We study two superluminal neutrino scenarios where δv\equiv (v-c)/c is a constant. To be consistent with the OPERA, Borexino, and ICARUS experiments and with the SN1987a observations, we assume that δv_ν on the Earth is about three order larger than that on the interstellar scale. To explain the theoretical challenges from the Bremsstrahlung effects and pion decays, we consider the deformed Lorentz invariance, and show that the superluminal neutrino dispersion relations can be realized properly while the modifications to the dispersion relations of the other Standard Model particles can be negligible. In addition, we propose the deformed energy and momentum conservation laws for a generic physical process. In Scenario I the momentum conservation law is preserved while the energy conservation law is deformed. In Scenario II the energy conservation law is preserved while the momentum conservation law is deformed. We present the energy and momentum conservation laws in terms of neutrino momentum in Scenario I and in terms of neutrino energy in Scenario II. In such formats, the energy and momentum conservation laws are exactly the same as those in the traditional quantum field theory with Lorentz symmetry. Thus, all the above theoretical challenges can be automatically solved. We show explicitly that the Bremsstrahlung processes are forbidden and there is no problem for pion decays.
Generally speaking, the existence of a superluminal neutrino can be attributed either to re-entrant Lorentz violation at ultralow energy from intrinsic Lorentz violation at ultrahigh energy or to spontaneous breaking of fundamental Lorentz invariance (possibly by the formation of a fermionic condensate). Re-entrant Lorentz violation in the neutrino sector has been discussed elsewhere. Here, the focus is on mechanisms of spontaneous symmetry breaking.
In this short note we remark that the OPERA measurement could be reconciled with information from SN1987a in the context of deformed special relativity without the loss of energy through Cherenkov-like process reported by Cohen and Glashow.
A particular Fermi-point-splitting (FPS) model is proposed, which allows, for finite values of the three-momentum, the group and phase velocities of the muon-flavor neutrino in vacuum to be superluminal (i.e., muon-neutrino velocities greater than c, the velocity of light in vacuum). Still, the proposed FPS model has a front velocity equal to c for all particles, which is known to be crucial for causality. If the muon-neutrino velocity is indeed superluminal as claimed by OPERA, the model predicts that at least one of the other two flavors of neutrinos has a subluminal velocity.
The toy fermion model coupled with Lagrange multiplier constraint field is proposed. The possibility of superluminal neutrino propagation as result of dynamical Lorentz symmetry breaking is studied.
We consider Lorentz- and CPT-violating dimension-5 operators to address the issue of superluminal neutrinos recently pointed out in OPERA experiments. We assume these operators in the photon and neutrino sectors coupled to Lorentz-violating backgrounds in a preferred frame defined by a time-like direction. We show that such operators can produce a curve with OPERA's slope that fits OPERA, MINOS and supernova SN1987a data.
In this article an idea is presented, which allows for the explanation of superluminal muon neutrinos. It is based on the introduction of a new superluminal, massless gauge boson coupling to the neutrino only, but not to other standard model particles. The model is discussed with regard to the Supernova 1987 (SN 1987) velocity bound on electron antineutrinos and the Cohen-Glashow constraint on superluminal neutrino propagation. The latter can be circumvented if - within the framework of the model - a sterile neutrino mixing with the active neutrino mass eigenstates is introduced. The suggestio…
OPERA collaboration has reported evidence of superluminal phenomenon for neutrinos. One of the possible ways to explain the superluminality is to have Lorentz symmetry violated. It has been shown that dispersion relations put forwards has the problem of physics laws vary in different inertial frames leading to conflicting results on Cherenkov-like radiation, pion decay and high energy neutrino cosmic ray. For theories with deformed Lorentz symmetry, by modifying conservation laws corresponding to energy and momentum in the usual Lorentz invariant theory, it is possible to have superluminal eff…
We revisit the bremsstrahlung process of a superluminal neutrino motivated by OPERA results. From a careful analysis of the plane wave solutions of the superluminal neutrino, we find that the squared matrix elements contain additional terms from Lorentz violation due to the modified spin sum for the neutrino. We point out that the coefficients of the decay rate and the energy loss rate significantly depend on the details of the model, although the results are parametrically similar to the ones obtained by Cohen and Glashow [1]. We illustrate this from the modified neutral current interaction o…
We argue that the recent measurement of the neutrino velocity to be higher than the velocity of light could be due to violation of Lorentz invariance by the muon neutrinos. This result need not undermine special-relativistic foundational notions of causality.
