Lorentz Invariance Violation Research Articles

Observation of anisotropic Dirac cones in the topological material Ti2Te2P

Anisotropic bulk Dirac (or Weyl) cones in three-dimensional systems have recently gained intense research interest as they are examples of materials with tilted Dirac (or Weyl) cones indicating the violation of Lorentz invariance. In contrast, the studies on anisotropic surface Dirac cones in topological materials which contribute to anisotropic carrier mobility have been limited. By employing angle-resolved photoemission spectroscopy and first-principles calculations, we reveal the anisotropic surface Dirac dispersion in a tetradymite material ${\mathrm{Ti}}_{2}{\mathrm{Te}}_{2}\mathrm{P}$ on the (001) plane of the Brillouin zone. We observe quasielliptical Fermi pockets at the $\overline{M}$ point of the Brillouin zone forming the anisotropic surface Dirac cones. Our calculations of the ${\mathbb{Z}}_{2}$ indices confirm that the system is topologically nontrivial with multiple topological phases in the same material. In addition, the observed nodal-line-like feature formed by bulk bands makes this system topologically rich.

Ultra-High-Energy Astroparticles as Probes for Lorentz Invariance Violation

Compelling evidence for Lorentz invariance violation (LIV) would demand a complete revision of modern physics. Therefore, searching for a signal or extending the validity of the invariance is fundamental for building our understanding of the extreme phenomena in the Universe. In this paper, we review the potential of ultra-high-energy astroparticles in setting limits on LIV. The standard framework of LIV studies in astroparticle physics is reviewed and its use on the electromagnetic and hadronic sectors are discussed. In particular, the current status of LIV tests using experimental data on ultra-high-energy photons and cosmic rays is addressed. A detailed discussion with improved argumentation about the LIV kinematics of the relevant interactions is shown. The main previous results are presented together with new calculations based on recently published astrophysical models.

An improvement for quantum tunneling radiation of fermions in the Kerr–Newman black hole

By introducing a specific aether-like vector in the Dirac equation with Lorentz Invariance Violation (LIV) in the curved spacetime, an improved method for quantum tunneling radiation of fermions is proposed. As an example, we apply this new method to the horizons of a stationary charged axisymmetric Kerr–Newman black hole. Considering LIV theory, we firstly obtain a modified dynamical equation for fermions with spin 12 in the Kerr–Newman spacetime and then solve the equation. We find the increase or decrease of both the Hawking temperature and entropy are related to constants a and c in the modified Dirac equation. The new Hawking temperature is about 1+2a+2cmkr21+2a times higher than that in the fiducial calculation, but the entropy will decrease. In this case, the evaporation of the black hole will be accelerated. We also make a brief discussion for the case of fermions with high spin.

Spectral Lag Transition of 32 Fermi Gamma-Ray Bursts and Their Application on Constraining Lorentz Invariance Violation

The positive-to-negative transition of spectral lag is an uncommon feature reported in a small number of gamma-ray bursts (GRBs). An application of such a feature has been made to constrain the critical quantum gravity energy (E QG) of the light photons under the hypothesis that the Lorentz invariance might be violated. Motivated by previous case studies, this paper systematically examined the up-to-date GRB sample observed by Fermi Gamma-ray Burst Monitor for the lag transition feature to establish a comprehensive physical limit on the Lorentz invariance violation (LIV). This search resulted in 32 GRBs with redshift available, which exhibit the lag transition phenomenon. We first fit each of the lag–E relations of the 32 GRBs with an empirical smoothly broken power-law function, and found that the lag transition occurs typically at about 400 keV. We then implemented the LIV effect into the fit, which enabled us to constrain the lower limit of the linear and quadratic values of E QG, which are typically distributed at 1.5 × 1014 and 8 × 105 GeV, respectively.

Topological chiral currents in the Gross-Neveu model extension

We unveil an interesting connection of Lorentz-violating quantum field theories, studied in the context of the standard model extension, and Hubbard-type models of topological crystalline phases. These models can be interpreted as a regularisation of the former and, as hereby discussed, explored with current quantum simulators based on ultra-cold atoms in optical Raman lattices. In particular, we present a complete analysis of the Creutz-Hubbard ladder under a generic magnetic flux, which regularises a Gross-Neveu model extension, and presents a characteristic circulating chiral current whose non-zero value arises from a specific violation of Lorentz invariance. We present a complete phase diagram with trivial insulators, ferromagnetic and anti-ferromagnetic phases, and current-carrying topological crystalline phases. These predictions are benchmarked using tools from condensed matter and quantum-information science, showing that self-consistent Hartree-Fock and strong-coupling Dzyaloshinskii-Moriya methods capture the essence of the phase diagram in different regimes, which is further explored using extensive numerical simulations based on matrix-product states.

