Optical resonators provide a powerful tool for testing aspects of Lorentz invariance. Here, we present a reanalysis of an experiment where a path asymmetry was created in an optical ring resonator by introducing a dielectric prism in one arm. The frequency difference of the two fundamental counter-propagating modes was then recorded as the apparatus was orientation-modulated in the laboratory. By assuming that the minimal Standard-Model Extension coefficients vanish we are able to place bounds on higher-order parity-odd Lorentz-violating coefficients of the Standard-Model Extension. The results presented in this work set the first constraints on two previously unbounded linear combinations of d=8 parity-odd nonbirefringent nondispersive coefficients of the photon sector.
I discuss progress towards "bootstrapping" a Lorentz-violating gravity theory: namely, extending a linear Lorentz-violating theory of a rank-2 tensor to a non-linear theory by coupling this field to its own stress-energy tensor.
We determine the sensitivity of a modern Michelson-Morley resonant-cavity experiment to the higher-order nonbirefringent and nondispersive coefficients of the Lorentz-violating Standard-Model Extension. Data from a recent year-long run of the experiment is used to place the first bounds on these coefficients.
We have recently proposed a Lorentz-violating energy-momentum relation entailing an exact momentum cutoff and studied various physical applications of that dispersion law. By a simple phenomenological approach we here study Lorentz violation effects on early Universe and pre-Planckian cosmological radiation. In particular, we predict an effective infinite speed of light soon after the Big Bang instant, leading to a straightforward solution of the horizon and flatness problems without recourse to inflation, cosmological scalar fields or other ad hoc energy sources.
We consider the black hole dynamical evolution in the framework of a Lorentz-violating spacetime endowed with a Schwarzchild-like momentum-dependent metric. Large deviations from the Hawking-Bekenstein predictions are obtained, depending on the values of the Lorentz-violating parameter lambda introduced. A non-trivial evolution comes out, following mainly from the existence of a non-vanishing minimum mass: for large Lorentz violations, most of the black hole evaporation takes place in the initial stage, which is then followed by a stationary stage (whose duration depends on the value of lambda…
We explore the impact of Lorentz violation on the inflationary scenario. More precisely, we study the inflationary scenario in the scalar-vector-tensor theory where the vector is constrained to be unit and time like. It turns out that the Lorentz violating vector affects the dynamics of the chaotic inflationary model and divides the inflationary stage into two parts; the Lorentz violating stage and the standard slow roll stage. We show that the universe is expanding as an exact de Sitter spacetime in the Lorentz violating stage although the inflaton field is rolling down the potential. Much mo…
A brief summary is given of recent developments concerning a Lorentz-violating extension of the standard model and its implications for experiments testing Lorentz and CPT symmetry.
In this talk, the stationary limit of Lorentz-violating electrodynamics is discussed. As illustrated by some simple examples, the general solution includes unconventional mixing of electrostatic and magnetostatic effects. I discuss a high-sensitivity null-type measurement, exploiting Lorentz-violating electromagnetostatic effects, that could improve existing limits on parity-odd coefficients for Lorentz violation in the photon sector.
We study the Lorentz and CPT violating effects on the branching ratio and the CP violating asymmetry of the lepton flavor violating interactions μ\to eγand τ\to μγ, in the model III version of the two Higgs doublet model. Here we consider that the Lorentz and CPT violating effects exist in the QED part of the interactions and enter into expressions in the lepton propagators and in the lepton-photon vertex. We observe that there exists a non-zero CP asymmetry. However, the Lorentz and CPT violating effects on the braching ratio and the CP asymmetry are negligibly small.
We study the Lorentz and CPT violating effects on the branching ratio BR, the CPT violating asymmetry A_{CPT} and the ratio of the decay width, including only the Lorentz violating effects, to the one obtained in the standard model, for the flavor dependent part of the lepton flavor conserving Z\to l^+ l^- (l=e,μ,τ) decay. The inclusion of the Lorentz and CPT violating effects to the standard model contribution is too small to be detected, since the corresponding coefficients are highly suppressed at the low energy scale.
We investigate whether postulating the existence of Lorentz-violating, CPT-conserving interactions allows three-neutrino solutions to the LSND anomaly that are also consistent with all other neutrino data. We show that Lorentz-violating interactions that couple only to one of the active neutrinos have the right properties to explain all the data. The details of the data make this solution unattractive. We find, for example, that a highly non-trivial energy dependence of the Lorentz-violating interactions is required.
