Lorentz invariant CPT breaking in the Dirac equation
Kazuo Fujikawa, Anca Tureanu
备注：
Talk given at the Memorial Meeting for Abdus Salam's 90th Birthday, Nanyang Technological University, Singapore, January 25-28, 2016 (to appear in the Proceedings)
If one modifies the Dirac equation in momentum space to $[γ^μp_μ-m-Δm(θ(p_{0})-θ(-p_{0})) θ(p_μ^{2})]ψ(p)=0$, the symmetry of positive and negative energy eigenvalues is lifted by $m\pm Δm$ for a small $Δm$. The mass degeneracy of the particle and antiparticle is thus lifted in a Lorentz invariant manner since the combinations $θ(\pm p_{0})θ(p_μ^{2})$ with step functions are manifestly Lorentz invariant. We explain an explicit construction of this CPT breaking term in coordinate space, which is Lorentz invariant but non-local at a distance scale of the Planck length. The application of this Lorentz invariant CPT breaking mechanism to the possible mass splitting of the neutrino and antineutrino in the Standard Model is briefly discussed.
This talk provides a status report on CPT violation in neutral-meson oscillations, focusing on implications of the CPT- and Lorentz-violating standard-model extension.
Overview of spontaneous Lorentz and CPT breaking mechanism in the context of the standard model contributed to the proceedings for the Coral Gables meeting.
A theoretical study of possible signals for CPT and Lorentz violation arising in hydrogen and antihydrogen spectroscopy is described. The analysis uses a CPT- and Lorentz-violating extension of quantum electrodynamics, obtained from a general Lorentz-violating extension of the minimal standard model with both CPT-even and CPT-odd terms. Certain 1S-2S transitions and hyperfine Zeeman lines exhibit effects at leading order in small CPT-violating couplings.
In this talk, the status of CPT tests with neutral mesons is reviewed in the context of quantum field theory and the Lorentz- and CPT-violating standard-model extension.
This talk summarizes some theoretical features and experimental implications of a general Lorentz-violating extension of the minimal SU(3) x SU(2) x U(1) standard model that allows for both CPT-even and CPT-odd effects. The theory would arise as the low-energy limit of a fundamental theory that is Lorentz and CPT covariant but in which spontaneous Lorentz breaking occurs. The use of neutral-meson oscillations and various QED systems to bound the apparent CPT and Lorentz violations is described.
Space-based experiments offer sensitivity to numerous unmeasured effects involving Lorentz and CPT violation. We provide a classification of clock sensitivities and present explicit expressions for time variations arising in such experiments from nonzero coefficients in the Lorentz- and CPT-violating Standard-Model Extension.
A general Lorentz-violating extension of the standard model of particle physics, allowing for both CPT-even and CPT-odd effects, is described. Some of its theoretical aspects and experimental implications are summarized.
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.
A theoretical framework extending QED in the context of the standard model is used to analyze a variety of Lorentz and CPT tests in atomic systems. Experimental signatures of possible Lorentz and CPT violation in these systems are investigated, and bounds are discussed.
This contribution to the CPT'16 meeting briefly highlights some of the recent progress in the phenomenology of Lorentz and CPT violation, with emphasis on research performed at the Indiana University Center for Spacetime Symmetries.
A general Lorentz-violating extension of the minimal SU(3) x SU(2) x U(1) standard model is described, including both CPT-even and CPT-odd terms. Some theoretical properties and experimental implications are given. The extension can be regarded as a low-energy limit of a physically relevant Lorentz-covariant fundamental theory in which spontaneous Lorentz violation occurs.
The breakdown of spacetime symmetries has recently been identified as a promising candidate signal for underlying physics, possibly arising through quantum-gravitational effects. This talk gives an overview over various aspects of CPT- and Lorentz-violation research. Particular emphasis is given to the interplay between CPT, Lorentz, and translation symmetry, mechanisms for CPT and Lorentz breaking, and the construction of a low-energy quantum-field description of such effect. This quantum field framework, called the SME, is employed to determine possible phenomenological consequences of CPT a…
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.
The theoretical and experimental prospects for Lorentz- and CPT-violating quantum electrodynamics in Penning traps are reviewed in this work. With the recent reported results for the measurements of magnetic moments for both protons and antiprotons, improvements with factors of up to 3000 for the constraints of various coefficients for Lorentz and CPT violation are obtained.