Modification of the mean free path of very high-energy photons due to a relativistic deformed kinematics

Ultra-high-energy physics is about to enter a new era thanks to the impressive results of experiments such as the Large High Altitude Air Shower Observatory, detecting photons of up to 1.4times 10^{15} eV (PeV scale). These new results could be used to test deviations with respect to special relativity. While this has been already explored within the approach of Lorentz Invariance Violation theories, in this work we consider, for the first time, modifications due to a relativistic deformed kinematics (which appear in Doubly Special Relativity, or DSR, theories). In particular, we study the mean free path of very high-energy photons due to electron-positron pair creation when interacting with low-energy photons of the cosmic microwave background. Depending on the energy scale of the relativistic deformed kinematics, present (or near future) experiments can be sensitive enough to be able to identify deviations from special relativity.

Cosmic Neutrinos as a Window to Departures from Special Relativity

We review the peculiarities that make neutrinos very special cosmic messengers in high-energy astrophysics, and, in particular, to provide possible indications of deviations from special relativity, as it is suggested theoretically by quantum gravity models. In this respect, we examine the effects that one could expect in the production, propagation, and detection of neutrinos, not only in the well-studied scenario of Lorentz Invariance Violation, but also in models which maintain, but deform, the relativity principle, such as those considered in the framework of Doubly Special Relativity. We discuss the challenges and the promising future prospects offered by this phenomenological window to physics beyond special relativity.

Covariant Space-Time Line Elements in the Friedmann–Lemaitre–Robertson–Walker Geometry

Most quantum gravity theories quantize space-time on the order of Planck length (ℓp ). Some of these theories, such as loop quantum gravity (LQG), predict that this discreetness could be manifested through Lorentz invariance violations (LIV) over travelling particles at astronomical length distances. However, reports on LIV are controversial, and space discreetness could still be compatible with Lorentz invariance. Here, it is tested whether space quantization on the order of Planck length could still be compatible with Lorentz invariance through the application of a covariant geometric uncertainty principle (GeUP) as a constraint over geodesics in FRW geometries. Space-time line elements compatible with the uncertainty principle are calculated for a homogeneous, isotropic expanding Universe represented by the Friedmann–Lemaitre–Robertson–Walker solution to General Relativity (FLRW or FRW metric). A generic expression for the quadratic proper space-time line element is derived, proportional to Planck length-squared, and dependent on two contributions. The first is associated to the energy–time uncertainty, and the second depends on the Hubble function. The results are in agreement with space-time quantization on the expected length orders, according to quantum gravity theories, and within experimental constraints on putative LIV.

TAIGA—A hybrid array for high energy gamma-ray astronomy and cosmic-ray physics

The concept of the TAIGA experiment is to combine wide-angle timing and imaging Cherenkov telescopes as well as electron and muon detectors. The TAIGA facility aims at gamma-ray astrophysics at energies from a few TeV to several PeV and cosmic-ray physics from 100 TeV to several EeV but also pursues searches for astrophysical nanosecond transients, axion-like particles, Lorentz invariance violation and other unexpected manifestations of New Physics. TAIGA-1, a hybrid detector complex with an area of 1 km2, operating since 2021 in the Tunka valley, 50 km to the West from the southernmost tip of lake Baikal, and the plans for its upgrade are presented.

Modified Hawking temperature and entropy of general stationary black holes by Lorentz invariance violation

Correction of Lorentz dispersion relation can be carried out through Lorentz invariance violation (LIV). In the curved space-time with the general stationary black holes, the fermions dynamic equations have been modified more accurately according to the modified Lorenz dispersion relation, and the equations have been solved to obtain a new expression of quantum tunneling rate, black hole Hawking temperature, black hole entropy, and other physical quantities of stationary black holes. These expressions not only are related to factors such as Lorentz invariance violation but also have more contents akin to black hole physics.

