Searches for Lorentz invariance violation (LIV) in the neutrino sector have traditionally focused on non-standard neutrino oscillations induced by LIV in vacuum. In this work, we study anisotropic LIV in matter. First, we review vacuum LIV phenomenology, explaining the energy and direction dependence of sidereal modulations for anisotropic coefficients in the Standard Model Extension. We then demonstrate that for high-energy neutrinos, the interplay between anisotropic LIV operators and the Earth's matter potential produces distinct, observable signatures absent in the vacuum case. We identify a crossover regime where the energy-dependent LIV Hamiltonian becomes comparable to the matter potential, leading to strong interference effects. By analyzing the propagation of neutrinos through a realistic Earth model, we establish three key phenomenological consequences: (1) direction-dependent resonant enhancements of oscillation probabilities, (2) a macroscopic breakdown of neutrino-antineutrino symmetry for CPT-even operators, and (3) a significant increase of the $ν_τ$ flux due to LIV-driven injection of high-energy neutrinos into the $τ$ regeneration cycle. These results highlight that accounting for the interplay between LIV and matter is essential for future LIV searches at large-scale neutrino telescopes.
In a model with Lorentz invariance violation implemented through modified dispersion relations, we estimate the rate for the decay process gamma -> 3 gamma and find that it provides a relevant bound on Lorentz invariance violation.
Searches for violations of Lorentz invariance using cosmic rays, gamma rays, and astrophysical neutrinos and the prospects for future tests using cosmic-ray showers are presented.
A non-local field theory which breaks discrete symmetries, including C, P, CP, and CPT, but preserves Lorentz symmetry, is presented. We demonstrate that at one-loop level the masses for particle and antiparticle remain equal due to Lorentz symmetry only. An inequality of masses implies breaking of the Lorentz invariance and non-conservation of the usually conserved charges.
The influence of vector backgrounds with restored Lorentz invariance on non-abelian gauge field theories is studied. Lorentz invariance is ensured by taking the average over a Lorentz invariant ensemble of background vectors. Like in the abelian case [hep-ph/0506210], the propagation of fermions is suppressed over long distances. Contrary to the fermionic sector, pure gauge configurations of the background suppress the long-distance propagation of the bosons only partially, i.e. not beyond the leading contribution for a large number of colours.
We point out that equivalence principle violations, while not dynamically equivalent, produce the same kinematical effects as Lorentz invariance violations for particle processes in a constant gravitational potential. This allows us to translate many experimental bounds on Lorentz invariance violations into bounds on equivalence principle violations. The most stringent bound suggests that a postive signal in an Eötvös experiment may be at least seven orders of magnitude beyond current technology.
We have examined Lorentz invariance and equivalence principle violations in the neutrino sector as manifested in neutrinoless double beta decay. We conclude that this rare decay cannot provide a useful view of these exotic processes.
A hypothetical violation of Lorentz invariance in the electrons' equation of motion (expressed within the Lorentz-violating extension of the standard model) leads to a change of the geometry of crystals and thus shifts the resonance frequency of an electromagnetic cavity. This allows experimental tests of Lorentz invariance of the electron sector of the standard model. The material dependence of the effect allows to separate it from an additional shift caused by Lorentz violation in electrodynamics, and to place independent limits on both effects. From present experiments, upper limits on Lore…
We discuss the consequences of Lorentz violation (as expressed within the Lorentz-violating extension of the standard model) for the hydrogen molecule, which represents a generic model of a molecular binding. Lorentz-violating shifts of electronic, vibrational and rotational energy levels, and of the internuclear distance are calculated. This offers the possibility of obtaining improved bounds on Lorentz invariance by experiments using molecules.
Neutrino experiments can be considered sensitive tools to test Lorentz and CPT invariance. Taking advantage of the great variety of neutrino experiments, including neutrino oscillations, weak decays, and astrophysical neutrinos, the generic experimental signatures of the breakdown of these fundamental symmetries in the neutrino sector are presented.
