Lorentz-violating Standard Model Extension Research Articles

Relating Noncommutative SO(2,3)★ Gravity to the Lorentz-Violating Standard-Model Extension

We consider a model of noncommutative gravity that is based on a spacetime with broken local SO(2,3) ★ symmetry. We show that the torsion-free version of this model is contained within the framework of the Lorentz-violating Standard-Model Extension (SME). We analyze in detail the relation between the torsion-free, quadratic limits of the broken SO(2,3) ★ model and the Standard-Model Extension. As part of the analysis, we construct the relevant geometric quantities to quadratic order in the metric perturbation around a flat background.

Magnetoelectric Effect in Lorentz-violating Extensions of the Standard Model

We demonstrate that an atom placed in a constant background interacting with the electronic axial-vector current exhibits a new type of parity-breaking transverse magnetoelectric polarizability. Within beyond-Standard-Model (BSM) frameworks, such as the Lorentz-violating Standard Model Extension, such constant backgrounds are considered to be condensates of Planck-scale fields, thus, precision measurements of the magnetoelectric polarizability is able to constrain non-trivial BSM physics. Indeed, we demonstrate that the contribution to this effect within the Standard Model due to weak interaction is strongly suppressed, the effect virtually being purely exotic. We calculate magnetoelectric polarizability for a simple atom and discuss its observability.

Gluonic Lorentz violation and chiral perturbation theory

By applying chiral-perturbation-theory methods to the QCD sector of the Lorentz-violating Standard-Model Extension, we investigate Lorentz violation in the strong interactions. In particular, we consider the CPT-even pure-gluon operator of the minimal Standard-Model Extension. We construct the lowest-order chiral effective Lagrangian for three as well as two light quark flavors. We develop the power-counting rules and construct the heavy-baryon chiral-perturbation-theory Lagrangian, which we use to calculate Lorentz-violating contributions to the nucleon self energy. Using the constructed effective operators, we derive the first stringent limits on many of the components of the relevant Lorentz-violating parameter. We also obtain the Lorentz-violating nucleon-nucleon potential. We suggest that this potential may be used to obtain new limits from atomic-clock or deuteron storage-ring experiments.

Lorentz-symmetry test at Planck-scale suppression with nucleons in a spin-polarizedCs133cold atom clock

We introduce an improved model that links the frequency shift of the $^{133}\text{Cs}$ hyperfine Zeeman transitions $\vert F = 3, m_F> \longleftrightarrow \vert F = 4, m_F >$ to the Lorentz-violating Standard-Model Extension (SME) coefficients of the proton and neutron. The new model uses Lorentz transformations developed to second order in boost and additionally takes the nuclear structure into account, beyond the simple Schmidt model used previously in SME analyses, thereby providing access to both proton and neutron SME coefficients including the isotropic coefficient $\tilde{c}_{TT}$. Using this new model in a second analysis of the data delivered by the FO2 dual Cs/Rb fountain at Paris Observatory and previously analysed in arXiv:hep-ph/0601024v1, we improve by up to 12 orders of magnitude the present maximum sensitivities (see arXiv:0801.0287v9) on the $\tilde{c}_{Q}$, $\tilde{c}_{TJ}$ and $\tilde{c}_{TT}$ coefficients for the neutron and on the $\tilde{c}_{TT}$ coefficient for the proton, reaching respectively $10^{-20}$, $10^{-17}$, $10^{-13}$ and $10^{-15}$ GeV.

Question of Lorentz violation in muon decay

Possibilities to test the Lorentz invariance of the weak interaction in muon decay are considered. We derive the direction-dependent muon-decay rate with a general Lorentz-violating addition to the W-boson propagator. We discuss measurements of the directional and boost dependence of the Michel parameters and of the muon lifetime as a function of absolute velocity. The total muon-decay rate in the Lorentz-violating Standard Model Extension is addressed. Suggestions are made for dedicated (re)analyses of the pertinent data and for future experiments.

Eikonal approximation, Finsler structures, and implications for Lorentz-violating photons in weak gravitational fields

The current article shall contribute to understanding the classical analogue of the minimal photon sector in the Lorentz-violating Standard-Model Extension (SME). It is supposed to complement all studies performed on classical point-particle equivalents of SME fermions. The classical analogue of a photon is not a massive particle being described by a usual equation of motion, but a geometric ray underlying the eikonal equation. The first part of the paper will set up the necessary tools to understand this correspondence for interesting cases of the minimal SME photon sector. In conventional optics the eikonal equation follows from an action principle, which is demonstrated to work in most (but not all) Lorentz-violating cases as well. The integrands of the action functional correspond to Finsler structures, which establishes the connection to Finsler geometry. The second part of the article treats Lorentz-violating light rays in a weak gravitational background by implementing the principle of minimal coupling. Thereby it is shown how Lorentz violation in the photon sector can be constrained by measurements of light bending at massive bodies such as the Sun. The phenomenological studies are based on the currently running ESA mission GAIA and the planned NASA/ESA mission LATOR. The final part of the paper discusses certain aspects of explicit Lorentz violation in gravity based on the setting of Finsler geometry.

