker constraints than above by a factor of $\sim2$.

Dynamics of neutrino wave packet in the Tachyon-like Dirac equation

In this study the tachyon-like Dirac equation, formulated by Chodos to describe superluminal neutrino, is solved. The analytical solutions are Gaussian wave packets obtained using the envelope method. It is shown that the superluminal neutrino behaves like a pseudo-tachyon, namely a particle with subluminal velocity and pure imaginary mass that fulfils the energy-momentum relation typical of classical tachyons. The obtained results are used to prove that the trembling motion of the particle position around the median, known as Zitterbewegung, also takes place for the superluminal neutrino, even if the oscillation velocity is always lower than the speed of light. Finally, the pseudo-tachyon wave packet is used to calculate the probability of oscillation between mass states, obtaining a formula analogous to the one obtained for the ordinary neutrino. This suggest that in the experiments concerning neutrino oscillation is not possible to distinguish tachyonic neutrinos from ordinary ones.

Lorentz Violation Footprints in the Spectrum of High-Energy Cosmic Neutrinos—Deformation of the Spectrum of Superluminal Neutrinos from Electron-Positron Pair Production in Vacuum

The observation of cosmic neutrinos up to 2 PeV is used to put bounds on the energy scale of Lorentz invariance violation through the loss of energy due to the production of e + e - pairs in the propagation of superluminal neutrinos. A model to study this effect, which allows us to understand qualitatively the results of numerical simulations, is presented.

Testing Lorentz invariance andCPTsymmetry using gamma-ray burst neutrinos

A recent work [Y. Huang and B.-Q. Ma, Commun. Phys. {\bf 1}, 62 (2018)] associated all four PeV neutrinos observed by IceCube to gamma-ray bursts (GRBs), and revealed a regularity which indicates a Lorentz violation scale $E_{\rm LV}=(6.5\pm0.4)\times10^{17}$ GeV with opposite sign factors $s=\pm 1$ between neutrinos and antineutrinos. The association of "time delay" and "time advance" events with neutrinos and antineutrinos (or vice versa) is only a hypothesis since the IceCube detector cannot tell the chirality of the neutrinos, and further experimental tests are needed to verify this hypothesis. We derive the values of the CPT-odd Lorentz violating parameters in the standard-model extension (SME) framework, and perform a threshold analysis on the electron-positron pair emission of the superluminal neutrinos (or antineutrinos). We find that different neutrino/antineutrino propagation properties, suggested by Y. Huang and B.-Q. Ma, can be described in the SME framework with both Lorentz invariance and CPT symmetry violation, but with a threshold energy constraint. A viable way on testing the CPT symmetry violation between neutrinos and antineutrinos is suggested.

IceCube’s astrophysical neutrino energy spectrum from CPT violation

The 6-year dataset of high-energy starting events (HESE) at IceCube indicates a spectrum of astrophysical neutrinos much softer than expected from the Fermi shock acceleration mechanism. On the other hand, IceCube's up-going muon neutrino dataset and Fermi-LAT's gamma-ray spectrum point to an $E^{-2}$ neutrino spectrum. If the HESE data above 200 TeV are fit with the latter flux, an excess at lower energies ensues, which then suggests a multicomponent spectrum. We show that the HESE dataset can be explained by a single $E^{-2}$ power-law neutrino flux from a muon-damped $p\gamma$ source if neutrino interactions are modified by CPT violation. The low-energy excess is naturally explained by the pileup of events from superluminal neutrino decay, and there is no cutoff at high energies due to the contribution of subluminal antineutrinos. The best-fit scenario with CPT violation also predicts the observation of Glashow resonance events in the near future.

Calculation of the decay rate of tachyonic neutrinos against charged-lepton-pair and neutrino-pair Cerenkov radiation

We consider in detail the calculation of the decay rate of high-energy superluminal neutrinos against (charged) lepton pair Cerenkov radiation, and neutrino pair Cerenkov radiation, i.e., against the decay channels and . Under the hypothesis of a tachyonic nature of neutrinos, these decay channels put constraints on the lifetime of high-energy neutrinos for terrestrial experiments as well as on cosmic scales. For the oncoming neutrino, we use the Lorentz-covariant tachyonic relation , where mν is the tachyonic mass parameter. We derive both threshold conditions as well as on decay and energy loss rates, using the plane-wave fundamental bispinor solutions of the tachyonic Dirac equation. Various intricacies of rest frame versus lab frame calculations are highlighted. The results are compared to the observations of high-energy IceCube neutrinos of cosmological origin.