Lorentz invariance is a well known fundamental concept of special relativity but its violation is predicted by some variations of quantum gravity, string theory, and some alternatives to general relativity. We study neutrino oscillation at the presence of the Lorentz invariance violation in vacuum, normal and nuclear media. It is shown that for very high energy neutrinos the neutrino oscillations due to mass difference is suppressed and its contribution to the conversion probability is negligibly small, but the contribution of the Lorentz invariance violation term is not zero. This means that …
Supersymmetry and Lorentz invariance are closely related as both are spacetime symmetries. Terms can be added to Lagrangians that explicitly break either supersymmetry or Lorentz invariance. It is possible to include terms which violate Lorentz invariance but maintain invariance under supersymmetric transformations. I illustrate this with some simple extensions of the original Wess-Zumino model.
The violation of the so-called Lorentz invariance relations between parton distribution functions is considered in a model independent way. It is shown that these relations are not violated in a generalized Wandzura-Wilczek approximation, indicating that numerically their violation may be small.
Depending on deformed canonical anti-commutation relations, massless neutrino oscillation based on Lorentz invariance violation in non-commutative field theory is discussed. It is found that the previous studies about massless neutrino oscillation within deformed canonical anti-commutation relations should satisfy the condition of new Moyal product and new non standard commutation relations. Furthermore, comparing the Lorentz Invariant Violation parameters $\mathit{A}$ in the previous studies with new Moyal product and new non standard commutation relations, we find that the orders of magnitud…
We revisit the derivation of the so-called Lorentz invariance relations between parton distributions. In the most important cases these relations involve twist-3 and transverse momentum dependent parton distributions. It is shown that these relations are violated if the path-ordered exponential is taken into account in the quark correlator.
Spontanous symmetry breaking usually gives spin 0 Goldstone bosons for the case of internal symmetries and spin 1/2 fermions for the supersymmetry. The spontaneous breaking of higher dimensional Lorentz symmetry can give vector Goldstone boson in 4-dimension.
We show that a general principle of physical independence or physical invariance of mathematical background manifold leads to a replacement of the common derivative operators by the covariant co-derivative ones. This replacement naturally induces a background matrix, by means of which we obtain an effective Lagrangian for the minimal standard model with supplement terms characterizing Lorentz invariance violation or anisotropy of space-time. We construct a simple model of the background matrix and find that the strength of Lorentz violation of proton in the photopion production is of the order…
I give a brief overview of recent work concerning possible signals of Lorentz violation in sensitive clock-based experiments in space. The systems under consideration include atomic clocks and electromagnetic resonators of the type planned for flight on the International Space Station.
Due to quantum gravity fluctuations at the Planck scale, the space-time manifold is no longer continuous, but discretized. As a result the Lorentz symmetry is broken at very high energies. In this article, we study the neutrino oscillation pattern due to the Lorentz Invariance Violation (LIV), and compare it with the normal neutrino oscillation pattern due to neutrino masses. We find that at very high energies, neutrino oscillation pattern is very different from the normal one. This could provide an possibility to study the Lorentz Invariance Violation by measuring the oscillation pattern of v…
In this work, in the light of the developments for indefinite metric theories made by Lee and Wick, we study perturbative unitarity in a Lorentz-invariance violating QED model with higher-order operators. We show that by following the Lee-Wick prescription it is possible to preserve unitarity in the model at one-loop order in the coupling.
The effects of Lorentz Invariance Violation(LIV) operators up to dimension 6 in long baseline neutrino experiments are discussed, in specific for DUNE and T2K. A phenomenological Lagrangian is proposed followed by a computation of the effective Hamiltonian of neutrino propagation in matter for mass eigenstates. It is shown that the simplest dimension 4 Lorentz violation parameter can decrease DUNE sensitivity to neutrino mass hierarchy. Also, a $χ^2$ analysis is performed to obtain the expected long-baseline constraints to the LIV operators up to dimension 6.
A complete list of the so-called Lorentz invariance relations between parton distribution functions is given and some of their consequences are discussed, such as the Burkhardt-Cottingham sum rule. The violation of these relations is considered in a model independent way. It is shown that several Lorentz invariance relations are not violated in a generalized Wandzura-Wilczek approximation, indicating that numerically their violation may be small.
