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This work tabulates measured and derived values of coefficients for Lorentz and CPT violation in the Standard-Model Extension. Summary tables are extracted listing maximal attained sensitivities in the matter, photon, neutrino, and gravity sectors. Tables presenting definitions and properties are also compiled.

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. [S0031-9007(99) PACS numbers: 11.30. Er, 12.20.Fv, 32.10.Fn, 32.80.Pj Experimental and theoretical studies of the spectrum of hydrogen (H) have historically been connected to several major advances in physics [1]. The recent production and observation of antihydrogen (H) [2,3] makes it plausible to consider a new class of spectroscopic measurements involving high-precision comparisons of the spectra of H and H [4]. The two-photon 1S-2S transition has received much attention because an eventual measurement of the line center to about 1 mHz, corresponding to a resolution of one part in 10 18 , appears feasible [5]. It has already been measured to 3.4 parts in 10 14 in a cold atomic beam of H [6] and to about 1 part in 10 12 in trapped H [7]. Proposed H spectroscopic investigations involve both beam and trapped-atom techniques [8,9].We consider here the use of spectroscopy of free or magnetically trapped H and H to search for CPT and Lorentz violation. The discrete symmetry CPT is an invariance of all local Lorentz-invariant quantum field theories of point particles [10], including the standard model and quantum electrodynamics (QED). However, the situation is less clear for a more fundamental theory combining the standard model with gravity, such as string theory, where spontaneous breaking of these symmetries may occur [11]. Low-energy manifestations would be suppressed by a power of the ratio of the low-energy scale to the Planck scale, so only a few exceptionally sensitive experiments are likely to detect them.In this paper, we show that effects of this type from the Planck scale can appear in H and H spectra at zeroth order in the fine-structure constant. Moreover, these effects are theoretically detectable not only in 1S-2S lines but also in hyperfine transitions.Our analysis is performed in the context of a standardmodel and QED extension [12] incorporating the idea of spontaneous CPT and Lorentz breaking at a more fundamental level. This quantum field theory appears at present to be the only existing candidate for a consistent extension of the standard model based on a microscopic theory of CPT and Lorentz violation. Desirable features such as energy-momentum conservation, gauge invariance, renormalizability, and microcausality are expected [12]. The theory has been applied to photon properties [12] [18]. To examine the spectra of free H and H, it suffices to perform a perturbative calculation in the context of relativistic quantum mechanics. In this approach, the unperturbed Hamiltonians and their eigenfunctions are the same for H and H. Moreover, all perturbative effects from conventional quantum electrodynamics are also identical for both systems. However, the CPT -and Lorentz-breaking couplings for the electron and positron can provide d...

Exceptional sensitivity to spacetime torsion can be achieved by searching for its couplings to fermions. Recent experimental searches for Lorentz violation are exploited to extract new constraints involving 19 of the 24 independent torsion components down to levels of order 10 ÿ31 GeV.DOI: 10.1103/PhysRevLett.100.111102 PACS numbers: 04.50. Kd, 04.20.ÿq, 11.30.Cp In Einstein's general relativity, gravity is the curvature of spacetime and energy-momentum density is its source. Among the numerous alternative theories of gravity, one popular class of models involves introducing an additional warping of spacetime called torsion [1][2][3]. In many models, the torsion has spin density as its source. Some scenarios allow torsion waves to propagate through spacetime, in analogy with the traveling curvature waves that form gravitational radiation in general relativity. In the special class of ''teleparallel'' models, the curvature of spacetime is itself determined in terms of the torsion.Theories extending general relativity via torsion are widely regarded as experimentally challenging to test because the effects of torsion typically are minuscule. Nature contains many sources of energy-momentum density sufficient to curve spacetime, such as stars and planets. However, sources of spin density strong enough to produce torsion effects are difficult to identify or create. Typical limits on torsion in the literature involve dynamical properties, being obtained from searches for spin-spin interactions or for torsion-mass effects [4].In this Letter, we discuss an alternative approach to searching for torsion, based on the little-appreciated fact that background torsion violates effective local Lorentz invariance. The key point is that nonzero torsion over a region of spacetime establishes a preferred orientation for a freely falling observer, which is the defining criterion for local Lorentz violation [5]. Certain tests of Lorentz symmetry can therefore be reinterpreted as torsion searches. Related ideas have been suggested by Lämmerzahl [6] and Shapiro [2]. Here, we use the exquisite sensitivities recently achieved in Lorentz-violation searches to extract tight new constraints on torsion components, including many previously unbounded in the literature.The recent surge of interest in tests of relativity stems from the realization that tiny violations of Lorentz symmetry could emerge from attempts to unify the known forces [7] and from the development of a comprehensive description of Lorentz and CPT violation in the context of realistic effective field theory, called the standard-model extension (SME) [8]. The SME categorizes Lorentz violations by the mass dimension of the corresponding operator in the Lagrange density, which offers a simple measure of their expected size [9]. The physical effects are controlled by coefficients for Lorentz violation, and many experiments have been performed to measure them [10]. This work shows these experiments can be reinterpreted as searches for nonzero torsion. We note in passing that...

A theoretical framework is introduced that describes possible CPT-violating effects in the context of quantum electrodynamics. Experiments comparing the anomalous magnetic moments of the electron and the positron can place tight limits on CPT violation. The conventional figure of merit adopted in these experiments, involving the difference between the corresponding g factors, is shown to provide a misleading measure of the precision of CPT limits. We introduce an alternative figure of merit, comparable to one commonly used in CPT tests with neutral mesons. To measure it, a straightforward extension of current experimental procedures is proposed. With current technology, a CPT bound better than about 1 part in 10 20 is attainable. [S0031-9007(97)03884-2] PACS numbers: 11.30. Er, 12.20.Fv, 13.40.Em, 14.60.Cd The CPT theorem [1] is a powerful result holding for local relativistic quantum field theories of point particles in flat spacetime. It states that such theories must be invariant under the combined operations of charge conjugation C, parity reversal P, and time reversal T. Among the implications of the theorem are the equality of particle and antiparticle masses and lifetimes.Invariance under CPT has been tested in a variety of experiments [2]. The tightest bound published to date arises from experiments with the neutral kaon system [3], where the CPT figure of merit(1) is known to be smaller than 2 parts in 10 18 . This remarkable precision is possible because neutral-kaon oscillations provide a natural interferometer with dimensionless sensitivity controlled by the mass difference between the physical K L and K S states: j͑m L 2 m S ͒͞m K j Ӎ 10 214 . The quoted precision for r K is thus attained via measurements with a precision of about 1 part in 10 4 .Atomic experiments have also confirmed CPT symmetry. High-precision comparisons of the anomalous magnetic moments of the electron and positron currently provide the most stringent bounds on CPT violation in lepton systems [4]. Denote the electron and positron g factors by g 2 and g 1 , respectively. Then, a conventional figure of merit used in these experiments is [2]which is known to be smaller than 2 parts in 10 12 . The experiments confine isolated single electrons or positrons in a Penning trap for the indefinite periods [4,5] and measure their cyclotron and anomaly frequencies to a precision of better than 1 part in 10 8 . These frequencies can be combined to determine g 2 2, which is of order 10 23 , and hence to yield the limit on r g .The figure of merit r g is poorer than r K by about 6 orders of magnitude, even though the experimental measurements involved in the g 2 2 experiments are about 4 orders of magnitude sharper. This discrepancy originates in the difference between the quantities entering the dimensionless figures of merit. One is a mass (energy) difference while the other is a coupling difference. Indeed, all CPT tests to date have looked for differences between particles and antiparticle masses, lifetimes, or couplings. An important ...