Neutrino Pair Cerenkov Radiation for Tachyonic Neutrinos

The emission of a charged light lepton pair by a superluminal neutrino has been identified as a major factor in the energy loss of highly energetic neutrinos. The observation of PeV neutrinos by IceCube implies their stability against lepton pair Cerenkov radiation. Under the assumption of a Lorentz-violating dispersion relation for highly energetic superluminal neutrinos, one may thus constrain the Lorentz-violating parameters. A kinematically different situation arises when one assumes a Lorentz-covariant, space-like dispersion relation for hypothetical tachyonic neutrinos, as an alternative to Lorentz-violating theories. We here discuss a hitherto neglected decay process, where a highly energetic tachyonic neutrino may emit other (space-like, tachyonic) neutrino pairs. We find that the space-like dispersion relation implies the absence of a q2 threshold for the production of a tachyonic neutrino-antineutrino pair, thus leading to the dominant additional energy loss mechanism for an oncoming tachyonic neutrino in the medium-energy domain. Surprisingly, the small absolute values of the decay rate and energy loss rate in the tachyonic model imply that these models, in contrast to the Lorentz-violating theories, are not pressured by the cosmic PeV neutrinos registered by the IceCube collaboration.

Ultra-fast neutrinos: What can we learn from a false discovery?

We overview the history of superluminal neutrinos, how they were first observed then refuted, and the emerged physical interpretations. It is shown that in certain cases such false experimental discoveries can help the development of science.

Searching for traces of Planck-scale physics with high energy neutrinos

High energy cosmic neutrino observations provide a sensitive test of Lorentz invariance violation, which may be a consequence of quantum gravity theories. We consider a class of non-renormalizable, Lorentz invariance violating operators that arise in an effective field theory description of Lorentz invariance violation in the neutrino sector inspired by Planck-scale physics and quantum gravity models. We assume a conservative generic scenario for the redshift distribution of extragalactic neutrino sources and employ Monte Carlo techniques to describe superluminal neutrino propagation, treating kinematically allowed energy losses of superluminal neutrinos caused by both vacuum pair emission and neutrino splitting. We consider EFTs with both non-renormalizable CPT-odd and non-renormalizable CPT-even operator dominance. We then compare the spectra derived using our Monte Carlo calculations in both cases with the spectrum observed by IceCube in order to determine the implications of our results regarding Planck-scale physics. We find that if the drop off in the neutrino flux above ~2 PeV is caused by Planck scale physics, rather than by a limiting energy in the source emission, a potentially significant pileup effect would be produced just below the drop off energy in the case of CPT-even operator dominance. However, such a clear drop off effect would not be observed if the CPT-odd, CPT-violating term dominates.

Quantum Decoherence of Neutrino Oscillation and Weak Measurement about Its Group Velocity

We theoretically explore the possibility of observing the quantum decoherence of neutrino oscillation due to the vacuum dispersion, that the wave-packet of neutrino spatially splits according to the different velocities of two mass eigenstates. We find that if this decoherence could be observed and the range of values of the mixing angle is known, then the superluminal neutrino phenomena could occur for some mixing angles as the consequence of a weak measurement about flavor mixing in the neutrino propagation. Our calculation gives the explicit dependence of group velocity shift to the decoherence factor and the weak value of neutrino's pre and post-selected states. We also study the related problems for the neutrino oscillation with three generations.

Theoretical particle limiting velocity from the bicubic equation: Neutrino example

There has been a lot of interest in measuring the velocities of massive elementary particles, particularly the neutrinos. Some neutrino experi- ments at first observed superluminal neutrinos, thus violating the velocity of light c as a limiting velocity. But, after eliminating some mistakes, such as, for the OPERA experiments plugging the cable correctly and calibrat- ing the clock correctly, the measured neutrino velocity complied with c. Pursuing the theoretical side of particle limiting velocities, here directly from the special relativistic kinematics, in which all physical quantities are in the overall mathematical consistency with each other, one treats formally the velocity of light c as yet to be deduced particle limiting ve- locity, and derives the bicubic equation for the particle limiting velocity in the arbitrary reference frame.

Propagation of superluminal PeV IceCube neutrinos: A high energy spectral cutoff or new constraints on Lorentz invariance violation

The IceCube observation of cosmic neutrinos with ${E}_{\ensuremath{\nu}}>60\text{ }\text{ }\mathrm{TeV}$, most of which are likely of extragalactic origin, allows one to severely constrain Lorentz invariance violation (LIV) in the neutrino sector, allowing for the possible existence of superluminal neutrinos. The subsequent neutrino energy loss by vacuum ${e}^{+}{e}^{\ensuremath{-}}$ pair emission (VPE) is strongly dependent on the strength of LIV. In this paper we explore the physics and cosmology of superluminal neutrino propagation. We consider a conservative scenario for the redshift distribution of neutrino sources. Then by propagating a generic neutrino spectrum, using Monte Carlo techniques to take account of energy losses from both VPE and redshifting, we obtain the best present constraints on LIV parameters involving neutrinos. We find that ${\ensuremath{\delta}}_{\ensuremath{\nu}e}={\ensuremath{\delta}}_{\ensuremath{\nu}}\ensuremath{-}{\ensuremath{\delta}}_{e}\ensuremath{\le}5.2\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}21}$. Taking ${\ensuremath{\delta}}_{e}\ensuremath{\le}5\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}21}$, we then obtain an upper limit on the superluminal velocity fraction for neutrinos alone of $1.0\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}20}$. Interestingly, by taking ${\ensuremath{\delta}}_{\ensuremath{\nu}e}=5.2\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}21}$, we obtain a cutoff in the predicted neutrino spectrum above 2 PeV that is consistent with the lack of observed neutrinos at those energies, and particularly at the Glashow resonance energy of 6.3 PeV. Thus, such a cutoff could be the result of neutrinos being slightly superluminal, with ${\ensuremath{\delta}}_{\ensuremath{\nu}}$ being $(0.5\text{ }\text{ }\text{to}\text{ }\text{ }1.0)\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}20}$.