Gamma-Ray Bursts at TeV Energies: Theoretical Considerations

Gamma-ray bursts (GRBs) are the most luminous explosions in the Universe and are powered by ultra-relativistic jets. Their prompt γ-ray emission briefly outshines the rest of the γ-ray sky, making them detectable from cosmological distances. A burst is followed by, and sometimes partially overlaps with, a similarly energetic but very broadband and longer-lasting afterglow emission. While most GRBs are detected below a few MeV, over 100 have been detected at high (≳0.1 GeV) energies, and several have now been observed up to tens of GeV with the Fermi Large Area Telescope (LAT). A new electromagnetic window in the very-high-energy (VHE) domain (≳0.1 TeV) was recently opened with the detection of an afterglow emission in the (0.1–1)TeV energy band by ground-based imaging atmospheric Cherenkov telescopes. The emission mechanism for the VHE spectral component is not fully understood, and its detection offers important constraints for GRB physics. This review provides a brief overview of the different leptonic and hadronic mechanisms capable of producing a VHE emission in GRBs. The same mechanisms possibly give rise to the high-energy spectral component seen during the prompt emission of many Fermi-LAT GRBs. Possible origins of its delayed onset and long duration well into the afterglow phase, with implications for the emission region and relativistic collisionless shock physics, are discussed. Key results for using GRBs as ideal probes for constraining models of extra-galactic background light and intergalactic magnetic fields, as well as for testing Lorentz invariance violation, are presented.

Nonminimal Lorentz invariance violation in light of the muon anomalous magnetic moment and long-baseline neutrino oscillation data

In light of the increasing hints of new physics at the muon $g\ensuremath{-}2$ and neutrino oscillation experiments, we consider the recently observed tension in the long-baseline neutrino oscillation experiments as a potential indication of Lorentz invariance violation. For this purpose, the latest data from T2K and $\mathrm{NO}\ensuremath{\nu}\mathrm{A}$ is analyzed in the presence of nonminimal Lorentz invariance violation. Indeed, we find that isotropic violation in dimensions $D=4$, 5, and 6 can alleviate the tension in neutrino oscillation data by about $0.4--2.4\ensuremath{\sigma}$ confidence level significance, with the isotropic coefficient ${\ensuremath{\gamma}}_{\ensuremath{\tau}\ensuremath{\tau}}^{(5)}=3.58\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}32}\text{ }\text{ }{\mathrm{GeV}}^{\ensuremath{-}1}$ yielding the best fit. At the same time, the anomalous muon $g\ensuremath{-}2$ result can be reproduced with an additional nonisotropic violation of ${d}^{zt}=\ensuremath{-}1.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}25}$. The analysis highlights the possibility of simultaneous relaxation of experimental tensions with Lorentz invariance violation of a mixed nature.

Some Aspects About Pushing the CPT and Lorentz Invariance Frontier With Neutrinos

The CPT symmetry, which combines Charge Conjugation, Parity, and Time Reversal, is a cornerstone of our model-building method, and its probable violation will endanger the most extended tool we presently utilize to explain physics, namely local relativistic quantum fields. However, the kaon system’s conservation constraints appear to be rather severe. We will show in this paper that neutrino oscillation experiments can enhance this limit by many orders of magnitude, making them an excellent instrument for investigating the basis of our understanding of Nature. As a result, verifying CPT invariance does not evaluate a specific model, but rather the entire paradigm. Therefore, as the CPT’s status in the neutrino sector, linked or not to Lorentz invariance violation, will be assessed at an unprecedented level by current and future long baseline experiments, distinguishing it from comparable experimental fingerprints coming from non-standard interactions is critical. Whether the entire paradigm or simply the conventional model of neutrinos is at jeopardy is significantly dependent on this.

First Combined Study on Lorentz Invariance Violation from Observations of Energy-dependent Time Delays from Multiple-type Gamma-Ray Sources. I. Motivation, Method Description, and Validation through Simulations of H.E.S.S., MAGIC, and VERITAS Data Sets

Gamma-ray astronomy has become one of the main experimental ways to test the modified dispersion relations (MDRs) of photons in vacuum, obtained in some attempts to formulate a theory of quantum gravity. The MDRs in use imply time delays that depend on the energy and that increase with distance following some function of redshift. The use of transient, or variable, distant and highly energetic sources already allows us to set stringent limits on the energy scale related to this phenomenon, usually thought to be of the order of the Planck energy, but robust conclusions on the existence of MDR-related propagation effects still require the analysis of a large population of sources. In order to gather the biggest sample of sources possible for MDR searches at teraelectronvolt energies, the H.E.S.S., MAGIC, and VERITAS collaborations enacted a joint task force to combine all their relevant data to constrain the quantum gravity energy scale. In the present article, the likelihood method used to combine the data and provide a common limit is described in detail and tested through simulations of recorded data sets for a gamma-ray burst, three flaring active galactic nuclei, and two pulsars. Statistical and systematic errors are assessed and included in the likelihood as nuisance parameters. In addition, a comparison of two different formalisms for distance dependence of the time lags is performed for the first time. In a second article, to appear later, the method will be applied to all relevant data from the three experiments.