A review is presented of some recent Lorentz and CPT tests in atomic and particle systems where the predominant interactions are described by quantum electrodynamics. A theoretical framework extending QED in the context of the standard model is used to analyze these systems. Experimental signatures of possible Lorentz and CPT violation are investigated, and bounds are discussed.
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.
This talk at the CPT'19 meeting outlines a few recent developments in Lorentz and CPT violation, with particular attention to results obtained by researchers at the Indiana University Center for Spacetime Symmetries.
Possible signals for indirect CPT violation arising in experiments with neutral kaons are considered in the context of a general CPT- and Lorentz-violating standard-model extension. Certain CPT observables can depend on the meson momentum and exhibit sidereal variations in time. Any leading-order CPT violation would be controlled by four parameters that can be separately constrained in appropriate experiments. Recent experiments bound certain combinations of these parameters at the level of about $10^{-20}$ GeV.
Experimental signals for indirect CPT violation in the neutral-meson systems are studied in the context of a general CPT- and Lorentz-violating standard-model extension. In this explicit theory, some CPT observables depend on the meson momentum and exhibit diurnal variations. The consequences for CPT tests vary significantly with the specific experimental scenario. The wide range of possible effects is illustrated for two types of CPT experiment presently underway, one involving boosted uncorrelated kaons and the other involving unboosted correlated kaon pairs.
Precision experiments with muons are sensitive to Planck-scale CPT and Lorentz violation that is undetectable in other tests. Existing data on the muonium ground-state hyperfine structure and on the muon anomalous magnetic moment could be analyzed to provide dimensionless figures of merit for CPT and Lorentz violation at the levels of $4\times 10^{-21}$ and $10^{-23}$.
An overview of recent progress on testing Lorentz and CPT symmetry using Penning traps is presented. The theory of quantum electrodynamics with Lorentz-violating operators of mass dimensions up to six is summarized. Dominant shifts in the cyclotron and anomaly frequencies of the confined particles and antiparticles due to Lorentz and CPT violation are derived. Existing results of the comparisons of charge-to-mass ratios and magnetic moments involving protons, antiprotons, electrons, and positrons are used to constrain various coefficients for Lorentz violation.
A modified Dirac equation with general Lorentz- and CPT-violating operators in the electromagnetic field is studied. Constraints on and possible sensitivities to Lorentz-violating coefficients in the nonminimal sector up to mass-dimension six can be obtained by analyzing Penning-trap results involving anomaly frequencies.
A review of Lorentz and CPT tests performed in atomic systems is presented. A theoretical framework extending QED in the context of the standard model is used to analyze a variety of systems. Experimental signatures of possible Lorentz and CPT violation in these systems are investigated. Estimated bounds attainable in future experiments and actual bounds obtained in recent experiments are given.
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.
In this talk, a brief summary is given of the possibility of using neutral-kaon oscillations to bound CPT- and Lorentz-breaking parameters in an extension of the minimal standard model.
Lorentz- and CPT-violating effects initiating two-body electromagnetic flavor-changing decays of charged leptons are studied in the framework of Lorentz-violating effective field theory. An analysis of data from experiments at the Paul Scherrer Institute and at the Stanford Linear Accelerator measuring the branching ratios of these decays provides 576 constraints on independent flavor-changing effects in the charged-lepton sector, consistent with no Lorentz and CPT violation at the level of parts in $10^{-13}$ GeV$^{-1}$ to $10^{-9}$ GeV$^{-1}$.
We consider neutrino oscillations in the minimal Standard-Model Extension describing general Lorentz and CPT violation. Among the models without neutrino mass differences is one with two degrees of freedom that reproduces most major observed features of neutrino behavior.
Signals for CPT and Lorentz violation at the Planck scale may arise in hydrogen and antihydrogen spectroscopy. We show that certain 1S-2S and hyperfine transitions can exhibit theoretically detectable effects unsuppressed by any power of the fine-structure constant.
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.
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.
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.
This talk discusses the sensitivity of electron-positron and proton-antiproton Penning-trap experiments to CPT- and Lorentz-violating effects in the context of an extension of the minimal standard model and quantum electrodynamics.
Tests of CPT and Lorentz symmetry using neutral-meson oscillations are studied within a formalism that allows for indirect CPT and T violation of arbitrary size and is independent of phase conventions. The analysis is particularly appropriate for studies of CPT and T violation in oscillations of the heavy neutral mesons D, B_d, and B_s. The general Lorentz- and CPT-breaking standard-model extension is used to derive an expression for the parameter for CPT violation. It varies in a prescribed way with the magnitude and orientation of the meson momentum and consequently also with sidereal time. …
Experiments using macroscopic samples of spin-polarized matter offer exceptional sensitivity to Lorentz and CPT violation in the electron sector. Data from existing experiments with a spin-polarized torsion pendulum provide sensitivity in this sector rivaling that of all other existing experiments and could reveal spontaneous violation of Lorentz symmetry at the Planck scale.
