Antimatter-gravity couplings,and Lorentz symmetry

Implications of possible CPT and Lorentz violation for antimatter-gravity experiments as well as other antimatter tests are considered in the context of the general field-theory-based framework of the Standard-Model Extension (SME).     

CPT and lorentz tests with muons

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 4x10(-21) and 10(-23).     

CPT-symmetry studies with antihydrogen

Various approaches to physics beyond the Standard Model can lead to small violations of CPT invariance. Since CPT symmetry can be measured with ultra-high precision, CPT tests offer an interesting phenomenological avenue to search for underlying physics. We discuss this reasoning in more detail, comment on the connection between CPT and Lorentz invariance, and review how CPT breaking would affect the (anti)hydrogen spectrum.     

CPT,Lorentz invariance,mass differences,and charge non-conservation

A non-local field theory that 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.     

CPT violation implies violation of Lorentz invariance

A interacting theory that violates CPT invariance necessarily violates Lorentz invariance. On the other hand, CPT invariance is not sufficient for out-of-cone Lorentz invariance. Theories that violate CPT by having different particle and antiparticle masses must be nonlocal.     

Clock-comparison tests of Lorentz and CPT symmetry in space

Clock-comparison experiments conducted in space can provide access to many unmeasured coefficients for Lorentz and CPT violation. The orbital configuration of a satellite platform and the relatively large velocities attainable in a deep-space mission would permit a broad range of tests with Planck-scale sensitivity.     

Remarks on possible CPT violations

We argue that it is certainly unusual, but not entirely anathema to present theoretical thinking that a breakdown of CPT invariance (and even Lorentz symmetry) might occur at some scale, be it the Planck mass or even the grand unification point. We discuss how the sensitivity of existing tests of CPT invariance can be greatly improved in neutrino oscillations irrespective of whether CP is conserved or not. Also the source of a possible CPT breakdown can be further analyzed in such experiments.     

Testing Relativity with Orbiting Oscillators

Clock-comparison experiments using a satellite platform can give Planck-scale sensitivity to many parameters for Lorentz and CPT violation that are difficult to measure on Earth. A discussion of the theoretical framework for such tests is given, with emphasis on comparisons of output frequencies of atomic clocks and of electromagnetic cavity oscillators.     

Casimir effect at finite temperature for pure-photon sector of the minimal Standard Model Extension

Dynamics between particles is governed by Lorentz and CPT symmetry. There is a violation of Parity (P) and CP symmetry at low levels. The unified theory, that includes particle physics and quantum gravity, may be expected to be covariant with Lorentz and CPT symmetry. At high enough energies, will the unified theory display violation of any symmetry? The Standard Model Extension (SME), with Lorentz and CPT violating terms, has been suggested to include particle dynamics. The minimal SME in the pure photon sector is considered in order to calculate the Casimir effect at finite temperature.     

QCD exotics

I review first some theoretical motivations for violation of Lorentz and/or CPT Invariance. Although the latter symmetries may be violated in a quantum gravity setting, nevertheless there are situations in which these violations are due to a given classical background geometry that may characterised early epochs of our Universe, and in fact be responsible for the observed dominance of matter over antimatter in the Universe. In this way I estimate some of the coefficients of the Standard Model Extension (SME), which is a framework for a field theoretic study of such a breakdown of fundamental symmetries. Then I describe briefly some tests of these symmetries, giving emphasis in low-energy antiproton physics and electric dipole moment measurements, of interest to this conference. I also mention the rôle of entangled states of neutral mesons in providing independent measurements of T(ime reversal) and CP Violation, thus providing independent tests of CPT symmetry, as well as novel (“smoking-gun” type) tests of decoherence-induced CPT violation, which may characterise some models of quantum gravity.     

Search for Lorentz invariance and CPT violation with the MINOS far detector

We searched for a sidereal modulation in the MINOS far detector neutrino rate. Such a signal would be a consequence of Lorentz and CPT violation as described by the standard-model extension framework. It also would be the first detection of a perturbative effect to conventional neutrino mass oscillations. We found no evidence for this sidereal signature, and the upper limits placed on the magnitudes of the Lorentz and CPT violating coefficients describing the theory are an improvement by factors of 20-510 over the current best limits found by using the MINOS near detector.     