This article presents prospects for Lorentz-violation searches with $t\bar{t}$ at the LHC and future colliders. After a short presentation of the Standard-Model Extension as a Lorentz-symmetry-breaking effective field theory, we will focus on $t\bar{t}$ production. We study the impact of Lorentz violation as a function of center-of-mass energy and evaluate the sensitivity of collider experiments to this signal.
This paper investigates a signature of Lorentz invariance violation with the $t\bar{t}$ production at the LHC and future hadron colliders. Possible deviations from the Lorentz symmetry remain poorly constrained in the top quark sector. With a dedicated analysis of $t\bar{t}$ events produced at the LHC, bounds in the top sector can be improved by up to three orders of magnitude relative to Tevatron, the only measurement existing so far. The sensitivity will be even further enhanced at the HL-LHC and future colliders.
We present how to further the search for Lorentz and CPT violation in the top-quark sector after the first measurement in this sector by D0. We compute the Lorentz-violating matrix element for top pair production via gluon fusion, which allows a similar but more precise measurement at the LHC. For CPT violation, we analyze single-top production, derive the modified matrix elements, and predict possible signals.
Lorentz invariance relations connecting twist-3 parton distributions with transverse momentum dependent twist-2 distributions have been proposed previously. These relations can be extracted from a covariant decomposition of the quark-quark correlator. It is argued, however, that the derivation of the Lorentz invariance relations fails if the path-ordered exponential is taken into account in the correlator. The model independent analysis is supplemented by an explicit calculation of the corresponding parton distributions in perturbative QCD with a quark target, and in a simple spectator model. …
In a new theory, local Lorentz invariance is a low-energy symmetry which no longer holds when a fermion energy E is well above 1 TeV. Here we find that the modified E(p) relation is consistent with observation, and is in fact nearly the same as in Einstein relativity. On the other hand, there is a strong modification of the fermion equation of motion and propagator at ultrahigh energy, which should lead to observable effects.
We consider tests of Lorentz invariance for the photon and fermion sector that use vacuum and matter-filled cavities. Assumptions on the wave-function of the electrons in crystals are eliminated from the underlying theory and accurate sensitivity coefficients (including some exceptionally large ones) are calculated for various materials. We derive the Lorentz-violating shift in the index of refraction n, which leads to additional sensitivity for matter-filled cavities ; and to birefringence in initially isotropic media. Using published experimental data, we obtain improved bounds on Lorentz vi…
The relation between the violation of Lorentz invariance and the dynamical effects in high energy gamma rays production is discussed. By using the framework of noncommutative classical electrodynamics, it is shown that full dynamical calculations are required to put bounds on the Lorentz violating scale by the phenomenological analysis of these processes as, for example, the synchrotron radiation from the CRAB nebula. It is observed that an improvement of the present bound on the scale of noncommutativity can be obtained only by astrophysical observations of gamma ray spectra in strong magneti…
Employing induced representations of the Lorentz group (Wigner's little group construction), formalism for constructing heavy particle effective Lagrangians is developed, and Lagrangian constraints enforcing Lorentz invariance of the S matrix are derived. The relationship between Lorentz invariance and reparameterization invariance is established and it is shown why a standard ansatz for implementing reparameterization invariance in heavy fermion effective Lagrangians breaks down at order 1/M^4. Formalism for fields of arbitrary spin and for self-conjugate fields is presented, and the extensio…
An interacting theory that violates CPT invariance necessarily violates Lorentz invariance. On the other hand, CPT invariance is not sufficient for out-of-cone Lorentz invariance. Theories that violate CPT by having different particle and antiparticle masses must be nonlocal.
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.
Extremely high-energy(EHE) cosmic rays might provide a chance to check a violation of the Lorentz symmetry of spacetime. Some theoretical consideration is described about why the Lorentz symmetry might break-down in EHE phenomena in this universe. Some models which introduce the violation of the Lorentz symmetry will be discussed.
Superconducting-gravimeter measurements are used to test the local Lorentz invariance of the gravitational interaction and of matter-gravity couplings. The best laboratory sensitivities to date are achieved via a maximum-reach analysis for 13 Lorentz-violating operators, with some improvements exceeding an order of magnitude.