Modified neutrino dispersion relations, which still obey the relativity principle, can have both a superluminal (muon-type) neutrino and a luminal (electron-type) neutrino, as long as neutrino-mass effects can be neglected. The idea is to allow for flavor-dependent deformed Lorentz transformations and an appropriate hierarchy of energy scales. If OPERA's result on a superluminal velocity of the muon-neutrino is confirmed, the model has a matching superluminal velocity of the corresponding charged lepton, the muon, at equal particle energy. Assuming that this model is not already ruled out, new…
We show that the superluminal muon neutrinos in the recent OPERA experiment can exist theoretically. The refutation of the OPERA experiment from some theoretical arguments is not universally valid, but resulting from some implicit assumptions. Our argument can accommodate both the OPERA experiment for superluminal neutrinos and the ICARUS experiment of no evidence for the analogues Cherenkov radiation of muon neutrinos from CERN to the LNGS.
We analyze the possibility of superluminal neutrino propagation delta v = (v - c)/c > 0 as indicated by OPERA data, in view of previous phenomenological constraints from supernova SN1987a and gravitational Cerenkov radiation. We argue that the SN1987a data rule out delta v ~ (E_ν/M_N)^N for N \le 2 and exclude, in particular, a Lorentz-invariant interpretation in terms of a 'conventional' tachyonic neutrino. We present two toy Lorentz-violating theoretical models, one a Lifshitz-type fermion model with superluminality depending quadratically on energy, and the other a Lorentz-violating modific…
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 to understand qualitatively the results of numerical simulations, is presented.
In this paper, we consider the apparent superluminal speed of neutrinos in their travel from CERN to Gran Susso, as measured by the OPERA experiment, within the framework of the Extended Lorentz Transformation Model. The model is based on a natural extension of Lorentz transformation by wick rotation. Scalar and Dirac's fields are considered and invariance under the new lorentz group is discussed. Moreover, an extension of quantum mechanics to accommodate new particles is considered using the newly proposed Generalized-$\mathbb{C}$ quantum mechanics. A two dimensional representation of the new…
From the data release of OPERA - CNGS experiment, and publicly announced on 23 September 2011, we cast a phenomenological model based on a Majorana neutrino state carrying a fictitious imaginary mass term, already discussed by Majorana in 1932. This mass term can be induced by the interaction with the matter of the Earth's crust during the 735 Km travel. Within the experimental errors, we prove that the model fits with OPERA, MINOS and supernova SN1987a data. Possible violations to Lorentz invariance due to quantum gravity effects have been considered.
Violation of Lorentz invariance (VLI) has been suggested as an explanation of the superluminal velocities of muon neutrinos reported by OPERA. In this note we show that the amount of VLI required to explain this result poses severe difficulties with the kinematics of the pion decay, extending its lifetime and reducing the momentum carried away by the neutrinos. We show that the OPERA experiment limits $α= (v_ν- c)/c < 4 \times 10^{-6}$. We then take recourse to cosmic ray data on the spectrum of muons and neutrinos generated in the earth's atmosphere to provide a stronger bound on VLI: $(v-c)/…
The IceCube observation of cosmic neutrinos with $E_ν > 60$ 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 $e^+e^-$ 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 neu…
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 $δ_ν$ and the LIV by considering the energy loss of superluminal neutrino during propagation. Given superluminal electron velocity ($δ_e \ge 0$), a very stringent constraint on superluminal neutrino velocity can be…
OPERA has claimed the discovery of superluminal propagation of neutrinos. We analyze the consistency of this claim with previous tests of special relativity. We find that reconciling the OPERA measurement with information from SN1987a and from neutrino oscillations requires stringent conditions. The superluminal limit velocity of neutrinos must be nearly flavor independent, must decrease steeply in the low-energy domain, and its energy dependence must depart from a simple power law. We construct illustrative models that satisfy these conditions, by introducing Lorentz violation in a sector wit…
We show that in the presence of a distance dependent Lorentz-violating time-like background one may find superluminal neutrinos at some high energy such as OPERA's scale. The similar behavior but approaching the subluminal branch is found to appear for inflaton field in the low energy scale. Thus this scenario seems to be suitable to acomplish both superluminal neutrinos and dark energy.