Causality and Statistics on the Groenewold–Moyal Plane

Quantum theories constructed on the noncommutative spacetime called the Groenewold–Moyal plane exhibit many interesting properties such as Lorentz and CPT noninvariance, causality violation and twisted statistics. We show that such violations lead to many striking features that may be tested experimentally. These theories predict Pauli forbidden transitions due to twisted statistics, anisotropies in the cosmic microwave background radiation due to correlations of observables in spacelike regions and Lorentz and CPT violations in scattering amplitudes.     

Lorentz and CPT violation in the Standard-Model Extension

Lorentz and CPT invariance are among the symmetries that can be investigated with ultrahigh precision in subatomic physics. Being spacetime symmetries, Lorentz and CPT invariance can be violated by minuscule amounts in many theoretical approaches to underlying physics that involve novel spacetime concepts, such as quantized versions of gravity. Regardless of the underlying mechanism, the low-energy effects of such violations are expected to be governed by effective field theory. This talk provides a survey of this idea and includes an overview of experimental efforts in the field.     

Test of CPT and Lorentz invariance from muonium spectroscopy

Following a suggestion from Kostelecky et al., we evaluated a test of CPT and Lorentz invariance from the microwave spectroscopy of muonium. Hamiltonian terms beyond the standard model violating CPT and Lorentz invariance would contribute frequency shifts deltanu(12) and deltanu(34) to nu(12) and nu(34), the two transitions involving muon spin flip, which were precisely measured in ground state muonium in a strong magnetic field of 1.7 T. The shifts would be indicated by anticorrelated oscillations in nu(12) and nu(34) at the Earth's sidereal frequency. No time dependence was found in nu(12) or nu(34) at the level of 20 Hz, limiting the size of some CPT and Lorentz-violating parameters at the level of 2x10(-23) GeV.     

Testing Lorentz invariance and CPT conservation with NuMI neutrinos in the MINOS near detector

A search for a sidereal modulation in the MINOS near detector neutrino data was performed. If present, this signature could be a consequence of Lorentz and CPT violation as predicted by the effective field theory called the standard-model extension. No evidence for a sidereal signal in the data set was found, implying that there is no significant change in neutrino propagation that depends on the direction of the neutrino beam in a sun-centered inertial frame. Upper limits on the magnitudes of the Lorentz and CPT violating terms in the standard-model extension lie between 10(-4) and 10(-2) of the maximum expected, assuming a suppression of these signatures by a factor of 10(-17).     

Lorentz and CPT tests with spin-polarized solids

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.     

A note on essential duality

By considering some simple models, it is shown that the essential duality condition for local nets of von Neumann algebras associated with Wightman fields need not be fulfilled if Lorentz covariance is dropped. These models illustrate a point made by Borchers in the proof of his two-dimensional CPT theorem for local nets: The Lorentz covariant net constructed from the wedge algebras of a given two-dimensional net may not be unique. It is also shown that in higher dimensions, the Lorentz boosts constructed by means of the modular groups of wedge algebras may act nonlocally in the directions parallel to the edge of the wedge.     

Electromagnetic interaction in theory with Lorentz invariant CPT violation

An attempt is made to incorporate the electromagnetic interaction in a Lorentz invariant but CPT violating non-local model with particle–antiparticle mass splitting, which is regarded as a modified QED. The gauge invariance is maintained by the Schwinger non-integrable phase factor but the electromagnetic interaction breaks C, CP and CPT symmetries. Implications of the present CPT breaking scheme on the electromagnetic transitions and particle–antiparticle pair creation are discussed. The CPT violation such as the one suggested in this Letter may open a new path to the analysis of baryon asymmetry since some of the Sakharov constraints are expected to be modified.     

Search for Lorentz and CPT violation effects in Muon spin precession

The spin precession frequency of muons stored in the (g-2) storage ring has been analyzed for evidence of Lorentz and CPT violation. Two Lorentz and CPT violation signatures were searched for a nonzero delta omega a(=omega a mu+ - omega a mu-) and a sidereal variation of omega a mu+/-). No significant effect is found, and the following limits on the standard-model extension parameters are obtained: bZ = -(1.0+/-1.1) x 10(-23) GeV; (m mu dZ0 + HXY)=(1.8+/-6.0) x 10(-23) GeV; and the 95% confidence level limits b perpendicular mu+ <1.4 x 10(-24) GeV and b perpendicular mu- <2.6 x 10(-24) GeV.