Test of Lorentz invariance using optical cavities

This paper indroduces the precision test of Lorentz invariance using ultra-stable and low-loss optical cavities. The effective-field theory widely adopted in the analysis of experimental data has been reviewed. The sensitivity of the cavity resonant frequency to the Lorentz-violating tensor field is discussed in detail. In addition, the polarization of the optical field has been added to the model, and our analysis shows that the frequency shift due to Lorentz violation is not sensitive to the polarization of the optical field.      

Lorentz violation from the Higgs portal

We study bounds and signatures of models where the Higgs doublet has an inhomogeneous mass or vacuum expectation value, being coupled to a hidden sector that breaks Lorentz invariance. This physics is best described by a low-energy effective Lagrangian in which the Higgs speed-of-light is smaller than c; such effect is naturally small because it is suppressed by four powers of the inhomogeneity scale. The Lorentz violation in the Higgs sector is communicated at tree level to fermions (via Yukawa interactions) and to massive gauge bosons, although the most important effect comes from one-loop diagrams for photons and from two-loop diagrams for fermions. We calculate these effects by deriving the renormalization-group equations for the speed-of-light of the Standard Model particles. An interesting feature is that the strong coupling dynamically makes the speed-of-light equal for all colored particles.     

CPT violation does not lead to violation of Lorentz invariance and vice versa

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 noncommutative space–time, which in place of the broken Lorentz symmetry possesses the twisted Poincaré invariance. With such a CPT-violating interaction and the addition of a C-violating (e.g., electroweak) interaction, the quantum corrections due to the combined interactions could lead to different properties for the particle and antiparticle, including their masses.     

On gravity localization under Lorentz violation in warped scenario

Recently Rizzo studied the Lorentz Invariance Violation (LIV) in a brane scenario with one extra dimension where he found a non-zero mass for the four-dimensional graviton. This leads to the conclusion that five-dimensional models with LIV are not phenomenologically viable. In this work we re-examine the issue of Lorentz Invariance Violation in the context of higher-dimensional theories. We show that a six-dimensional geometry describing a string-like defect with a bulk-dependent cosmological constant can yield a massless 4D graviton, if we allow the cosmological constant variation along the bulk, and thus can provides a phenomenologically viable solution for the gauge hierarchy problem.     

Constraining Lorentz invariance violation from the continuous spectra of short gamma-ray bursts

In some quantum gravity theories, a foamy structure of space-time may lead to Lorentz invariance violation(LIV). As the most energetic explosions in the Universe, gamma-ray bursts(GRBs) provide an effect way to probe quantum gravity effects. In this paper, we use the continuous spectra of 20 short GRBs detected by the Swift satellite to give a conservative lower limit of quantum gravity energy scale MQG. Due to the LIV effect, photons with different energy have different velocities. This will lead to the delayed arrival of high energy photons relative to low energy ones. Based on the fact that the LIV-induced time delay cannot be longer than the duration of a GRB,we present the most conservative estimate of the quantum gravity energy scales from 20 short GRBs. The strictest constraint, M_(QG) 5.05 × 10~(14) GeV in the linearly corrected case, is from GRB 140622 A. Our constraint on MQG,although not as tight as previous results, is the safest and most reliable so far.     

Study of Lorentz violation in INTEGRAL gamma-ray bursts

We search for possible time lags caused by quantum gravitational effects using gamma-ray bursts (GRBs) detected by INTEGRAL. The advantage of this satellite is that we have at our disposal the energy and arrival time of every detected single photon, which enhances the precision of the time resolution. We present a new method for seeking time lags in unbinned data using a maximum likelihood method and support our conclusions with Monte Carlo simulations. The analysis establishes a conservative lower bound on the Lorentz invariance violation scale, which is several orders of magnitude below the Planck mass, whose value may however increase if better statistics of GRBs were available. Furthermore, we disagree with previous studies in which a non-monotonic function of the redshift was used to perform a linear fit.     

Lorentz violation constrained by triplicity of lepton families and neutrino oscillations

In this paper we postulate an algebraic model to relate the triplet characteristic of lepton families to Lorentz violation. Inspired by the two-to-one mapping between the group SL(2, C) and the Lorentz group via the Pauli grading (the elements of SL(2, C) expressed by direct sum of unit matrix and generators of SU (2) group), we grade the SL(3, C) group with the generators of SU(3), i. e. the Gell-Mann matrices, then express the SU(3) group in terms of three SU(2) subgroups, each of which stands for a lepton species and is mapped into the proper Lorentz group as in the case of the group SL(2,C). If the mapping from group SL(3,C) to the Lorentz group is constructed by choosing one SU(2) subgroup as basis, then the other two subgroups display their impact only by one more additional generator to that of the original Lorentz group. Applying the mapping result to the Dirac equation, it is found that only when the kinetic vertex γμξμ is extended to encompass γμξμ can the Dirac-equation-form be conserved. The generalized vertex is useful in producing neutrino oscillations and mass differences.     