The superluminal is reported in OPERA neutrino experiment (arXiv:1109.4897v2), this result is consistent with previous MINOS experiment about neutrino velocity (Phys. Rev. D 76, 072005 (2007)). Here we propose a Dirac equation of tachyon for superluminal neutrino in which the mass matrix is anti-hermitian. Additionally we find that this anti-hermitian mass matrix which is responsible for superluminal can only be for neutrinos, while other results of Standard Model are unchanged. In case that Lorentz invariant is remained, the masses of neutrinos are estimated based on available data of experim…
Precise tests of Lorentz invariance in neutrinos can be performed using long baseline experiments such as MINOS and OPERA or neutrinos from astrophysical sources. The MINOS collaboration reported a measurement of the muonic neutrino velocities that hints to super-luminal propagation, very recently confirmed at 6 sigma by OPERA. We consider a general parametrisation which goes beyond the usual linear or quadratic violation considered in quantum-gravitational models. We also propose a toy model showing why Lorentz violation can be specific to the neutrino sector and give rise to a generic energy…
The use of the vacuum lepton pair production process ($ν\to νe^- e^+ $), a viable reaction for superluminal neutrinos, to put constraints on Lorentz violations requires a dynamical framework. Different choices of dynamical matrix elements and modified dispersion relations for neutrinos, leading to numerical factors differing by one order of magnitude in the results for the pair production decay width, are used to show the uncertainties on these constraints.
With the help of the Seiberg-Witten map, one can obtain an effective action of a deformed QED from a noncommutative QED. Starting from the deformed QED, we investigate the propagation of photons in the background of electromagnetic field, up to the leading order of the noncommutativity parameter. In our setting (both the electric and magnetic fields are parallel to the coordinate axis $x^1$ and the nonvanishing component of the noncommutativity parameter is $θ^{23}$), we find that the electric field has no effect on the propagation of photons, but the velocity of photons can be larger than the…
This report presents a brief review on the experimental measurements of the muon neutrino velocities from the OPERA, Fermilab and MINOS experiments and that of the (anti)-electron neutrino velocities from the supernova SN1987A, and consequently on the theoretical attempts to attribute the data as signals for superluminality of neutrinos. Different scenarios on how to understand and treat the background fields in the effective field theory frameworks are pointed out. Challenges on interpreting the OPERA result as a signal of neutrino superluminality are briefly reviewed and discussed. It is als…
Lorentz-violating neutrino parameters have been severely constrained on the basis of astrophysical considerations. In the high-energy limit, one generally assumes a superluminal dispersion relation of an incoming neutrino of the form E ~ |p|v, where E is the energy, p is the momentum and $v = sqrt(1 + delta) > 1. Lepton-pair creation due to a Cerenkov-radiation-like process (nu -> nu + e^- + e^+) becomes possible above a certain energy threshold, and bounds on the Lorentz-violating parameter delta can be derived. Here, we investigate a related process, nu_i -> nu_i + nu_f + bar_nu_f, where nu_…
The OPERA collaboration has claimed the discovery of supeluminal neutrino propagation. However the superluminal interpretation of the OPERA result was refuted by Cohen and Glashow because it was shown that such superluminal neutrinos would lose energy rapidly via the bremsstrahlung of electron-positron pairs (arXiv:1109.6562). We note that the superluminal interpretation is still possible if there exists a new (dark) neutrino which can propagate with a superluminal velocity and which couples with usual neutrinos only via the mass mixing leading to neutrino oscillations. It is supposed that the…
We extend a recent approach to Deformed Special Relativity based on deformed dispersion laws, entailing modified Lorentz transformations and, at the same time, noncommutative geometry and intrinsically discrete spacetime. In so doing we obtain the explicit form of the modified Lorentz transformations for a special class of modified momentum-energy relations often found in literature and arising from elementary particle physics. Actually, our theory looks as a very simple and natural extension of special relativity to include a momentum cut-off at the Planck scale. In particular, the new Lorent…