Lorentz-violating inflationary magnetogenesis

A non-conformally invariant coupling between the inflaton and the photon in the minimal Lorentz-violating standard model extension is analyzed. For specific forms of the Lorentz-violating background tensor, the strong-coupling and back-reaction problems of magnetogenesis in de Sitter inflation with scale $${\sim }10^{16}\,\hbox {GeV}$$ are evaded, the electromagnetic-induced primordial spectra of (Gaussian and non-Gaussian) scalar and tensor curvature perturbations are compatible with cosmic microwave background observations, and the inflation-produced magnetic field directly accounts for cosmic magnetic fields.

Classical kinematics for isotropic, minimal Lorentz-violating fermion operators

In this article a particular classical, relativistic Lagrangian based on the isotropic fermion sector of the Lorentz-violating (minimal) Standard Model extension is considered. The motion of the associated classical particle in an external electromagnetic field is studied, and the evolution of its spin, which is introduced by hand, is investigated. It is shown that the particle travels along trajectories that are scaled versions of the standard ones. Furthermore there is no spin precession due to Lorentz violation, but the rate is modified at which the longitudinal and transverse spin components transform into each other. This demonstrates that it is practical to consider classical physics within such an isotropic Lorentz-violating framework and it opens the pathway to study a curved background in that context.

Limits on Lorentz Violation from ForbiddenβDecays

Forbidden (slow) β decays offer new opportunities to test the invariance of the weak interaction under Lorentz transformations. Within a general effective field theory framework we analyze and reinterpret the only two relevant experiments, performed in the 1970s, dedicated to search for a preferred direction in space in first- and second-forbidden β decays. We show that the results of these experiments put strong and unique limits on Lorentz violation, and in particular on the presence of several interactions in the modern Lorentz-violating standard model extension. We discuss prospects to improve on these limits.

Testing Lorentz invariance in the weak decay of polarized atoms

Symmetries of space time, and Lorentz and CPT symmetry in particular, are a cornerstone of modern physics and lie at the foundation of quantum field theory (QFT) and Einstein's theory of general relativity, the two most successful theories in physics which together describe the four fundamental forces of nature. However, the inability to incorporate gravity as described by general relativity into the QFT standard model of particle physics, which very successfully combines the electromagnetic, strong and weak interactions, has led to the development of alternative so-called Grand Unified Theories (GUTs) or theories of quantum gravity. Since many of these theories break Lorentz symmetry at some small level 1-4, experimental searches for Lorentz-violating effects could help shed light on new physics beyond the standard model (SM) and provide clues as to the nature of quantum gravity. Parameterization of such effects within the Lorentz-violating Standard Model Extension (SME) developed by A. Kostelecky 5 has allowed direct comparison of many experiments, ranging from table-top precision measurements to observations of ultra-high energy cosmic and gamma rays to astrophysical observations. The SME has proven to be a remarkable tool in the search for Lorentz violation across the landscape of experimental physics. Up until the present, experimental results have taken the form of upper bounds on the SME coefficients and are tabulated in the Data Tables for Lorentz and CPT Violation 6. On a closer look, however, Lorentz invariance has been tested poorly in the weak interaction 7, 8, which is all the more surprising since violations of fundamental symmetries could be observed only in the weak sector: The first discovery of a violation of presumed (discrete) space-time symmetry was that of parity violation in nuclear β decay 9. C. S. Wu and her collaborators found that when a specific nucleus (60Co) was placed in a magnetic field, electrons from the beta decay were preferentially emitted in the direction opposite that of the aligned angular momentum of the nucleus. When it is possible to distinguish these two cases in a mirror, parity is not conserved. If the mirror not only reverses spatial direction but also changes matter to antimatter, then the experiment in front of the mirror would look just like its mirror image. The separate violations of P symmetry and C symmetry cancel to preserve CP symmetry. These symmetry violations arise only from the weak interaction, not from the strong and electromagnetic interactions, and therefore shows up strongly only in beta decay. Until 1964 it was thought that the combination CP was a valid symmetry of the Universe. That year, Christenson, Cronin, Fitch, and Turlay performed their historic experiment to see if the long-lived neutral K meson could occasionally decay to π+ π−. They found that indeed it did 10! And the observed CP violation implies, by CPT invariance, violations of T-symmetry as well.

Orbital effects of Lorentz-violating standard model extension gravitomagnetism around a static body: a sensitivity analysis

We analytically work out the long-term rates of the change of the six osculating Keplerian orbital elements of a test particle acted upon by the Lorentz-violating gravitomagnetic acceleration due to a static body, as predicted by the standard model extension. We neither restrict to any specific spatial orientation for the symmetry-violating vector nor make a priori simplifying assumptions concerning the orbital configuration of the perturbed test particle. Thus, our results are quite general, and can be applied for sensitivity analyses to a variety of specific astronomical and astrophysical scenarios. We find that, apart from the semimajor axis a, all the other orbital elements undergo non-vanishing secular variations. By comparing our results to the latest determinations of the supplementary advances of the perihelia of some planets of the solar system, we preliminarily obtain sx = (0.9 ± 1.5) × 10−8, sy = ( − 4 ± 6) × 10−9 and sz = (0.3 ± 1) × 10−9. Bounds from the terrestrial LAGEOS and LAGEOS II satellites are of the order of s ∼ 10−3–10−4.