Lorentz violation constrained by triplicity of lepton families and neutrino oscillations

In this paper we postulate an algebraic model to relate the triplet characteristic of lepton families to Lorentz violation. Inspired by the two-to-one mapping between the group SL（2, C） and the Lorentz group via the Pauli grading （the elements of SL（2, C） expressed by direct sum of unit matrix and generators of SU（2） group）, we grade the SL（3,C） group with the generators of SU（3）, i. e. the Gell-Mann matrices, then express the SU（3） group in terms of three SU（2） subgroups, each of which stands for a lepton species and is mapped into the proper Lorentz group as in the case of the group SL（2,C）. If the mapping from group SL（3,C） to the Lorentz group is constructed by choosing one SU（2） subgroup as basis, then the other two subgroups display their impact only by one more additional generator to that of the original Lorentz group. Applying the mapping result to the Dirac equation, it is found that only when the kinetic vertex -γμθ^μ is extended to encompass γ5γμθ^μ can the Dirac-equation-form be conserved. The generalized vertex is useful in producing neutrino oscillations and mass differences.     

Spatial curvature and large scale Lorentz violation

The tension between the Hubble constant values obtained from local measurements and cosmic microwave background (CMB) measurements has motivated us to consider the cosmological model beyond ΛCDM. We investigate the cosmology in the large scale Lorentz violation model with a non-vanishing spatial curvature. The degeneracy among spatial curvature, cosmological constant, and cosmological contortion distribution makes the model viable in describing the known observational data. We obtain some constraints on the spatial curvature by comparing the relationship between measured distance modulus and red-shift with the predicted one, the evolution of matter density over time, and the evolution of effective cosmological constant. The implications of the large scale Lorentz violation model with the non-vanishing spatial curvature under these constrains are discussed.     

Relativistic Anandan quantum phase in the Lorentz violation background

We study the influence of a classical background based on the violation of the Lorentz symmetry on the relativistic Anandan quantum phase. We show that the choice of the Lorentz symmetry violation background provides an abelian contribution for the relativistic Anandan quantum phase.     

CP symmetry and its violation in fundamental interactions

The concept of discrete symmetries in classical and quantum physics is reviewed. An account is given ofCP violation observed in theK-meson system and of other experiments whereCP symmetry has been tested. The present theoretical ideas onCP violation within the standard model, and problems needing extension of the model are described. Finally, ideas and experimental approaches toCP violation beyond the standard model are reviewed in brief.     

Associted Production of Z Boson and a Pair of New Quarks at LHC

The associated production of Z boson and a pair of new quarks at the Large Hadron Collider （LHC） is studied. The cross sections for both sequential fermions and vector-like fermions are presented. It is found that for sequential fermions the cross sections can reach 1 - 10^2 /b for heavy quark mass mQ from 1000 GeV to 200 GeV. For vector-like quarks, the cross sections are suppressed by mixing parameter sin OL. Focusing on process pp → b＇b＇, we investigate the possibility of detecting the 6l 4- 2j signal. For a b＇ with light mass and a large branching ratio of b＇ → bZ, it is found that only several signal events （ parton level ） can be produced with 1000 fb^-1 integrated luminosity. Although the signal events are rare, all the final states are produced centrally and multi lepton final states are clear at hadron collider, which could be easily detected.     

Looking for a Possible Breakdown of Local Lorentz Invariance for Electromagnetic Phenomena: Theory and First Experimental Results

We propose a new electromagnetic test of breakdown of local Lorentz invariance. It is based essentially on the detection of a non-zero force between a circular steady current and a charge, both at rest in the Earth frame. A preliminary experimental run gave a positive evidence for such an effect, which appears strongly dependent on the orientation of the circuit. Possible theoretical interpretations are briefly discussed.     

Parity violation in electron scattering

By comparing the cross sections for left- and right-handed electrons scattered from various unpolarized nuclear targets, the small parity-violating asymmetry can be measured. These asymmetry data probe a wide variety of important topics, including searches for new fundamental interactions and important features of nuclear structure that cannot be studied with other probes. A special feature of these experiments is that the results are interpreted with remarkably few theoretical uncertainties, which justifies pushing the experiments to the highest possible precision. To measure the small asymmetries accurately, a number of novel experimental techniques have been developed.     

Lorentz Invariant Decompositions of the State Vector Spaces and the Basis Problem

We consider a representation of the state reduction which depends neither on its reality nor on the details of when and how it emerges. Then by means of the representation we find necessary conditions, even if not the sufficient ones, for a decomposition of the state vector space to be a solution to the basis problem. The conditions are that the decomposition should be Lorentz invariant and orthogonal and that the associated projections should be continuous. They are shown to be able to determine a decomposition in each of a few examples considered if the other circumstances are taken into account together.     

Measuring Higgs CP properties through top quark production at a photon collider

We study resonant effects of heavy Higgs bosons on the top-pair production process at a photon linear collider. Observables which can be obtained by circular polarization of colliding photons and polarization measurement through the angular distribution of the top quark decays are useful not only for measuring the Higgs CP parity but also for resolving degeneracy of Higgs bosons.