We suggest that the recently observed superluminal neutrino propagation observed by OPERA may have an environmental origin that can simultaneously explain the DAMA/LIBRA annual modulation. Our proposal can be unambiguously tested by the prediction that OPERA will also observe an annual modulation in the speed of neutrinos. Experiments geographically distant from Gran Sasso will however not be able to observe these effects. We do not rely upon any violation of Lorentz symmetry except for spontaneous breaking of translational invariance. We discuss implications for the CRESST experiment, also lo…
The superluminal neutrinos detected by OPERA indicates Lorentz invariance violation (LIV) of the neutrino sector at the order of $10^{-5}$. We study the implications of the result in this work. We find that such a large LIV implied by OPERA data will make the neutrino production process $π\to μ+ ν_μ$ kinematically forbidden for neutrino energy greater than about 5 GeV. The OPERA detection of neutrinos at 40 GeV can constrain the LIV parameter to be smaller than $3\times 10^{-7}$. Furthermore the neutrino decay in the LIV framework will modify the neutrino spectrum greatly. The atmospheric neut…
Lorentz symmetry violation (LSV) is often discussed using models of the $THεμ$ type which involve, basically, energy independent parameters. However, if LSV is generated at the Planck scale or at some other fundamental length scale, it can naturally preserve Lorentz symmetry as a low-energy limit (deformed Lorentz symmetry, DLS). Deformed relativistic kinematics (DRK) would be consistent with special relativity in the limit $k$ (wave vector) $\to ~0$ and allow for a deformed version of general relativity and gravitation. We present an updated discussion of the possible implications of this pat…
Previous studies on high-energy gamma-ray burst neutrinos from IceCube suggest a neutrino speed variation at the Lorentz violation~(LV) scale of $\sim 6.4\times 10^{17}$~GeV, with opposite velocity variances between neutrinos and antineutrinos. Within a space-time 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~($ν\rightarrowνee^{+}$) for the superluminal~(anti)neutrino is performed. We …
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 …
We consider a braneworld scenario in the simplest setting, $M_4 \times S^1$, with a 4D Minkowski metric induced on the brane, and establish the possibility of superluminal propagation. If the brane is at rest, the 4D Lorentz symmetry of the brane is exact, but if the brane is in motion, it is broken globally by the compactification. By measuring bulk fields, an observer on the brane sees a slice through a higher-dimensional field profile, which carries an imprint of the extra dimensions even when the brane is at rest. If the brane is in motion we find that bulk fields can propagate outside the…
If the observation by OPERA of apparently superluminal neutrinos is correct, the Lagrangian for second-generation leptons must break Lorentz invariance. We calculate the effects of an energy-independent change in the neutrino speed on another observable, the charged pion decay rate. The rate decreases by an factor [1 - 3/(1 - (m_mu)^2 / (m_pi) ^ 2) (< v_(nu) > - 1)], where < v_(nu) > is the (directionally averaged) neutrino speed in the pion's rest frame. This provides a completely independent experimental observable that is sensitive to the same forms of Lorentz violation as a neutrino time o…
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…
In a recent study, Cohen and Glashow argue that superluminal neutrinos of the type recently reported by OPERA should be affected by anomalous Cherenkov-like processes. This causes them to loose much of their energy before reaching the OPERA detectors. Related concerns were reported also by Gonzalez-Mestres and Bi et. al., who argued that pions cannot decay to superluminal neutrinos over part of the energy range studied by OPERA. We observe here that these arguments are set within a framework in which Lorentz symmetry is broken, by the presence of a preferred frame. We further show that these a…
We revisit Lorentz violation in the Type IIB string theory with D3-branes and D7-branes. We study the relativistic particle velocities in details, and show that there exist both subluminal and superluminal particle propagations. In particular, the additional contributions to the particle velosity δv\equiv (v-c)/c from string theory is proportional to both the particle energy and the D3-brane number density, and is inversely proportional to the string scale. Thus, we can realize the background dependent Lorentz violation naturally by varying the D3-brane number density in space time. To explain…
A relativistic theory for neutrino superluminality is presented (in principle, the same mechanism applies also to other fermions). The theory involves the standard-model particles and one additional heavy sterile neutrino with an energy-scale close to or above the electroweak one, all particles propagating in the usual 3+1 spacetime dimensions. Lorentz violation results from spontaneous symmetry breaking in the sterile-neutrino sector. The theory tries, as far as possible, to be consistent with the existing experimental data from neutrino physics and to keep the number of assumptions minimal. …