Lorentz symmetry is an important concept in modern physics. Precision pulsar timing was used to put tight constraints on the coefficients for Lorentz violation in the pure-gravity sector of the Standard-Model Extension (SME). We extend the analysis to Lorentz-violating matter-gravity couplings, utilizing three small-eccentricity relativistic neutron star (NS) -- white dwarf (WD) binaries. We obtain compelling limits on various SME coefficients related to the neutron, the proton, and the electron. These results are complementary to limits obtained from lunar laser ranging and clock experiments.
In this work we outline the two most commonly used test theories (RMS and SME) for testing Local Lorentz Invariance (LLI) of the photon. Then we develop the general framework of applying these test theories to resonator experiments with an emphasis on rotating experiments in the laboratory. We compare the inherent sensitivity factors of common experiments and propose some new configurations. Finally we apply the test theories to the rotating cryogenic experiment at the University of Western Australia, which recently set new limits in both the RMS and SME frameworks [hep-ph/0506074].
The general features of renormalization and the renormalization group in QED and in general quantum field theories in curved spacetime with additional Lorentz- and CPT-violating background fields are reviewed.
We propose a new Lorentz invariant violating extension for the pure photonic sector of the Standard Model due to the condensation of topological defects in the context of the Julia-Toulouse mechanism. Possible physical consequences leading to direct measurable effects over the confining properties of the elementary particles are explored.
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.
The static limit of Lorentz-violating electrodynamics in vacuum and in media is investigated. Features of the general solutions include the need for unconventional boundary conditions and the mixing of electrostatic and magnetostatic effects. Explicit solutions are provided for some simple cases. Electromagnetostatics experiments show promise for improving existing sensitivities to parity-odd coefficients for Lorentz violation in the photon sector.
The prospects are explored for testing Lorentz- and CPT-violating quantum electrodynamics in experiments with Penning traps. We present the Lagrange density of Lorentz-violating spinor electrodynamics with operators of mass dimensions up to six, and we discuss some of its properties. The theory is used to derive Lorentz- and CPT-violating perturbative shifts of the energy levels of a particle confined to a Penning trap. Observable signals are discussed for trapped electrons, positrons, protons, and antiprotons. Existing experimental measurements on anomaly frequencies are used to extract new o…
In Lorentz-violating electrodynamics a steady current (and similarly a static charge) generates both static magnetic and electric fields. These induced fields, acting on interfering particles, change the interference pattern. We find that particle interference experiments are sensitive to small Lorentz violating effects, and thus they can be used to improve current bounds on some Lorentz-violating parameters.
In this work, we present CPT- and Lorentz-violating corrections to observable quantities in electron-proton scattering. We also show how the theoretical prediction can be used together with data to establish bounds on a coefficient for CPT and Lorentz violation in the QCD sector.
We show that the general Lorentz- and CPT-violating extension of quantum electrodynamics is one-loop renormalizable. The one-loop Lorentz-violating beta functions are obtained, and the running of the coefficients for Lorentz and CPT violation is determined. Some implications for theory and experiment are discussed.
The classification of Lorentz- and CPT-violating operators in nonabelian gauge field theories is performed. We construct all gauge-invariant terms describing propagation and interaction in the action for fermions and gauge fields. Restrictions to the abelian, Lorentz-invariant, and isotropic limits are presented. We provide two illustrative applications of the results to quantum electrodynamics and quantum chromodynamics. First constraints on nonlinear Lorentz-violating effects in electrodynamics are obtained using data from experiments on photon-photon scattering, and corrections from nonmini…
We extend Lorentz-violating Supersymmetry models to include vector superfields. The CPT-preserving model generalizes easily, while the obvious attempt at generalizing the CPT-violating model meets serious obstructions. Generalizations of the CPT-preserving but Lorentz-Violating model to higher dimensions are also straightforward. Compactification is used to reduce the six-dimensional theory to an ${\cal{N}} =2$ Lorentz-violating theory in four dimensions, while the ten-dimensional theory is used to produce an ${\cal{N}}=4$ Lorentz-violating theory. This may be useful in future constructions in…
We consider an extension of the Standard Model with isotropic nonbirefringent Lorentz violation in the photon sector and restrict the discussion to the case of a "fast" photon with a phase velocity larger than the maximum attainable velocity of the quarks and leptons. With our conventions, this case corresponds to a negative Lorentz-violating parameter $κ$ in the action. The decay rate of a neutral pion into two nonstandard photons is calculated as a function of the 3-momentum of the initial pion and the negative Lorentz-violating parameter $κ$ of the final photons.