Applications of the general theory of quantum electrodynamics with Lorentz- and CPT-violating operators of mass dimensions up to six are presented to Penning-trap experiments comparing charge-to-mass ratios between particles and antiparticles. Perturbation theory is used to derive Lorentz- and CPT-violating contributions to the energy levels and cyclotron frequencies of confined particles and antiparticles. We show that whether the experimental {\it interpreted} quantity $(|q|/m)_{\overline{w}}/(|q|/m)_{w} - 1$ is a clean measure of a CPT test depends on the context of the relevant theory. Exi…
The CPT theorem has been tested to very high precision in a variety of experiments involving particles and antiparticles confined within Penning traps. These tests include comparisons of anomalous magnetic moments and charge-to-mass ratios of electrons and positrons, protons and antiprotons, and hydrogen ions and antiprotons. We present a theoretical analysis of possible signals for CPT and Lorentz violation in these systems. We use the framework of Colladay and Kostelecký, which consists of a general extension of the $SU(3) \times SU(2) \times U(1)$ standard model including possible CPT and L…
The theoretical prospects for quantum electrodynamics with Lorentz-violating operators of mass dimensions up to six are revisited in this work. The dominant effects due to Lorentz and CPT violation are studied in measurements of magnetic moments of particles confined in Penning traps. Using recently reported experimental results, new coefficients for Lorentz violation are constrained and existing bounds of various coefficients are improved.
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.
The effects of perturbative Lorentz and CPT violation on neutrino oscillations are studied. Features include neutrino-antineutrino oscillations, direction dependence, and unconventional energy behavior. Leading-order corrections arising from renormalizable operators are derived in the general three-flavor effective field theory. The results are applied to neutrino-beam experiments with long baselines, which offer excellent sensitivity to the accompanying effects. Key signatures of Lorentz and CPT violation using neutrino beams include sidereal variations in the oscillation probabilities arisin…
Signals for Lorentz and CPT violation can appear in a wide range of experiments including hadron colliders like the LHC. We present a calculation of the Lorentz-violating cross section for top-quark pair production via gluon fusion. This process dominates at the LHC, and analysis of LHC data should permit sharpening the constraints on top-quark Lorentz violation obtained recently by the D0 Collaboration. We also present a separate calculation of single-top production, which is sensitive to CPT violation. Data from the LHC can be used to measure coefficients for CPT violation in the top-quark s…
Neutrino oscillations in the presence of Lorentz violation can present novel observable signals in both long- and short-baseline experiments. In this talk we describe the theory and its different regimes depending on properties of the experiments. CPT violation, its systematic search and possible connections to latest results are also presented.
The prospects are explored for testing Lorentz and CPT symmetry in the muon sector via the spectroscopy of muonium and various muonic atoms, and via measurements of the anomalous magnetic moments of the muon and antimuon. The effects of Lorentz-violating operators of both renormalizable and nonrenormalizable dimensions are included. We derive observable signals, extract first constraints from existing data on a variety of coefficients for Lorentz and CPT violation, and estimate sensitivities attainable in forthcoming experiments. The potential of Lorentz violation to resolve the proton radius …
An overview of recent progress on searches for Lorentz- and CPT-violating signals with confined particles and antiparticles in Penning traps is presented. In the context of the Standard-Model Extension (SME), leading-order shifts in the cyclotron and anomaly frequencies of a confined particle and antiparticle due to Lorentz and CPT violation are provided. The two frequencies are then related to comparisons of charge-to-mass ratios and magnetic moments between particles and antiparticles. Applying reported results from Penning-trap experiments leads to new limits on various coefficients for Lor…
Colladay and Kostelecky have proposed a framework for studying Lorentz and CPT violation in a natural extension of the Standard Model. Although numerous bounds exist on the Lorentz and CPT violating parameters in the gauge boson and fermion sectors, there are no published bounds on the parameters in the Higgs sector. We determine these bounds. The bounds on the CPT-even asymmetric coefficients arise from the one-loop contributions to the photon propagator, those from the CPT-even symmetric coefficients arise from the equivalent c_{μν} coefficients in the fermion sector, and those from the CPT-…
Violations of the Lorentz and CPT symmetries can appear as observable effects in the direct production of top quarks and their subsequent decays. Earlier results for the $q\bar{q}$ production process for $t\bar{t}$ pairs have been extended to include the gluon fusion process which dominates at the LHC. In addition results are obtained for testing CPT symmetry through single top quark production.