Towards Superluminal Physics: Compromising Einstein's Special Relativity and Faster-Than-Light Particles

Throughout the violation of momentum-velocity parallelism and deformation of the Einstein equivalence principle, the model of faster- than-light motion, wherein both the Minkowski energy-momentum space and the Lorentz invariance, laying the foundations of Special Relativity and Standard Model, is constructed. Recently announced and denounced CERN's superluminal neutrinos are confronted.

Equations for massless and massive spin-1/2 particles with varying speed and neutrino in matter

The modified Dirac equations describing massless and massive spin-1/2 particles violating the Lorentz invariance are considered. The equation for massless fermions with varying speed is formulated in the 16-component first-order form. The projection matrix, which is the density matrix, extracting solutions to the equation has been obtained. Exact solutions to the equation and energy spectrum for a massive neutrino are obtained in the presence of background matter. We have considered as subluminal as well as superluminal propagations of neutrinos. The bounds on the Lorentz invariance violation parameter from astrophysical observations by IceCube, OPERA, MINOS collaborations and by the SN1987A supernova are obtained for superluminal neutrinos.

Limiting superluminal electron and neutrino velocities using the 2010 Crab Nebula flare and the IceCube PeV neutrino events

The observation of two PeV-scale neutrino events reported by Ice Cube allows one to place constraints on Lorentz invariance violation (LIV) in the neutrino sector. After first arguing that at least one of the PeV IceCube events was of extragalactic origin, I derive an upper limit for the difference between putative superluminal neutrino and electron velocities of ⩽∼5.6×10-19 in units where c=1, confirming that the observed PeV neutrinos could have reached Earth from extragalactic sources. I further derive a new constraint on the superluminal electron velocity, obtained from the observation of synchrotron radiation from the Crab Nebula flare of September, 2010. The inference that the >1GeV γ-rays from synchrotron emission in the flare were produced by electrons of energy up to ∼5.1PeV indicates the non-occurrence of vacuum Ćerenkov radiation by these electrons. This implies a new, strong constraint on superluminal electron velocities δe⩽∼5×10-21. It immediately follows that one then obtains an upper limit on the superluminal neutrino velocity alone of δν⩽∼5.6×10-19, many orders of magnitude better than the time-of-flight constraint from the SN1987A neutrino burst. However, if the electrons are subluminal the constraint on |δe|⩽∼8×10-17, obtained from the Crab Nebula γ-ray spectrum, places a weaker constraint on superluminal neutrino velocity of δν⩽∼8×10-17.

Stringent constraint on neutrino Lorentz invariance violation from the two IceCube PeV neutrinos

It has been speculated that Lorentz-invariance violation (LIV) might be generated by quantum-gravity (QG) effects. As a consequence, particles may not travel at the universal speed of light. In particular, superluminal extragalactic neutrinos would rapidly lose energy via the bremssthralung of electron-positron pairs (nu -> nu e+ e-), damping their initial energy into electromagnetic cascades, a figure constrained by Fermi-LAT data. We show that the two cascade neutrino events with energies around 1 PeV recently detected by IceCube -if attributed to extragalactic diffuse events, as it appears likely- can place the strongest bound on LIV in the neutrino sector, namely delta =(v^2-1) < O(10^(-18)), corresponding to a QG scale M_QG ~ 10^5 M_Pl (M_QG >~ 10^(-4) M_Pl) for a linear (quadratic) LIV, at least for models inducing superluminal neutrino effects (delta > 0).

Decay kinematics in the aether: Pion decay, kaon decay, and superluminal Cherenkov radiation

Pion and kaon decay, π → μ + νμ, K → μ + νμ, into muons and GeV neutrinos is investigated with regard to a possible superluminal neutrino speed. Photonic Cherenkov emission by superluminal high-energy charges is shown to be forbidden by causality violation. A proper causality interpretation of decay processes outside the lightcone involving superluminal particles requires an absolute spacetime conception based on a distinguished frame of reference (aether frame). The universal reference frame is physically manifested as the rest frame of the cosmic microwave background (CMB) radiation. The propagation of particles and radiation modes in the CMB rest frame is determined by dispersive wave equations coupled to isotropic permeability tensors. The decay of ∼50 GeV pions and ∼85 GeV kaons generating the CERN neutrino beam to Gran Sasso (CNGS) is analyzed in this context. Causality constraints on the group velocity of the ∼17 GeV muon neutrinos produced in the decay are derived and compared to recent experimental bounds on the neutrino speed.