We study the decay widths of the processes H^+\to W^+ H^0 (h^0,A^0), including the Lorentz violating effects and analyze the possible CPT violating asymmetry arising from CPT odd coefficients. We observe that these effects are too small to be detected, since the corresponding coefficients are highly suppressed at the low energy scale.
In this work we analyse a non-minimal Lorentz-violating extension of the electroweak theory in the fermionic sector. Firstly we analyse the relation between the CKM rotation in the quark sector and possible contributions of this new coupling to flavour changing neutral currents (FCNC) processes. In sequel we look for non-diagonal terms through possible leptonic flavour violation (LFV) decays. Strong bounds are presented to the Lorentz violating parameters of both the quark and the leptonic sectors.
Lorentz-violating theories of gravity typically contain constrained vector fields. We show that the lowest-order coupling of such vectors to $\mathrm{U}(1)$-symmetric scalars can naturally give rise to baryogenesis in a manner akin to the Affleck-Dine mechanism. We calculate the cosmology of this new mechanism, demonstrating that a net $B-L$ can be generated in the early Universe, and that the resulting baryon-to-photon ratio matches that which is presently observed. We discuss constraints on the model using solar system and astrophysical tests of Lorentz violation in the gravity sector. Gener…
The correspondence between Riemann-Finsler geometries and effective field theories with spin-independent Lorentz violation is explored. We obtain the general quadratic action for effective scalar field theories in any spacetime dimension with Lorentz-violating operators of arbitrary mass dimension. Classical relativistic point-particle lagrangians are derived that reproduce the momentum-velocity and dispersion relations of quantum wave packets. The correspondence to Finsler structures is established, and some properties of the resulting Riemann-Finsler spaces are investigated. The results prov…
We study the recently proposed Lorentz-violating dispersion relation for fermions and show that it leads to two distinct cubic operators in the momentum. We compute the leading order terms that modify the non-relativistic equations of motion and use experimental results for the hyperfine transition in the ground state of the ${}^9\textrm Be^+$ ion to bound the values of the Lorentz-violating parameters $η_1$ and $η_2$ for neutrons. The resulting bounds depend on the value of the Lorenz-violating background four-vector in the laboratory frame.
Remnant low-energy effects of Planck-scale Lorentz breaking in candidate fundamental theories typically include modified one-particle dispersion relations. Theoretical constraints on such modifications are discussed leading to the exclusion of a variety of previously considered Lorentz-violating parameters. In particular, the fundamental principle of coordinate independence, the role of an effective dynamical framework, and the conditions of positivity and causality are investigated.
A new model for neutrino oscillations is introduced, in which mass-like behavior is seen at high energies, but various behavior can be predicted at low energies. The model employs no neutrino masses, but instead relies on the Lorentz-violating parameters a and c. Oscillations into antineutrinos and sterile neutrinos are also considered.
We study the Lorentz and CPT violating effects on the ratio \frac{BR_{LorVio}}{BR_{SM}}, where BR_{LorVio} (BR_{SM}) is the branching ratios coming from the Lorentz violating effects (the SM), for the decays H^0\to f^+ f^- (f= quarks and charged leptons) and H^0\to ZZ (W^+ W^-). We observe that these new effects are too small to be detected, especially for f^+ f^- output, since the corresponding coefficients are highly suppressed at the low energy scale.
Perturbative calculations in quantum field theory often require the regularization of infrared divergences. In quantum electrodynamics, such a regularization can for example be accomplished by a photon mass introduced via the Stueckelberg method. The present work extends this method to the QED limit of the Lorentz- and CPT-violating Standard-Model Extension.
A three-parameter model of neutrino oscillations based on a simple Lorentz- and CPT-violating texture is presented. The model is consistent with established data and naturally generates low-energy and neutrino-antineutrino anomalies of the MiniBooNE type. A one-parameter extension incorporates the MINOS anomaly, while a simple texture enhancement accommodates the LSND signal.