One possible feature of quantum gravity may be the violation of Lorentz invariance. In this paper we consider one particular manifestation of the violation of Lorentz invariance, namely modified dispersion relations for massive neutrinos. We show how such modified dispersion relations may affect atmospheric neutrino oscillations. We then consider how neutrino telescopes, such as ANTARES, may be able to place bounds on the magnitude of this type of Lorentz invariance violation.
We present a class of interacting nonlocal quantum field theories, in which the CPT invariance is violated while the Lorentz invariance is present. This result rules out a previous claim in the literature that the CPT violation implies the violation of Lorentz invariance. Furthermore, there exists the reciprocal of this theorem, namely that the violation of Lorentz invariance does not lead to the CPT violation, provided that the residual symmetry of Lorentz invariance admits the proper representation theory for the particles. The latter occurs in the case of quantum field theories on a noncomm…
The Newton limit of gravity is studied in the presence of Lorentz-violating gravitational operators of arbitrary mass dimension. The linearized modified Einstein equations are obtained and the perturbative solutions are constructed and characterized. We develop a formalism for data analysis in laboratory experiments testing gravity at short range and demonstrate that these tests provide unique sensitivity to deviations from local Lorentz invariance.
We calculate twist-3 parton ditribution functions (PDFs) using cut and uncut diagrams. Uncut diagrams lead to a Dirac delta function term. No such term appears when cut diagrams are used. We show that a $δ(x)$ is necessary to satisfy the Lorentz invariance relations of twist-3 PDFs, except for the Burkhardt-Cottingham sum rule in QCD.
The chiral anomaly in the context of an extended standard model with minimal Lorentz invariance violation is studied. Taking into account bounds from measurements of the speed of light, we argue that the chiral anomaly and its consequences are general results valid even beyond the relativistic symmetry.
In this letter we reconsider the role of Lorentz invariance in the dynamical generation of the observed internal symmetries. We argue that, generally, Lorentz invariance can only be imposed in the sense that all Lorentz non-invariant effects caused by the spontaneous breakdown of Lorentz symmetry are physically unobservable. Remarkably, the application of this principle to the most general relativistically invariant Lagrangian, with arbitrary couplings for all the fields involved, leads by itself to the appearance of a symmetry and, what is more, to the massless vector fields gauging this symm…
Neutrinos can be used to search for deviations from exact Lorentz invariance. The worldwide experimental program in neutrino physics makes these particles a remarkable tool to search for a variety of signals that could reveal minute relativity violations. This paper reviews the generic experimental signatures of the breakdown of Lorentz symmetry in the neutrino sector.
Trying to combine standard quantum field theories with gravity leads to a breakdown of the usual structure of space-time at around the Planck length, 1.6*10^{-35} m, with possible violations of Lorentz invariance. Calculations of preferred-frame effects in quantum gravity have further motivated high precision searches for Lorentz violation. Here, we explain that combining known elementary particle interactions with a Planck-scale preferred frame gives rise to Lorentz violation at the percent level, some 20 orders of magnitude higher than earlier estimates, unless the bare parameters of the the…
We discuss the effect of hypothetical violation of Lorentz invariance at high energies on the formation of atmospheric showers by very-high-energy gamma rays. In the scenario where Lorentz invariance violation leads to a decrease of the photon velocity with energy the formation of the showers is suppressed compared to the Lorentz invariant case. Absence of such suppression in the high-energy part of spectrum of the Crab nebula measured independently by HEGRA and H.E.S.S. collaborations is used to set lower bounds on the energy scale of Lorentz invariance violation. These bounds are competitive…
We analyze the consequences of violation of Lorentz and $CPT$ invariance in the massless neutrino sector by deforming the canonical anti-commutation relations for the fields. We show that, for particular choices of the deformation, oscillation between massless neutrino species takes place when only Lorentz invariance is violated. On the other hand, if both Lorentz and $CPT$ invariances are violated, we show that there is no oscillation between massless neutrino species. Comparing with the existing experimental data on neutrino oscillations, we obtain bounds on the parameter for Lorentz invaria…
We develop a new comagnetometer using $^{21}$Ne atoms with nuclear spin $I=3/2$ and Rb atoms polarized by spin-exchange with K atoms to search for tensor interactions that violate local Lorentz invariance. We frequently reverse orientation of the experiment and search for signals at the first and second harmonics of the sidereal frequency. We constrain 4 of the 5 spatial Lorentz-violating coefficients $c^n_{jk}$ that parameterize anisotropy of the maximum attainable velocity of a neutron at a level of $10^{-29}$, improving previous limits by 2 to 4 orders of magnitude and placing the most stri…
Using a deformed dispersion relation for gravitational waves, Advanced LIGO and Advanced Virgo have been able to place constraints on violations of local Lorentz invariance as well as the mass of the graviton. We summarise the method to obtain the current bounds from the 10 significant binary black hole detections made during the first and second observing runs of the above detectors.