Classical Lagrangians for momentum dependent Lorentz violation

Certain momentum-dependent terms in the fermion sector of the Lorentz-violating Standard Model Extension (SME) yield solvable classical lagrangians of a type not mentioned in the literature. These cases yield new relatively simple examples of Finsler and pseudo-Finsler structures. One of the cases involves antisymmetric $d$-type terms and yields a new example of a relatively simple covariant lagrangian.

Cavity Bounds on Higher-Order Lorentz-Violating Coefficients

We determine the sensitivity of a modern Michelson-Morley resonant-cavity experiment to higher-order nonbirefringent and nondispersive coefficients of the Lorentz-violating standard-model extension. Data from a recent year-long run of the experiment are used to place the first experimental bounds on coefficients associated with nonrenormalizable Lorentz-violating operators.

Lorentz-violating gravitoelectromagnetism

The well-known analogy between a special limit of general relativity and electromagnetism is explored in the context of the Lorentz-violating standard-model extension. An analogy is developed for the minimal standard-model extension that connects a limit of the $CPT$-even component of the electromagnetic sector to the gravitational sector. We show that components of the post-Newtonian metric can be directly obtained from solutions to the electromagnetic sector. The method is illustrated with specific examples including static and rotating sources. Some unconventional effects that arise for Lorentz-violating electrostatics and magnetostatics have an analog in Lorentz-violating post-Newtonian gravity. In particular, we show that even for static sources, gravitomagnetic fields arise in the presence of Lorentz violation.

Time delay and Doppler tests of the Lorentz symmetry of gravity

Modifications to the classic time-delay effect and Doppler shift in general relativity (GR) are studied in the context of the Lorentz-violating standard-model extension (SME). We derive the leading Lorentz-violating corrections to the time-delay and Doppler shift signals, for a light ray passing near a massive body. It is demonstrated that anisotropic coefficients for Lorentz violation control a time-dependent behavior of these signals that is qualitatively different from the conventional case in GR. Estimates of sensitivities to gravity-sector coefficients in the SME are given for current and future experiments, including the recent Cassini solar conjunction experiment.

Search forCPTand Lorentz Violation inB0−B¯0Oscillations with Dilepton Events

We report results of a search for CPT and Lorentz violation in B(0)-B[over ](0) oscillations using inclusive dilepton events from 232 x 10(6) Upsilon(4S)-->BB[over ] decays recorded by the BABAR detector at the PEP-II B Factory at SLAC. We find 2.8sigma significance, compatible with no signal, for variations in the complex CPT violation parameter z at the Earth's sidereal frequency and extract values for the quantities Deltaa(micro) in the general Lorentz-violating standard-model extension. The spectral powers for variations in z over the frequency range 0.26 yr(-1) to 2.1 solar day(-1) are also compatible with no signal.

Eliminating the CPT-odd f coefficient from the Lorentz-violating standard model extension

The fermionic f coefficient in the Lorentz-violating standard model extension presents a puzzle. Thus far, no observable quantity that depends upon f has ever been found. We show that this is because f is actually unnecessary. It has absolutely no effects at leading order and can be completely absorbed into other coefficients of the theory by a redefinition of the field.

Infinitesimally nonlocal Lorentz violation

We introduce a new Lorentz-violating modification to a scalar quantum field theory. This interaction, while super-renormalizable by power counting, is fundamentally different from the interactions previously considered within the Lorentz-violating standard model extension. The Lagrange density is nonlocal, because of the presence of a Hilbert transform term; however, this nonlocality is also very weak. The theory has reasonable stability and causality properties and, although the Lorentz-violating interaction possesses a single vector index, the theory is nonetheless CPT even. As an application, we analyze the possible effects of this new form of Lorentz violation on neutral meson oscillations. We find that under certain circumstances, the interaction may lead to quite peculiar sidereal modulations in the oscillation frequency.

Dirac theory within the Standard-Model Extension

The modified Dirac equation in the Lorentz-violating Standard-Model Extension (SME) is considered. Within this framework, the construction of a Hermitian Hamiltonian to all orders in the Lorentz-breaking parameters is investigated, discrete symmetries and the first-order roots of the dispersion relation are determined, and various properties of the eigenspinors are discussed.

Cosmological constraints on Lorentz violation in electrodynamics.

Infrared, optical, and ultraviolet spectropolarimetry of cosmological sources is used to constrain the pure electromagnetic sector of a general Lorentz-violating standard-model extension. The coefficients for Lorentz violation are bounded to less than 3 x 10(-32).