Possible Lorentz-violating effects in the cosmic microwave background are studied. We provide a systematic classification of renormalizable and nonrenormalizable operators for Lorentz violation in electrodynamics and use polarimetric observations to search for the associated violations.
The current paper summarizes the content of a talk given on vacuum Cherenkov radiation emitted by Lorentz-violating fermions that are described in the context of the Standard-Model Extension. The decay rate will be obtained for various sets of controlling coefficients that will subsequently be constrained using cosmic-ray data.
This paper investigates how the nonzero temperature affects the differential cross-section for mesons scattering in a Lorentz-violating extension of the scalar electrodynamics. We initially discuss some features of the model and extract the zero temperature Feynman rules. Temperature effects are introduced using the Thermo Field Dynamics (TFD) formalism. It is shown that the corrections induced on the meson scattering are very large in the high-temperature regime. Furthermore, our results also suggest that temperature effects may contribute to new constraints on the Lorentz-violating parameter…
A general method is presented to build all gauge-invariant terms in gauge field theories, including quantum electrodynamics and quantum chromodynamics. It is applied to two experiments, light-by-light scattering and deep inelastic scattering, to extract first bounds on certain nonminimal coefficients for Lorentz violation.
Effective field theories with explicit Lorentz violation are intimately linked to Riemann-Finsler geometry. The quadratic single-fermion restriction of the Standard-Model Extension provides a rich source of pseudo-Riemann-Finsler spacetimes and Riemann-Finsler spaces. An example is presented that is constructed from a 1-form coefficient and has Finsler structure complementary to the Randers structure.
We calculate a finite momentum-dependent part of the photon polarization operator in a simple model of Lorentz-violating quantum electrodynamics nonperturbatively at all orders of Lorentz-violating parameters. We sum one-particle reducible diagrams into the modified photon propagator, and determine the physical photon dispersion relation as the location of its pole. The photon dispersion relation, as well as its group velocity, acquires the one-loop momentum-dependent radiative correction. We constrain the Lorentz-violating parameters for heavy charged fermions (muon, $τ$-lepton, top-quark) fr…
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…
Radiative corrections in quantum field theories with small departures from Lorentz symmetry alter structural aspects of the theory, in particular the definition of asymptotic single-particle states. Specifically, the mass-shell condition, the standard renormalization procedure as well as the Lehmann-Symanzik-Zimmermann reduction formalism are affected.
An analysis of spinor redefinitions in the context of the Lorentz-violating QED extension is performed. Certain parameters that apparently violate Lorentz invariance are found to be physically irrelevant as they can be removed from the lagrangian using an appropriate redefinition of the spinor field components. It is shown that conserved currents may be defined using a modified action of the complex extension of the Lorentz group on the redefined spinors. This implies a natural correspondence between the apparently Lorentz-violating theory and conventional QED. Redefinitions involving derivati…
We give a complete classification of mass dimension five Lorentz-non-invariant interactions composed from the Standard Model fields, using the effective field theory approach. We identify different classes of Lorentz violating operators, some of which are protected against transmutation to lower dimensions even at the loop level. Within each class of operators we determine a typical experimental sensitivity to the size of Lorentz violation.
The formulation and some experimental implications of a general Lorentz-violating extension of the standard model are reviewed. The theory incorporates both CPT-preserving and CPT-breaking terms. It is otherwise a conventional quantum field theory, obtained under the assumption that Lorentz symmetry is spontaneously broken in an underlying model. The theory contains the usual standard-model gauge structure, and it is power-counting renormalizable. Energy and momentum are conserved. Despite the violation of Lorentz symmetry, the theory exhibits covariance under Lorentz transformations of the ob…
We have analyzed Maxwell-Chern-Simons-Higgs BPS vortices in a Lorentz-violating CPT-odd context. The Lorentz violation induces profiles with a conical behavior at the origin. For some combination of the coefficients for Lorentz violation there always exists a sufficiently large winding number for which the magnetic field flips its sign.