Space-based clock-comparison experiments can provide Planck-scale sensitivity to many parameters for Lorentz and CPT violation that are difficult to measure on Earth. The principal advantages are a reduced timescale for data collection, reduced suppression for certain effects, and access to certain parameters not possible with Earth-based experiments.
One possible ramification of unified theories of nature such as string theory that may underlie the conventional standard model is the possible spontaneous breakdown of Lorentz and CPT symmetry. In this talk, the formalism for inclusion of such effects into a low-energy effective field theory is presented. An extension of the standard model that includes Lorentz- and CPT-breaking terms is developed. The restriction of the standard model extension to the QED sector is then discussed.
A review of recent theoretical work investigating tests of Lorentz and CPT symmetry in atomic and particle systems is presented. A variety of tests in matter and antimatter are discussed, including measurements of anomalous magnetic moments in Penning traps, comparisons of atomic-clock transitions, high-precision spectroscopic measurements of hydrogen and antihydrogen, experiments with muons, experiments with mesons, and tests of Lorentz symmetry with a spin-polarized torsion pendulum.
In recent years, the breakdown of spacetime symmetries has been identified as a promising research field in the context of Planck-scale phenomenology. For example, various theoretical approaches to the quantum-gravity problem are known to accommodate minute violations of CPT invariance. This talk covers various topics within this research area. In particular, some mechanisms for spacetime-symmetry breaking as well as the Standard-Model Extension (SME) test framework will be reviewed; the connection between CPT and Lorentz invariance in quantum field theory will be exposed; and various experime…
In this conference proceedings, some comments on the present status and recent growth of efforts to find Lorentz and CPT violation are given by extracting metrics from the annually updated "Data Tables for Lorentz and CPT Violation." They reveal that tests span all the sectors of particle and gravitational physics, and have shown remarkable and consistent growth. Through numerous innovations and refinements in experiments, a large body of data has been amassed with ever-increasing precisions. The Tables are available through the Cornell preprint archive at arXiv:0801.0287.
In this proceedings, a summary is presented of recent research investigating ways in which high-precision atomic clocks on the International Space Station could search for violations of Lorentz and CPT symmetry. Space-based searches offer certain experimental advantages over Earth-based experiments investigating these symmetries. The results are based on work published in Physical Review Letters, volume 82, article 090801, 2002.
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.
A general formalism is presented for violations of Lorentz and CPT symmetry in the neutrino sector. The effective hamiltonian for neutrino propagation in the presence of Lorentz and CPT violation is derived, and its properties are studied. Possible definitive signals in existing and future neutrino-oscillation experiments are discussed. Among the predictions are direction-dependent effects, including neutrino-antineutrino mixing, sidereal and annual variations, and compass asymmetries. Other consequences of Lorentz and CPT violation involve unconventional energy dependences in oscillation leng…
Possibilities for observing signals of CPT and Lorentz violation in the spectroscopy of hydrogen and antihydrogen are considered. We show that transitions between the c and d hyperfine sublevels in the 1S state can exhibit theoretically detectable effects that would be unsuppressed by powers of the fine-structure constant. This transition may therefore offer some advantages over 1S-2S two-photon spectroscopy.
We present a theoretical analysis of signals for CPT and Lorentz violation in g-2 and charge-to-mass-ratio experiments on electrons and positrons in Penning traps. Experiments measuring anomaly frequencies are found to be the most sensitive to CPT violation. We find that the conventional figure of merit for CPT breaking, involving the difference of the electron and positron g factors, is inappropriate in this context, and an alternative is introduced. Bounds of approximately one part in 10^{20} are attainable.
The prospects are explored for testing Lorentz and CPT symmetry in the top-quark sector. We present the relevant Lagrange density, discuss physical observables, and describe the signals to be sought in experiments. For top-antitop pair production via quark or gluon fusion with subsequent semileptonic or hadronic decays, we obtain the matrix element in the presence of Lorentz violation using the narrow-width approximation. The issue of testing CPT symmetry in the top-quark sector is also addressed. We demonstrate that single-top production and decay is well suited to a search for CPT violation,…