Motivated by ideas about quantum gravity, a tremendous amount of effort over the past decade has gone into testing Lorentz invariance in various regimes. This review summarizes both the theoretical frameworks for tests of Lorentz invariance and experimental advances that have made new high precision tests possible. The current constraints on Lorentz violating effects from both terrestrial experiments and astrophysical observations are presented.
Lorentz invariance, the fundamental symmetry of Einstein's theory of Special Relativity, has been established and tested by many classical and modern experiments. However, many theories that unify the Standard Model of particle physics and General Relativity predict a violation of Lorentz invariance at the Planck scale. While this energy range cannot be reached by current experiments, minute deviations from Lorentz symmetry may be present at lower energies. Astrophysical experiments are very suitable to search for these deviations, since their effects accumulate as photons travel across large …
The violation of Lorentz invariance (LI) has been invoked in a number of ways to explain issues dealing with ultrahigh energy cosmic ray (UHECR) production and propagation. These treatments, however, have mostly been limited to examples in the proton-neutron system and photon-electron system. In this paper we show how a broader violation of Lorentz invariance would allow for a series of previously forbidden decays to occur, and how that could lead to UHECR primaries being heavy baryonic states or Higgs bosons.
We propose a way to recover Lorentz invariance of the perturbative S matrix in the Discrete Light-Cone Quantization (DLCQ) in the continuum limit without spoiling the trivial vacuum.
It was recently suggested that possible small volations of Lorentz invariance could explain the existence of UHECR beyond the GZK cutoff and the observations of multi-TeV gamma-rays from Mkn 501. Our analysis of Lorentz-violating kinematics shows that in addition to the modified threshold conditions solving cosmic ray puzzles we should expect a strong suppression of electromagnetic processes like bremsstrahlung and pair creation. This leads to drastic effects in electron-photon cascade development in the atmosphere and in detectors.
We propose a new theory of gravitation on noncommutative space-time which is invariant under the general coordinate transformations, while the local Lorentz invariance is realized as twisted gauge symmetry. Our theory is remarkably simpler compared to the existing formulations of noncommutative gravity.
The unitarity in Lorentz invariance violating QED consisting of standard fermions and higher-order photons of the Myers-Pospelov theory is studied. We find ghost states associated to the higher-order character of the theory which could render the $S$ matrix nonunitary. An explicit calculation to check perturbative unitarity in the process of electron-positron scattering is performed and it is found to be possible to preserve unitarity.
We calculate the decay width of the photon splitting into three photons in a model of quantum electrodynamics with broken Lorentz invariance. We show that this process can lead to a cut-off in the very-high-energy part of a photon spectra of astrophysical sources. We obtain the 95\% CL bound on the Lorentz violating mass scale for photons from the analysis of the very-high-energy part of the Crab Nebula spectrum, obtained by HEGRA. This bound improves previous constraints by more than an order of magnitude.
Possibilities to test the Lorentz invariance of the weak interaction in muon decay are considered. We derive the direction-dependent muon-decay rate with a general Lorentz-violating addition to the W-boson propagator. We discuss measurements of the directional and boost dependence of the Michel parameters and of the muon lifetime as a function of absolute velocity. The total muon-decay rate in the Lorentz-violating Standard Model Extension is addressed. Suggestions are made for dedicated (re)analyses of the pertinent data and for future experiments.
It is shown that, in spite of the appearances, the standard expression for the oscillation probability of ultrarelativistic neutrinos is Lorentz invariant.