We study an extension of QED involving a light pseudoscalar (an axion-like particle), together with a very massive fermion which has Lorentz-violating interactions with the photon and the pseudoscalar, including a nonminimal Lorentz-violating coupling. We investigate the low energy effective action for this model, after integration over the fermion field, and show that interesting results are obtained, such as the generation of a correction to the standard coupling between the axion-like particle and the photon, as well as Lorentz-violating effects in the interaction energy involving electroma…
We study the possibility of constructing Lorentz-violating supersymmetric quantum field theories under the assumption that these theories have to be described by lagrangians which are renormalizable by weighted power counting. Our investigation starts from the observation that at high energies Lorentz-violation and the usual supersymmetry algebra are algebraically compatible. Demanding linearity of the supercharges we see that the requirement of renormalizability drastically restricts the set of possible Lorentz-violating supersymmetric theories. In particular, in the case of supersymmetric ga…
We study the effects of the minimal extension of the standard model including Lorentz violation on the Casimir force between two parallel conducting plates in vacuum. We provide explicit solutions for the electromagnetic field using scalar field analogy, for both the cases in which the Lorentz violating terms come from the CPT-even or CPT-odd terms. We also calculate the effects of the Lorentz violating terms for a fermion field between two parallel conducting plates and analyze the modifications of the Casimir force due to the modifications of the Dirac equation. In all cases under considerat…
Quantum-gravity effects are expected to be suppressed by the Planck mass. For experimental progress it is therefore important to identify potential signatures from Planck-scale physics that are amenable to ultrahigh-precision tests. It is argued that minuscule violations of Lorentz and CPT symmetry are candidate signals. In addition, theoretical and experimental aspects of the Standard-Model Extension, which describes the emergent low-energy effects, are discussed.
The Standard Model extension with additional Lorentz violating terms allows for redefining the equation of motion of a propagating left-handed fermionic particle. The obtained Dirac-type equation can be embedded in a generalized Lorentz-invariance preserving-algebra through the definition of Lorentz algebra-like generators with a light-like preferred axis. The resulting modification to the fermionic equation of motion introduces some novel ingredients to the phenomenological analysis of the cross section of the tritium $β$-decay. Assuming lepton number conservation, our formalism provides a na…
The CPT-odd and Lorentz-violating Carroll-Field-Jackiw modification of electrodynamics is discussed and we study its effects on the energy spectrum of hydrogen, as well as in the generation of a momentum-dependent electric dipole moment for charged leptons. We also briefly comment on the possibility of the detection of Lorentz violation in measurements of vacuum birefringence in resonant cavities. The bounds found are based on local laboratory experimental limits and are not competitive with the ones coming from astrophysical considerations.
A Lorentz violating modification of massless QED is proposed, with higher order space derivatives for the photon field. The fermion dynamical mass generation is studied with the Schwinger-Dyson approach, and it is found that the resulting mass is many orders of magnitude smaller than the (Plank-) mass scale introduced by the higher order derivative terms. This is due to a suppressing factor, non-analytic in the fine structure constant and exponentially small. This scenario is an alternative to the Higgs mechanism for the electron mass, which arises here from Lorentz violating effects at high e…
I present a unified formulation of anomalous contributions in quantum field theories by calculating directly the effective action using the background field and covariant-derivative expansion technique. I use this method to determine uniquely the induced Chern-Simons term from the a Lorentz and CPT violating term in fermion QED Lagrangian. The outstanding ambiguity is resolved by properly taken into account the noncommutivity of $A$ and $\partial$. The resulting vacuum polarization tensor acquires a non-Feynman diagram anomalous contribution which accounts for the discrepancy between the prese…
Synchrotron radiation is analyzed in the classical effective Lorentz invariance violating model of Myers-Pospelov. Within the full far-field approximation we compute the electric and magnetic fields, the angular distribution of the power spectrum and the total emitted power in the m-th harmonic, as well as the polarization. We find the appearance of rather unexpected and large amplifying factors, which go together with the otherwise negligible naive expansion parameter. This opens up the possibility of further exploring Lorentz invariance violations by synchrotron radiation measurements in ast…
Asymptotic single-particle states in quantum field theories with small departures from Lorentz symmetry are investigated perturbatively with focus on potential phenomenological ramifications. To this end, one-loop radiative corrections for a sample Lorentz-violating Lagrangian contained in the Standard-Model Extension (SME) are studied at linear order in Lorentz breakdown. It is found that the spinor kinetic operator, and thus the free-particle physics, is modified by Lorentz-violating operators absent from the original Lagrangian. As a consequence of this result, both the standard renormaliza…