We digress on the implications of recent claims of superluminal neutrino propagation. No matter how we turn it around such behaviour is very odd and sits uncomfortably even within "far-fetched" theories. In the context of non-linear realizations of the Lorentz group (where superluminal misbehaviour is run of the mill) one has to accept rather contrived constructions to predict superluminal properties for the neutrino. The simplest explanation is to require that at least one of the mass states be tachyonic. We show that due to neutrino mixing, the flavor energy does not suffer from the usual ru…
Recently two collaborations, Tibet and HAWC, presented new measurements of gamma-ray spectrum from Crab Nebula \cite{Amenomori:2019rjd},\cite{Abeysekara:2019edl} which continues beyond $100$ TeV. We use these data to establish two-sided constraints on parameters of Lorentz Invariance violation in quantum electrodynamics. The limits on Lorentz violating mass scale for quartic dispersion relation are $4.1\times 10^{14}\ \mbox{GeV}$ (photon splitting) and $1.9\times 10^{13}\ \mbox{GeV}$ (photon decay) for superluminal case, and $1.4\times 10^{12}$ GeV (suppression of shower formation) for sublumi…
Recent time-of-flight measurements on muon neutrinos in the OPERA neutrino oscillation experiment have found anomalously short times compared to the light travel-times, corresponding to a superluminal velocity, $v-1=2.37\pm0.32\times 10^{-5}$ in units where $c=1$. We show that cosmological bounds rule out an explanation involving a Lorentz invariant tachyonic neutrino. At the OPERA energy scale, nucleosynthesis constraints imply $v-1<0.86\times 10^{-12}$ and the Cosmic Microwave Background observations imply $v-1<7.1\times 10^{-23}$. The CMB limit on the velocity of a tachyon with an energy of…
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 …
We present new two-sided constraints on Lorentz Invariance violation energy scale for photons with quartic dispersion relation from recent gamma ray observations by Tibet-AS$γ$ and LHAASO experiments. The constraints are based on the consideration of the processes of photon triple splitting (superluminal scenario) and the suppression of shower formation (subluminal). The constraints in subluminal scenario are better than the pair production constraints and are the strongest in the literature.
The original Abelian U(1) Higgs model in flat spacetime is enlarged by the addition of one real scalar with a particular potential. It is then shown that, while maintaining the original masses of the vector boson and Higgs scalar, there exists a time-dependent homogeneous solution of the classical field equations, which corresponds to dynamical breaking of Lorentz invariance (DBLI). The same DBLI mechanism holds for the standard model enlarged by the addition of a real isosinglet scalar with an appropriate potential. The resulting DBLI with an assumed TeV energy scale would manifest itself pri…
The observation of two PeV-scale neutrino events reported by Ice Cube can, in principle, allows one to place constraints on Lorentz invariance violation (LIV) in the neutrino sector. After first arguing that at least one of the IceCube events was of extragalactic origin, I derive an upper limit for {\it the difference} between putative superluminal neutrino and electron velocities of $\le \sim 5.6 \times 10^{-19}$ 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…
Cosmological scenarios with k-essence are invoked in order to explain the observed late-time acceleration of the universe. These scenarios avoid the need for fine-tuned initial conditions (the "coincidence problem") because of the attractor-like dynamics of the k-essence field ϕ. It was recently shown that all k-essence scenarios with Lagrangians p=L(X)/ϕ^2, necessarily involve an epoch where perturbations of ϕpropagate faster than light (the "no-go theorem"). We carry out a comprehensive study of attractor-like cosmological solutions ("trackers") involving a k-essence scalar field ϕand anothe…
We discuss the possibility of explaining the observation of ultra-high-energy cosmic rays with energy above the GZK cutoff, saving the relativity principle and the (possibly deformed) Lorentz symmetry, as proposed recently by several authors. Since it is known that the Lie group structure of the Lorentz group cannot be deformed, we study the deformations (up to isomorphisms) of the mass-shell, considered as an abstract three-dimensional homogeneous space. We find that in the massive case the mass-shell cannot be deformed and in the massless case there are deformations, but their physical inter…