The optical theorem in action: radiation of an electron in a Lorentz-violating vacuum

According to the optical theorem, the imaginary part of the one-loop radiative shift of the electron energy in an external field (IP1L) determines the total probability of photon emission by the electron. We calculate IP1L and then the probability and power of radiation of an electron in a constant background tensor field, which simulates the violation of Lorentz invariance in the framework of the Standard Model Extension. Using current experimental constraints on the background field strength, we show that the considered radiation effect can manifest itself under astrophysical conditions at ultrahigh electron energy.

Testing the Pauli Exclusion Principle with the VIP-2 Experiment

Violations of the Pauli Exclusion Principle (PEP), albeit small, could be motivated by physics beyond the Standard Model, ranging from violation of Lorentz invariance to extra space dimensions. This scenario can be experimentally constrained through dedicated, state-of-the-art X-ray spectroscopy, searching for a forbidden atomic transition from the L shell to the K shell already occupied by two electrons. The VIP-2 Experiment located at the underground Gran Sasso National Laboratories of INFN (Italy) tests PEP violations by introducing new electrons via a direct current in a copper conductor, measuring the X-ray energies through a silicon drift detector. Bayesian and frequentist analyses of approximately six months of data taken with the fully operational setup is presented, setting the strongest limit to date on the PEP violation shown by the VIP collaboration. The upper bound on PEP violation are placed at 90% CL β2/2≤6.8×10−42 with the Bayesian approach, and β2/2≤7.1×10−42 with the frequentist CLs technique.

The Asymmetry of the Cosmic Microwave Background Radiation as Signature of Local Lorentz Invariance Violation

A difference in electric potential in a static conductor inside a static magnetic field and an anisotropic and asymmetric distribution of neutrons emitted in nuclear reactions induced by ultrasound are assumed as marks of local Lorentz invariance (LLI) violation. The asymmetry of the two experiments is related to the asymmetry of the Cosmic Microwave Background Radiation (CMBR). As common directions of asymmetry are found in these three cases, a fundamental asymmetry of the interactions is suggested which can also shed new light on the question of symmetry breaking in the history of the Universe.

LIV effects on the quantum stochastic motion in an acoustic FRW-geometry

It is well known in the literature that vacuum fluctuations can induce a random motion of particles which is sometimes called quantum Brownian motion or quantum stochastic motion. In this paper, we consider Lorentz Invariance Violation (LIV) in an acoustic spatially flat Friedman–Robertson–Walker (FRW) geometry. In particular, we are looking for the LIV effects in the stochastic motion of scalar and massive test particles. This motion is induced by a massless quantized scalar field on this geometry, which in turn is derived from an Abelian Higgs model with LIV. Deviations in the velocity dispersion of the particles proportional to the LIV parameter are found.

Effective electromagnetic actions for Lorentz violating theories exhibiting the axial anomaly

The CPT odd contribution to the effective electromagnetic action deriving from the vacuum polarization tensor in a large class of fermionic systems exhibiting Lorentz invariance violation (LIV) is calculated using thermal field theory methods, focusing upon corrections depending on the chemical potential. The systems considered exhibit the axial anomaly and their effective actions are described by axion electrodynamics whereby all the LIV parameters enter in the coupling Θ(x) to the unmodified Pontryagin density. A preliminary application to type-I tilted Weyl semimetals is briefly presented.

Testing Lorentz invariance of electrons with LHAASO observations of PeV gamma-rays from the Crab Nebula

The Large High Altitude Air Shower Observatory (LHAASO) recently reported the detection of gamma-ray emissions with energies up to 1.1PeV from the Crab Nebula. Using the absence of vacuum Cherenkov effect by inverse-Compton electrons, we improve previous bounds to linear-order Lorentz invariance violation (LV) in the dispersion relations of electrons by 104 times. We show that the LV effect on electrons is severely constrained, compatible with certain type of LV as expected by some models of quantum gravity (QG), such as the string/D-brane inspired space-time foam. We argue that such models are supported by the Crab Nebula constraints from the LHAASO observations, as well as various LV phenomenologies for photons to date.