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 natural explanation for the tritium $β$-decay end-point via an effective neutrino mass term without the need of a sterile right-handed state.
We present the full two-loop beta-functions for the MSSM including R-parity violating couplings. We analyse the effect of two-loop running on the bounds on R-parity violating couplings, on the nature of the LSP and on the stop masses.
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.
The contribution of the R-parity violating minimal supersymmetric standard model to the neutron beta decay at the one-loop level is investigated. It is found that the baryon number and R-parity violating interactions contribute to the D correlation through one-loop corrections, while the tree level prediction is vanishing. The Fierz interference term is also investigated at the one-loop level by considering the lepton number and R-parity violating interactions. We show that future experimental progress can provide us with better constraints on some of the combinations of R-parity violating cou…
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.
In the decay chain B(d) --> Psi + K --> Psi + (pi l nu), neutral K mixing follows on the heels of neutral B mixing. This "cascade mixing" leads to an interference which probes cos(2*beta), where beta is one of the three CP-violating phase angles which characterize CP violation in the Standard Model. Widely-discussed future B-system experiments will determine trigonometric functions of these three phase angles, leaving the underlying angles themselves discretely ambiguous. A determination of cos(2*beta) through cascade mixing would eliminate all the discrete ambiguities entirely.
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 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.
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.
Taking the established nonzero value of $θ_{13}$, we study the possibility of extracting the Dirac CP-violating phase by a beta beam facility with a boost factor $100<γ<450$. We compare the performance of different setups with different baselines, boost factors and detector technologies. We find that an antineutrino beam from $^6$He decay with a baseline of $L=1300$ km has a very promising CP discovery potential using a 500 kton Water Cherenkov (WC) detector. Fortunately this baseline corresponds to the distance between FermiLAB to Sanford underground research facility in South Dakota.
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.
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.
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.
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…
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 consider recently observed neutrinoless double beta decay in the context of the minimal supersymmetric standard model with R-parity violating couplings lambda^{'}. We observe that most of the current experimental bounds on the R-parity violating couplings do not exclude the possibility that the neutrinoless double beta decay is caused by R-parity violation. But if we consider K-bar{K} oscillation, we observe that we have to make the R-parity violating couplings generation-dependent to accomodate with the observed neutrinoless double beta decay. And furthermore, we need some mechanism to can…
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.
Using a generalized procedure for obtaining the equation of motion of a propagating fermionic particle, we examine previous claims for a lightlike preferred axis embedded in the framework of Lorentz-invariance violation with preserved algebra. In a high energy scale, the corresponding equation of motion is reduced to a conserving lepton number chiral (VSR) equation, and in a low energy scale, the Dirac equation for a free is recovered. The new dynamics introduces some novel ingredients (modified cross section) to the phenomenology of the tritium beta decay end-point.
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.
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…
We perform a study of neutrinoless double beta ($0νββ$) decay mediated by the lightest neutralino of arbitrary mass in the Minimal Supersymmetric Standard Model (MSSM) under the presence of R-parity violating trilinear interactions. In this scenario, the exchange of the lightest neutralino can result in $0νββ$ decay of either long-range or short-range behaviour, depending on the neutralino mass. Using nuclear matrix elements calculated in the Interacting Boson Model, we use an interpolation between the long- and short-range behaviours with an approximate formula. The non-observation of $0νββ$ …
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.
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.
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.
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.
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 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.
We show that a detector placed near a beta-beam storage ring can probe lepton number violating interactions, as predicted by supersymmetric theories with R-parity non-conservation. In the presence of such interactions, nu_tau can be produced during beta-decay leading to tau leptons through weak interactions. Alternatively, electron neutrinos from beta-decay of radioactive ions can produce tau leptons in a nearby detector through these interactions. The muons from the decay of these tau leptons can be readily identified in a small iron calorimeter detector and will signal violation of R-parity.
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 present a new contribution of the R-parity violating supersymmetry (SUSY) to neutrinoless double beta decay via the pion exchange between decaying neutrons. The pion coupling to the final state electrons is induced by the R-parity violating SUSY interactions. We have found this pion-exchange mechanism to dominate over the conventional two-nucleon one. The latter corresponds to direct interaction between quarks from two decaying neutrons without any light hadronic mediator like pion. The constraints on the certain R-parity violating SUSY parameters are extracted from the current experimental…
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 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 explore the possibility that the weak interaction violates Lorentz, and in particular rotational, invariance in neutron and allowed nuclear beta decay. A broad class of Lorentz-violating effects is considered, in which the standard propagator of the W-boson acquires an additional Lorentz-violating tensor. The general decay rate for allowed beta decay that incorporates such a modified propagator is derived. The resulting Lorentz-violating signals are discussed for the different types of beta-decay transitions, Fermi, Gamow-Teller, and mixed. We study the implications of our formalism for ded…
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…
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…
Radiative corrections arising from Lorentz violation in the fermion sector induce a nonzero amplitude for vacuum photon splitting. At one loop, the on-shell amplitude acquires both CPT-even and CPT-odd contributions forbidden in conventional electrodynamics.
